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1. Classifying (Weak) Coideal Subalgebras of Weak Hopf C ¦ -Algebras

Author

Vainerman, Leonid, Vallin, Jean-Michel, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Mathematics::Operator Algebras, Mathematics::Category Theory, Mathematics::Quantum Algebra, Coactions and corepresentations of quantum groupoids, Mathematics::Rings and Algebras, Reconstruction theorem, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], C∗-categories
Abstract

International audience; We develop a general approach to the problem of classification of weak coideal C ¦-subalgebras of weak Hopf C ¦-algebras. As an example, we consider weak Hopf C ¦-algebras and their weak coideal C ¦-subalgebras associated with Tambara Yamagami categories.

Published
2020

2. Varying the Horndeski Lagrangian within the Palatini approach

Author

Mikhail S. Volkov, Thomas Helpin, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, media_common.quotation_subject, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Type (model theory), 01 natural sciences, General Relativity and Quantum Cosmology, Theoretical physics, High Energy Physics::Theory, 0103 physical sciences, Tensor, 010306 general physics, Computer Science::Databases, media_common, Physics, Variables, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Isotropy, torsion, Astronomy and Astrophysics, Connection (mathematics), field theory: scalar, High Energy Physics - Theory (hep-th), Metric (mathematics), Torsion (algebra), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Scalar field
Abstract

We analyse what happens when the Horndeski Lagrangian is varied within the Palatini approach by considering the metric and connection as independent variables. Assuming the connection to be torsionless, there can be infinitely many metric-affine versions $L_{\rm P}$ of the original Lagrangian which differ from each other by terms proportional to the non-metricity tensor. After integrating out the connection, each $L_{\rm P}$ defines a metric theory, which can either belong to the original Horndeski family, or it can be of a more general DHOST type, or it shows the Ostrogradsky ghost. We analyse in detail the subclass of the theory for which the equations are linear in the connection and find that its metric-affine version is ghost-free. We present a detailed classifications of homogeneous and isotropic cosmologies in these theories. Taking into consideration other pieces of the Horndeski Lagrangian which are non-linear in the connection leads to more complex metric-affine theories which generically show the ghost. In some special cases the ghost can be removed by carefully adjusting the non-metricity contribution, but it is unclear if this is always possible. Therefore, the metric-affine generalisations of the Horndeski theory can be ghost-free, but not all of them are ghost-free, neither are they the only metric-affine theories for a gravity-coupled scalar field which can be ghost-free., Comment: 36 pages, 7 figures, many comments and references added; to appear in JCAP

Published
2020
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3. Dynamic magnetostriction for antiferromagnets

Author

Stam Nicolis, Thomas Nussle, Pascal Thibaudeau, CEA Le Ripault (CEA Le Ripault), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Thibaudeau, Pascal, Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)

Subjects
[PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], Magnetism, [PHYS.PHYS.PHYS-COMP-PH] Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], FOS: Physical sciences, [PHYS.MECA.MSMECA] Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], 02 engineering and technology, 01 natural sciences, [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], Condensed Matter - Strongly Correlated Electrons, Magnetization, symbols.namesake, Poisson bracket, 0103 physical sciences, Statistical physics, 010306 general physics, Physics, Condensed Matter - Materials Science, Toy model, Magnetic moment, Strongly Correlated Electrons (cond-mat.str-el), Materials Science (cond-mat.mtrl-sci), Computational Physics (physics.comp-ph), [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], 021001 nanoscience & nanotechnology, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Phase space, symbols, [PHYS.PHYS.PHYS-CLASS-PH] Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], 0210 nano-technology, Hamiltonian (quantum mechanics), Physics - Computational Physics, Symplectic geometry
Abstract

In this paper we study the switching properties of the dynamics of magnetic moments, that interact with an elastic medium. To do so we construct a Hamiltonian framework, that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. It is convenient to describe the magnetic moments as bilinears of anticommuting variables that are their own conjugates. However, we show how it is possible to avoid having to deal directly with the anticommuting variables themselves, only using them to deduce non-trivial constraints on the magnetoelastic couplings. We construct the appropriate Poisson bracket and a geometric integration scheme, that is symplectic in the extended phase space and that allows us to study the switching properties of the magnetization, that are relevant for applications, for the case of a toy model for antiferromagnetic NiO, under external stresses. In the absence of magnetoelastic coupling, we recover the results reported in the literature and in our previous studies. In the presence of the magnetoelastic coupling, the characteristic oscillations of the mechanical system have repercussions on the N\'eel order parameter dynamics. This is particularly striking for the spin accumulation which is more than doubled by the coupling to the strain ; here as well, the mechanical oscillations are reflected on the magnetic dynamics. As a consequence of such a stress induced strain, the switching time of the magnetization is slightly faster and the amplitude of the magnetization enhanced., Comment: 13 pages, 7 figures

Published
2019
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4. Deformed General Relativity and Quantum Black Holes Interior

Author

Karim Noui, Jibril Ben Achour, Denis Arruga, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
lcsh:QC793-793.5, General relativity, Constraint algebra, gravitation: model, gravitation: deformation, FOS: Physical sciences, General Physics and Astronomy, polymer: model, General Relativity and Quantum Cosmology (gr-qc), Loop quantum gravity, constraint: algebra, 01 natural sciences, General Relativity and Quantum Cosmology, Legendre transformation, symbols.namesake, 0103 physical sciences, Effective field theory, general relativity, symmetry: rotation, 010306 general physics, modified gravity, Physics, black hole: quantum, loop quantum gravity, 010308 nuclear & particles physics, constraint: Hamiltonian, lcsh:Elementary particle physics, Covariance, black holes, Constraint (information theory), Hamiltonian constraint, Classical mechanics, covariance, black hole: model, symbols, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], phase space: deformation, Einstein equation
Abstract

Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance can not be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study homogeneous solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition., 29 pages, invited contribution to special Issue: "Probing New Physics with Black holes", Matched the published version in Universe

Published
2019
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5. A metric-affine version of the Horndeski theory

Author

Thomas Helpin, Mikhail S. Volkov, Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, Nuclear and High Energy Physics, Horndeski theory, scalar tensor, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), algebra, 01 natural sciences, General Relativity and Quantum Cosmology, 0103 physical sciences, 010306 general physics, Palatini approach, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 04.50.Kd, Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Action (physics), Connection (mathematics), field theory: scalar, Algebra, 04.20.-q, High Energy Physics - Theory (hep-th), Metric (mathematics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Affine transformation, geometry: Weyl
Abstract

We study the metric-affine versions of scalar-tensor theories whose connection enters the action only algebraically. We show that the connection can be integrated out in this case, resulting in an equivalent metric theory. Specifically, we consider the metric-affine generalisations of the subset of the Horndeski theory whose action is linear in second derivatives of the scalar field. We determine the connection and find that it can describe a scalar-tensor Weyl geometry without a Riemannian frame. Still, as this connection enters the action algebraically, the theory admits the dynamically equivalent (pseudo)-Riemannian formulation in the form of an effective metric theory with an extra K-essence term. This may have interesting phenomenological applications., 8 pages, to appear in the thematic issue of Int. Journ. Mod. Phys. A - proceedings of the 10th Friedmann Seminar on Gravitation and Cosmology, St. Petersburg, Russia, June 23-29, 2019

Published
2019
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6. Metric formulation of the simple theory of 3d massive gravity

Author

Marc Geiller, Karim Noui, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), AstroParticule et Cosmologie (APC (UMR_7164)), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, dimension: 3, General relativity, FOS: Physical sciences, alternative theories of gravity, General Relativity and Quantum Cosmology (gr-qc), derivative: high, Lorentz covariance, invariance: Lorentz, 01 natural sciences, symmetry breaking, General Relativity and Quantum Cosmology, Theoretical physics, 0103 physical sciences, Lorentz gauge, action: nonlinear, gravitation: massive, 010306 general physics, Physics, 010308 nuclear & particles physics, graviton: massive, Graviton, Equations of motion, field equations, 16. Peace & justice, Action (physics), Nonlinear system, Massive gravity, High Energy Physics - Theory (hep-th), graviton: propagation, Metric (mathematics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Einstein equation
Abstract

We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal Lorentz gauge symmetry is broken. The absence of Lorentz invariance, which in this model is the mechanism underlying the propagation of a massive graviton, does however prevent from writing a purely metric non-linear action for the theory. Nonetheless, in this letter, we explain how to disentangle, at the non-linear level, the metric and non-metric degrees of freedom in the equations of motion. Focusing on the metric part, we show that it satisfies modified Einstein equations with higher derivative terms. As a particular case, these equations reproduce a well-studied model known as minimal massive gravity. In the general case, we obtain new metric field equations for massive gravity in three dimensions starting from the simple first order action. These field equations are consistent through a mechanism known as "third way consistency", which our theory therefore provides a new example of., 5 pages, published version

Published
2019
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7. Hairy Schwarzschild-(A)dS black hole solutions in degenerate higher order scalar-tensor theories beyond shift symmetry

Author

Hongguang Liu, J. Ben Achour, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)

Subjects
General relativity, higher-order, gravitation: model, scalar tensor, Scalar (mathematics), kinetic, alternative theories of gravity, 01 natural sciences, General Relativity and Quantum Cosmology, vacuum: solution, Lagrangian formalism, 0103 physical sciences, anti-de Sitter, black hole, Symmetry breaking, 010306 general physics, Mathematical physics, Physics, 010308 nuclear & particles physics, Graviton, Order (ring theory), solar system, Schwarzschild, Symmetry (physics), field theory: scalar, Black hole, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], time dependence, Schwarzschild radius
Abstract

We derive the general conditions for a large family of shift symmetry breaking degenerate higher order scalar-tensor (DHOST) theories to admit stealth black hole solutions. Such black hole configurations correspond to vacuum solutions of general relativity and admit a scalar hair which does not gravitate, revealing itself only at the perturbative level. We focus our investigation on hairy Schwarzschild-(A)dS or pure Schwarzschild solutions, dressed with a linear time-dependent scalar hair, and assuming a constant kinetic term. We also discuss subclasses of this family which satisfy the observational constraint ${c}_{\mathrm{grav}}={c}_{\text{light}}$, as well as the recent constraint ensuring the absence of graviton decay. We provide at the end concrete examples of DHOST Lagrangians satisfying our conditions. This work provides a first analysis of exact black hole solutions in shift symmetry breaking DHOST theories beyond Horndeski.

Published
2019
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8. SL(2,$\mathbb Z$)-action for ribbon quasi-Hopf algebras

Author

Farsad, Vanda, Gainutdinov, Azat M., Runkel, Ingo, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)

Subjects
group: representation, Braided tensor categories, SL(2, algebra: Hopf, category: tensor, Mathematics::Category Theory, Mathematics::Quantum Algebra, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], category: representation, Mapping class group representations, structure, Quasi-Hopf algebras, Z)
Abstract

International audience; We study the universal Hopf algebra L of Majid and Lyubashenko in the case that the underlying ribbon category is the category of representations of a finite dimensional ribbon quasi-Hopf algebra A . We show that L=A⁎ with coadjoint action and compute the Hopf algebra structure morphisms of L in terms of the defining data of A . We give explicitly the condition on A which makes Rep A factorisable and compute Lyubashenko's projective SL(2,Z) -action on the centre of A in this case.

Published
2019
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9. Minimally Modified Gravity: a Hamiltonian Construction

Author

Shinji Mukohyama, Karim Noui, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
High Energy Physics - Theory, dimension: 4, General relativity, gravitation: model, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, Gravitation, unitary gauge, symbols.namesake, phase space, 0103 physical sciences, general relativity, Mathematical physics, Physics, diffeomorphism: invariance, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], constraint: Hamiltonian, Astronomy and Astrophysics, Invariant (physics), Hamiltonian constraint, High Energy Physics - Theory (hep-th), gravitation: scalar tensor, Phase space, symbols, ADM formalism, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Diffeomorphism, Hamiltonian (quantum mechanics), gravitation: local
Abstract

Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the symmetry under 3D diffeomorphisms. Here, we construct these theories from a Hamiltonian point of view. We start with the phase space of general relativity in the ADM formalism. Then, we find the conditions that the Hamiltonian must satisfy for the theory to propagate (up to) two gravitational degrees of freedom with the assumptions that the lapse and the shift are not dynamical, and the theory remains invariant under 3D diffeomorphisms. This construction enables us to recover the well-known "cuscuton" class of scalar-tensor theories in the unitary gauge. We also exhibit a new class of interesting theories, that we dubb $f({\cal H})$ theories, where the usual Hamiltonian constraint $\cal H$ of general relativity is replaced by $f({\cal H})$ where $f$ is an arbitrary function., 20 pages

Published
2019
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10. Perturbations of a rotating black hole in DHOST theories

Author

David Langlois, Christos Charmousis, Karim Noui, Marco Crisostomi, Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR7158 / UMR_E_9005 / UM_112)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR_7158 / UMR_E_9005 / UM_112)), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, black hole: rotation, geometry, Physics and Astronomy (miscellaneous), General relativity, Astrophysics::High Energy Astrophysical Phenomena, scalar tensor, FOS: Physical sciences, Perturbation (astronomy), General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, 0103 physical sciences, general relativity, 010306 general physics, black hole: hair, Physics, black hole: spin, 010308 nuclear & particles physics, Gravitational wave, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], perturbation: tensor, Degenerate energy levels, perturbation: linear, parametrization, perturbation: scalar, Classical mechanics, High Energy Physics - Theory (hep-th), Rotating black hole, gravitational radiation: emission, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Teukolsky equation, gravitation: higher-order
Abstract

We study linear perturbations of a rotating black hole solution that has been recently discovered in degenerate higher-order scalar-tensor (DHOST) theories. We find a parametrization which permits the explicit resolution of the scalar perturbation while the tensor perturbation is obtained as a Teukolsky equation supplemented by an effective source term. The effective source term is related to the black hole hair and can be computed exactly for any value of the black hole spin. We discuss how the perturbations of the geometry and thus the emitted gravitational waves could be modified in comparison with general relativity., Comment: 6 pages

Published
2019
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11. Direct measurement of a beta function and an indirect check of the Schwinger effect near the boundary in Dirac-Weyl semimetals

Author

María A. H. Vozmediano, M. N. Chernodub, Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Length scale, High Energy Physics - Theory, Conformal anomaly, Dirac (software), FOS: Physical sciences, 01 natural sciences, Electric charge, renormalization, Renormalization, beta function, Condensed Matter - Strongly Correlated Electrons, Electric field, 0103 physical sciences, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Beta function (physics), 010306 general physics, numerical calculations, Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Strongly Correlated Electrons (cond-mat.str-el), 010308 nuclear & particles physics, Screening effect, charge: electric, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], anomaly: conformal, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], electric field, pair production, High Energy Physics - Theory (hep-th), Quantum electrodynamics, screening: length, screening: effect
Abstract

The electric field inside typical conductors drops down exponentially with the screening length determined by an intrinsic length scale of the system such as the density of mobile carriers. We show that in a classically conformal system with boundaries, where the intrinsic length scale is absent, the screening of an external electric field is governed by the quantum conformal anomaly associated with the renormalization of the electric charge. The electric field decays algebraically with a fractional power determined by the beta function of the system. We argue that this `anomalous conformal screening effect' is an indirect manifestation of the Schwinger pair production in relativistic field theory. We discuss the experimental feasibility of the proposed phenomenon in Dirac and Weyl semimetals what would allow direct experimental access to the beta function., Comment: 5 pages, 4 figures

Published
2019
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12. Towards a new friction model for shallow water equations through an interactive viscous layer

Author

Hoang-Minh Le, François James, Mathilde Legrand, Pierre-Yves Lagrée, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Institut Jean Le Rond d'Alembert (DALEMBERT), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics (Saint-Venant), École des Ponts ParisTech (ENPC)-Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement (Cerema)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Institut Denis Poisson ( IDP ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ) -Université d'Orléans ( UO ), Institut Jean Le Rond d'Alembert ( DALEMBERT ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics ( Saint-Venant ), École des Ponts ParisTech ( ENPC ) -Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement ( Cerema ) -EDF R&D ( EDF R&D ), and EDF ( EDF ) -EDF ( EDF )

Subjects
76N17, friction law, 010504 meteorology & atmospheric sciences, von Kármán equation, Hydrostatic pressure, Perfect fluid, Föppl–von Kármán equations, 01 natural sciences, 65M08, 010305 fluids & plasmas, Physics::Fluid Dynamics, Superposition principle, Mathematics - Analysis of PDEs, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], viscous layer, 0103 physical sciences, 35L65, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Prandtl equation, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Shallow water equations, 2010 AMS subject classifications: Primary: 35L60, 35Q35, 0105 earth and related environmental sciences, Mathematics, von Kármán equation 2010 AMS subject classifications: 35L60, Numerical Analysis, Finite volume method, Applied Mathematics, [ PHYS.MECA.MEFL ] Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], shallow water, Mechanics, Computational Mathematics, Boundary layer, Waves and shallow water, Modeling and Simulation, Analysis, Analysis of PDEs (math.AP)
Abstract

The derivation of shallow water models from Navier–Stokes equations is revisited yielding a class of two-layer shallow water models. An improved velocity profile is proposed, based on the superposition of an inviscid fluid and a viscous layer inspired by the Interactive Boundary Layer interaction used in aeronautics. This leads to a new friction law which depends not only on velocity and depth but also on the variations of velocity and thickness of the viscous layer. The resulting system is an extended shallow water model consisting of three depth-integrated equations: the first two are mass and momentum conservation in which a slight correction on hydrostatic pressure has been made; the third one, known as von Kármán equation, describes the evolution of the viscous layer. This coupled model is shown to be conditionally hyperbolic, and a Godunov-type finite volume scheme is also proposed. Several numerical examples are provided and compared to the Multi-Layer Saint-Venant model. They emphasize the ability of the model to deal with unsteady viscous effects. They illustrate also the phase-lag between friction and topography, and even recover possible reverse flows.

Published
2019
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13. Higher rank isomonodromic deformations and $W$-algebras

Author

P. Gavrylenko, Oleg Lisovyy, Nikolai Iorgov, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Fédération de recherche Denis Poisson ( FRDP ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), and Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS)

Subjects
Vertex (graph theory), High Energy Physics - Theory, Pure mathematics, Isomonodromic deformations, Rank (linear algebra), [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Block (permutation group theory), FOS: Physical sciences, Conformal map, 01 natural sciences, symbols.namesake, Matrix (mathematics), 0103 physical sciences, Ramanujan tau function, 0101 mathematics, Mathematical Physics, Mathematics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 010308 nuclear & particles physics, Conformal field theory, 010102 general mathematics, W-algebras, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), High Energy Physics - Theory (hep-th), symbols, [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph], Exactly Solvable and Integrable Systems (nlin.SI), Central charge
Abstract

We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest example is given by the tau function of the Fuji-Suzuki-Tsuda system, expressed as a Fourier transform of the 4-point conformal block with respect to intermediate weight. Along the way, we generalize the result of Bowcock and Watts on the minimal set of matrix elements of vertex operators of the $W_N$-algebra for generic central charge and prove several properties of semi-degenerate vertex operators and conformal blocks for $c=N-1$., 31 pages, 1 figure

Published
2019
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14. Boundary-corner entanglement for free bosons

Author

Clément Berthiere, Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, Electronic structure and strongly correlated systems, Dirichlet distribution, symbols.namesake, Condensed Matter - Strongly Correlated Electrons, Lattice (order), 0103 physical sciences, entropy: entanglement, Boundary value problem, Quantum field theory, 010306 general physics, numerical calculations, Entropy (arrow of time), Mathematical physics, Boson, Physics, Condensed Matter::Quantum Gases, field theory: conformal, Strongly Correlated Electrons (cond-mat.str-el), Cauchy stress tensor, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], critical phenomena, 021001 nanoscience & nanotechnology, boundary condition, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), central charge, symbols, holography, 0210 nano-technology, Central charge
Abstract

In quantum field theories defined on a spacetime with boundaries, the entanglement entropy exhibits subleading, boundary-induced corrections to the ubiquitous area law. At critical points described by conformal field theories (CFTs), and when the entangling surface intersects the physical boundary of the space, new universal terms appear in the entropy and encode valuable information about the boundary CFT. In $2+1$ dimensions, the universal subleading boundary term is logarithmic with coefficient $b(\theta)$ depending on the angle $\theta$ at which the entangling surface intersects the boundary, as well as on the boundary conditions (BCs). In this paper, we conduct a numerical study of $b(\theta)$ for free bosons on finite-size square lattices. We find a surprisingly accurate fit between our lattice results and the corresponding holographic function available in the literature. We also comment on the ratio $b''(\pi/2)/A_T$, where $A_T$ is the central charge in the near boundary expansion of the stress tensor, for which a holographic analysis suggests that it may be a universal quantity. Though we show evidence that this ratio is violated for the free boson with Dirichlet BCs, we conjecture its validity for free bosons evenly split between Dirichlet and Neumann BCs., Comment: 12 pages, 8 figures; v2: typos corrected, matches published version

Published
2019
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15. Kinetic equation for Lifshitz scalar

Author

Shinji Mukohyama, Yota Watanabe, Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, cosmological model, geometry, dispersion relation, Critical phenomena, Scalar (mathematics), kinetic, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Wigner, scaling: Lifshitz, Computer Science::Digital Libraries, 01 natural sciences, General Relativity and Quantum Cosmology, Gravitation, Dispersion relation, 0103 physical sciences, distribution function, 010306 general physics, Scaling, Mathematical physics, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], critical phenomena, field theory in curved space, field theory: scalar, Distribution function, Formal aspects of field theory, High Energy Physics - Theory (hep-th), space-time, gravitation, velocity: group, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Critical exponent, Scalar field
Abstract

Employing the method of Wigner functions on curved spaces, we study classical kinetic (Boltzmann-like) equations of distribution functions for a real scalar field with the Lifshitz scaling. In particular, we derive the kinetic equation for $z=2$ on general curved spaces and for $z=3$ on spatially flat spaces under the projectability condition $N=N(t)$, where $z$ is the dynamical critical exponent and $N$ is the lapse function. We then conjecture a form of the kinetic equation for a real scalar field with a general dispersion relation in general curved geometries satisfying the projectability condition, in which all the information about the non-trivial dispersion relation is included in the group velocity and which correctly reproduces the equations for the $z=2$ and $z=3$ cases as well as the relativistic case. The method and equations developed in the present paper are expected to be useful for developments of cosmology in the context of Ho\v{r}ava-Lifshitz gravity., Comment: 15 pages, v2: published version

Published
2018
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16. Combinatorial Quantisation of $GL(1|1)$ Chern-Simons Theory I: The Torus

Author

Aghaei, Nezhla, Gainutdinov, Azat M., Pawelkiewicz, Michal, Schomerus, Volker, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, algebra: Hopf, Chern-Simons term, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], supersymmetry: algebra, monodromy, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, torus, Mathematical Physics (math-ph), group: modular, High Energy Physics::Theory, High Energy Physics - Theory (hep-th), Riemann surface, GL(1|1), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), quantization, supersymmetry, Z), Mathematical Physics, group: SL(2
Abstract

Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. This paper is the first in a series where we propose a new quantisation scheme for such super-group Chern-Simons theories on 3-manifolds of the form $\Sigma \times \mathbb{R}$. It is based on a simplicial decomposition of an n-punctured Riemann surface $\Sigma=\Sigma_{g,n}$ of genus g and allows to construct observables of the quantum theory for any g and n from basic building blocks, most importantly the so-called monodromy algebra. In this paper we restrict to the torus case, i.e. we assume that $\Sigma = T^2$, and to the gauge super-group G=GL(1|1). We construct the corresponding space of quantum states for the integer level k Chern-Simons theory along with an explicit representation of the modular group SL(2,Z) on these states. The latter is shown to be equivalent to the Lyubachenko-Majid action on the centre of a restricted version of the quantised universal enveloping algebra of the Lie super-algebra gl(1|1) at the primitive k-th root of unity., Comment: 46 pages

Published
2018
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17. Zilch vortical effect

Author

M. N. Chernodub, Alberto Cortijo, Karl Landsteiner, Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
cylinder, causality, fermion: chiral, Angular velocity, finite temperature, current: density, 01 natural sciences, rotation, Gravitation, Quantization (physics), 0103 physical sciences, optical, photon: gas, duality: violation, invariance: gauge, Boundary value problem, 010306 general physics, temperature dependence, Physics, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Photon gas, helicity, Helicity, boundary condition, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], anomaly: gravitation, field theory in curved space, Formal aspects of field theory, Quantum electrodynamics, Chiral fermions, quantization, Current density
Abstract

International audience; We study the question of whether a helicity-transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge-invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant “zilch” current. In order to avoid problems of causality, we quantize the system on a cylinder of finite radius and then discuss the limit of infinite radius. We find that net helicity and zilch currents are only generated in the case of the finite radius and are due to duality-violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the well-known temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies.

Published
2018
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18. Light primordial exotic compact objects as all dark matter

Author

Martti Raidal, Ville Vaskonen, Sergey Solodukhin, Hardi Veermäe, CERN Theoretical Physics Department, CERN [Genève], National Institute of Chemical Physics and Biophysics = Keemilise ja bioloogilise füüsika instituut [Estonie] (NICPB | KBFI), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Fédération de recherche Denis Poisson ( FRDP ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Fédération de recherche Denis Poisson (FDP), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
[ PHYS.ASTR ] Physics [physics]/Astrophysics [astro-ph], Astrophysics, Parameter space, 01 natural sciences, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology (hep-ph), curvature: primordial, Boson, Physics, [PHYS]Physics [physics], radiation: emission, Gravastar, General Relativity and Cosmology, hep-ph, suppression, boson: star, Alternative gravity theories, High Energy Physics - Phenomenology, wormhole, astro-ph.CO, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Astrophysics::Earth and Planetary Astrophysics, Hawking radiation, Astrophysics - Cosmology and Nongalactic Astrophysics, Astrophysics and Astronomy, Cosmology and Nongalactic Astrophysics (astro-ph.CO), gr-qc, polymer, Astrophysics::High Energy Astrophysical Phenomena, Dark matter, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Astrophysics::Cosmology and Extragalactic Astrophysics, gravastar, [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], star: collapse, sphere: fuzzy, 0103 physical sciences, Gravitational collapse, Wormhole, 010306 general physics, black hole: radiation, Particle Physics - Phenomenology, 010308 nuclear & particles physics, dark matter: relic density, Stars, 13. Climate action, curvature: fluctuation, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], [ PHYS.HPHE ] Physics [physics]/High Energy Physics - Phenomenology [hep-ph], [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]
Abstract

The radiation emitted by horizonless exotic compact objects (ECOs), such as wormholes, 2-2-holes, fuzzballs, gravastars, boson stars, collapsed polymers, superspinars etc., is expected to be strongly suppressed when compared to the radiation of black holes. If large primordial curvature fluctuations collapse into such objects instead of black holes, they do not evaporate or evaporate much slower than black holes and could thus constitute all of the dark matter with masses below $M < 10^{-16}M_\odot.$ We reevaluate the relevant experimental constraints for light ECOs in this mass range and show that very large new parameter space down to ECO masses $M\sim 10\,{\rm TeV}$ opens up for light primordial dark matter. A new dedicated experimental program is needed to test this mass range of primordial dark matter., 6 pages, 2 figures; minor changes to match the published version

Published
2018
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19. A remarkably simple theory of 3d massive gravity

Author

Karim Noui, Marc Geiller, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, Nuclear and High Energy Physics, dimension: 3, perturbation, Perturbation (astronomy), FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, topological, Theoretical physics, symbols.namesake, 0103 physical sciences, Minkowski space, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, gravitation: massive, Minkowski, 010306 general physics, Physics, Coupling constant, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Space-Time Symmetries, graviton: massive, Graviton, Hamiltonian, Massless particle, Nonlinear system, Massive gravity, High Energy Physics - Theory (hep-th), self-duality, symbols, lcsh:QC770-798, nonlinear, Hamiltonian (quantum mechanics), Classical Theories of Gravity, simplex
Abstract

We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad formulation. The quadratic action for the perturbations around a Minkowski background reproduces the action of self-dual massive gravity, in agreement with the expectation that the theory propagates a massive graviton. We confirm this result at the non-linear level with a Hamiltonian analysis, and show that this new theory does indeed possess a single massive degree of freedom. The action depends on four coupling constants, and we identify the various massive and topological (or massless) limits in the space of parameters. This richness, along with the simplicity of the action, opens a very interesting new window onto massive gravity., Comment: 20+9 pages

Published
2018
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20. Casimir Effect in Yang-Mills Theory in D=2+1

Author

Vladimir Alexandrovich Goy, Alexander Molochkov, Ha Huu Nguyen, M. N. Chernodub, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)

Subjects
deconfinement, High Energy Physics::Lattice, Phase (waves), General Physics and Astronomy, Yang–Mills theory, Space (mathematics), Scaling dimension, 01 natural sciences, Deconfinement, glueball: mass, gauge field theory: SU(2), effect: Casimir, 0103 physical sciences, Gauge theory, 010306 general physics, numerical calculations, Physics, scaling: dimension, 010308 nuclear & particles physics, Glueball, [PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat], [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], chromoelectric, suppression, back reaction, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Casimir effect, Quantum electrodynamics, gauge field theory: Yang-Mills, temperature: 0, space-time: dimension: 3, Elementary Particles and Fields, gauge field theory: nonabelian
Abstract

International audience; We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principles numerical simulations. Working in two spatial dimensions at zero temperature, we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.

Published
2018
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21. Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

Author

Thomas Basile, Xavier Bekaert, Euihun Joung, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Fédération de recherche Denis Poisson ( FRDP ), and Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
High Energy Physics - Theory, Nuclear and High Energy Physics, Pure mathematics, Dimension (graph theory), FOS: Physical sciences, algebra, spin: high, 01 natural sciences, [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], 0103 physical sciences, SO(2, Order (group theory), lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, any-dimensional, 010306 general physics, Spin-½, Physics, Higher Spin Symmetry, N), 010308 nuclear & particles physics, Singleton, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Computer Science::Information Retrieval, mathematical methods, Higher Spin Gravity, Dual (category theory), Character (mathematics), Tensor product, High Energy Physics - Theory (hep-th), gravitation, twist, Symmetrization, lcsh:QC770-798, duality, singleton
Abstract

We explore the relation between the singleton and adjoint modules of higher-spin algebras via so(2,d) characters. In order to relate the tensor product of the singleton and its dual to the adjoint module, we consider a heuristic formula involving symmetrization over the variables of the character. We show that our formula reproduces correctly the adjoint-module character for type-A (and its high-order extensions) and type-B higher-spin gravity theories in any dimension. Implications and subtleties of this symmetrization prescription in other models are discussed., 50 pages, 2 figures; v2: references added, typos corrected and discussion concerning the proposed formula extended

Published
2018
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22. Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra

Author

Thomas Basile, Xavier Bekaert, Euihun Joung, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, Nuclear and High Energy Physics, Gravity (chemistry), spectrum: linear, FOS: Physical sciences, Conformal map, spin, 01 natural sciences, symmetry: global, algebra: conformal, symmetry: algebra, Gravitation, 0103 physical sciences, lcsh:Nuclear and particle physics. Atomic energy. Radioactivity, 010306 general physics, Physics, Higher Spin Symmetry, Conformal Field Theory, 010308 nuclear & particles physics, Conformal field theory, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Degrees of freedom, Spectrum (functional analysis), Higher Spin Gravity, Symmetry (physics), Algebra, regularization, High Energy Physics - Theory (hep-th), gravitation, symmetry: conformal, Regularization (physics), lcsh:QC770-798
Abstract

The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their characters involve divergent sums over spins. We propose a suitable regularization adapted to their evaluation and observe that their characters are actually equal. This result holds in the case of type-A and type-B (and their higher-depth generalizations) theories and confirms previous observations on a remarkable rearrangement of dynamical degrees of freedom in conformal higher-spin gravity after regularization., 47 pages, 1 figures; v2: references and appendix D on formal CHS theory (Segal's formulation) added

Published
2018
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23. Holographic calculation of entanglement entropy in the presence of boundaries

Author

Amin Faraji Astaneh, Sergey N. Solodukhin, Dmitri V. Fursaev, Clément Berthiere, Fédération de recherche Denis Poisson ( FRDP ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
High Energy Physics - Theory, Mathematics - Differential Geometry, dimension: 4, dimension: 3, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], surface: minimal, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Quantum entanglement, Squashed entanglement, 01 natural sciences, multiplet: gauge, General Relativity and Quantum Cosmology, [ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th], [ PHYS.GRQC ] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Quantum mechanics, 0103 physical sciences, FOS: Mathematics, anti-de Sitter, entropy: entanglement, Boundary value problem, 010306 general physics, Entropy (arrow of time), Multiplet, Mathematical physics, Physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], 010308 nuclear & particles physics, weak coupling, boundary condition, Hypersurface, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), space-time, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], holography, [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph], Anti-de Sitter space, supersymmetry, Joint quantum entropy
Abstract

When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary contribution to the logarithmic term in the entanglement entropy in dimensions $d=3$ and $d=4$ when the entangling surface is orthogonal to the boundary. In particular, we compute a boundary term in the entropy of ${\mathcal{N}}=4$ super-gauge multiplet at weak coupling. This result is compared with the holographic calculation of the entropy based on the Ryu-Takayanagi proposal adapted appropriately to the present situation. We find a complete agreement between these two calculations provided the boundary conditions imposed on the gauge multiplet preserve $1/2$ of the supersymmetry and the extension of the boundary into the AdS bulk is a minimal hypersurface., v3: minor corrections, accepted for publication in PRD

Published
2017
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24. Holographic calculation of boundary terms in conformal anomaly

Author

Amin Faraji Astaneh, Sergey N. Solodukhin, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Energy Physics - Theory, Mathematics - Differential Geometry, Nuclear and High Energy Physics, dimension: 4, dimension: 3, Conformal anomaly, surface: minimal, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Boundary (topology), General Relativity and Quantum Cosmology (gr-qc), Curvature, 01 natural sciences, General Relativity and Quantum Cosmology, Theoretical physics, 0103 physical sciences, FOS: Mathematics, anti-de Sitter, entropy: entanglement, Boundary value problem, 010306 general physics, Physics, field theory: conformal, 010308 nuclear & particles physics, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], anomaly: conformal, Boundary conformal field theory, Supersymmetry, lcsh:QC1-999, boundary condition, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), Quantum electrodynamics, curvature, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], holography, Anti-de Sitter space, Anomaly (physics), supersymmetry, lcsh:Physics
Abstract

In the presence of boundaries the integrated conformal anomaly is modified by the boundary terms so that the anomaly is non-vanishing in any (even or odd) dimension. The boundary terms are due to extrinsic curvature whose exact structure in $d=3$ and $d=4$ has recently been identified. In this note we present a holographic calculation of those terms in two different prescriptions for the holographic description of the boundary CFT. We stress the role of supersymmetry when discussing the holographic description of ${\cal N}=4$ SYM on a $4$-manifold with boundaries., 21 pages, v.2: modifications in non-minimal case due to overlooked contributions, conclusions unchanged

Published
2017
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25. {Lipschitz regularity for integro-differential equations with coercive {H}amiltonians and application to large time behavior}

Author

Guy Barles, Olivier Ley, Erwin Topp, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Departamento de Matematica y C.C., Universidad de Santiago de Chile [Santiago] (USACH)-Facultad de Ciencia, ANR-12-BS01-0020, ANR WKBHJ, 3150100, Fondecyt Postdoctoral Grant, ANR-12-BS01-0008-01, ANR HJnet, 79150056, Conicyt PIA Grant, NC130017, Millenium Nucleus Center for Analysis of PDE, ANR-12-BS01-0008,HJnet,Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux(2012), ANR-12-BS01-0020,WKBHJ,KAM faible au-delà de Hamilton-Jacobi(2012), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Integro-differential equations, Differential equation, Mathematics::Analysis of PDEs, General Physics and Astronomy, Space (mathematics), 01 natural sciences, Mathematics - Analysis of PDEs, FOS: Mathematics, Applied mathematics, Ergodic theory, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Lipschitz regularity, 0101 mathematics, Mathematical Physics, Mathematics, Applied Mathematics, 010102 general mathematics, Degenerate energy levels, comparison principle, Statistical and Nonlinear Physics, strong maximum principle, Lipschitz continuity, Parabolic partial differential equation, large time behavior, Term (time), 010101 applied mathematics, Nonlinear system, nonlinear PDEs, 35R09, 35B51, 35B65, 35D40, 35B10, 35B40, Analysis of PDEs (math.AP)
Abstract

International audience; In this paper, we provide suitable adaptations of the " weak version of Bernstein method " introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed " uniformly el-liptic " (maybe in the nonlocal sense) but which do not satisfy the usual " growth condition " on the gradient term allowing to use (for example) the Ishii-Lions' method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.

Published
2017
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26. Probalistic and piecewise deterministic models in biology

Author

Bertrand Cloez, Renaud Dessalles, Alexandre Genadot, Florent Malrieu, Aline Marguet, Romain Yvinec, Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Networks, Algorithms and Probabilities (RAP), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Bordeaux (UB), Quality control and dynamic reliability (CQFD), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université Francois Rabelais [Tours], Université Paris-Saclay, École polytechnique (X), Physiologie de la reproduction et des comportements [Nouzilly] (PRC), Institut National de la Recherche Agronomique (INRA)-Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Agence Nationale de la Recherche PIECE 12-JS01-0006-01, Chaire 'Modélisation Mathématique et Biodiversité ', Société de Mathématiques Appliquées et Industrielles (SMAI). FRA., Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut National de la Recherche Agronomique (INRA)-Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Institut Français du Cheval et de l'Equitation [Saumur]-Institut National de la Recherche Agronomique (INRA), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National de la Recherche Agronomique (INRA)-Institut Français du Cheval et de l'Equitation [Saumur] (IFCE)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie ( MISTEA ), Institut National de la Recherche Agronomique ( INRA ) -Institut national d’études supérieures agronomiques de Montpellier ( Montpellier SupAgro ), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] ( MaIAGE ), Institut National de la Recherche Agronomique ( INRA ), Networks, Algorithms and Probabilities ( RAP ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Université de Bordeaux ( UB ), Quality control and dynamic reliability ( CQFD ), Institut de Mathématiques de Bordeaux ( IMB ), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Bordeaux - Sud-Ouest, Fédération de recherche Denis Poisson ( FRDP ), Centre National de la Recherche Scientifique ( CNRS ) -Université d'Orléans ( UO ), École polytechnique ( X ), Physiologie de la reproduction et des comportements [Nouzilly] ( PRC ), and Institut National de la Recherche Agronomique ( INRA ) -Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours-Centre National de la Recherche Scientifique ( CNRS )

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], probabilistic model, [SDV.OT]Life Sciences [q-bio]/Other [q-bio.OT], modèle probabiliste, processus de markov, Probabilités, [ SDV.OT ] Life Sciences [q-bio]/Other [q-bio.OT], biological model, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], modèle biologique, Probability, Autre (Sciences du Vivant)
Abstract

International audience; We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by [30], are a very general class ofMarkov processes and are being increasingly popular in biological applications. They also give new interest-ing challenges from the theoretical point of view. We give here different examples on the long time behaviorof switching Markov models applied to population dynamics, on uniform sampling in general branching mod-els applied to structured population dynamic, on time scale separation in integrate-and-fire models used in neuroscience, and, finally, on moment calculus in stochastic models of gene expression.

Published
2016

27. On the persistence regime for Lotka-Volterra in randomly fluctuating environments

Author

Pierre-André Zitt, Florent Malrieu, Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), ANR-12-JS01-0006,PIECE,Ergodicité, contrôle et statistique pour les PDMP(2012), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, and Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Persistence (psychology), Extinction, Probability (math.PR), 01 natural sciences, 010101 applied mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Range (statistics), FOS: Mathematics, Quantitative Biology::Populations and Evolution, Statistical physics, 0101 mathematics, MSC : 60J99, 34A60, Invariant probability measure, Mathematics - Probability, Mathematics
Abstract

International audience; In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benaïm and Lobry (2015) recently established that randomly switching between two environments that are both favorable to the same species may lead to different regimes: extinction of one species or the other, or persistence of both species. Our purpose here is to describe more accurately the range of parameters leading to these regimes, and the support of the invariant probability measure in case of persistence.

Published
2016

28. Functional inequalities for Gaussian convolutions of compactly supported measures: explicit bounds and dimension dependence

Author

Nathael Gozlan, Pierre-André Zitt, Florent Malrieu, Jean-Baptiste Bardet, Laboratoire de Mathématiques Raphaël Salem (LMRS), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Statistics and Probability, Pure mathematics, Inequality, Gaussian, media_common.quotation_subject, Poincaré inequality, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Measure (mathematics), MSC2010: 60E15, 39B62, 26D10, Convolution, 010104 statistics & probability, symbols.namesake, Dimension (vector space), FOS: Mathematics, 0101 mathematics, logarithmic Sobolev inequality, Mathematics, media_common, Probability (math.PR), 010102 general mathematics, transport-entropy inequality, Functional Analysis (math.FA), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Functional Analysis, Distribution (mathematics), symbols, Focus (optics), Mathematics - Probability
Abstract

International audience; The aim of this paper is to establish various functional inequalities for the convolution of a compactly supported measure and a standard Gaussian distribution on Rd. We especially focus on getting good dependence of the constants on the dimension. We prove that the Poincaré inequality holds with a dimension-free bound. For the logarithmic Sobolev inequality, we improve the best known results (Zimmermann, JFA 2013) by getting a bound that grows linearly with the dimension. We also establish transport-entropy inequalities for various transport costs.

Published
2015
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29. Le cocycle brownien de degré deux comme bruit blanc sur les droites affines de l'espace

Author

Jérôme Depauw, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Pure mathematics, mouvement brownien à plusieurs paramètres, Degree (graph theory), Plane (geometry), 010102 general mathematics, Dimension (graph theory), 60H40 (60D05), 0102 computer and information sciences, General Medicine, White noise, multiparameter brownian motion, 16. Peace & justice, 01 natural sciences, brownian sheet, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics::Probability, 010201 computation theory & mathematics, drap brownien, Calculus, 0101 mathematics, Brownian motion, Mathematics
Abstract

International audience; Inspired by the work of Čencov on multiparameter Lévy's Brownian motion, we show that the white noise on the straight lines in dimension three generates a cocycle of degree two, whose restrictions to plans have the law of plane Brownian sheets. We check that this degree two cocycle is the same than the one studied by us in a preceding work. Consequently we give here another proof of the existence of the degree two Brownian cocycle in dimension three. Moreover this construction is adapted to the numerical simulation.

Published
2006
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30. Digestion Modelling in the Small Intestine : Impact of Dietary Fibre

Author

Masoomeh Taghipoor, Philippe Lescoat, Jean-René Licois, Christine Georgelin, Guy Barles, Unité de Recherches Avicoles (URA), Institut National de la Recherche Agronomique (INRA), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Recherches Avicoles (SRA), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours

Subjects
Dietary Fiber, 030309 nutrition & dietetics, [SDV]Life Sciences [q-bio], fibre alimentaire, Dynamical Systems (math.DS), intestin grêle, rétention d'eau, Intestine, Small, Food science, Mathematics - Dynamical Systems, Tissues and Organs (q-bio.TO), 0303 health sciences, Chemistry, Applied Mathematics, 04 agricultural and veterinary sciences, General Medicine, 040401 food science, medicine.anatomical_structure, Biological Physics (physics.bio-ph), Modeling and Simulation, Digestion, modèle dynamique, Bolus (digestion), General Agricultural and Biological Sciences, Statistics and Probability, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, Insoluble dietary fiber, Soluble dietary fiber, Models, Biological, General Biochemistry, Genetics and Molecular Biology, 03 medical and health sciences, Modelling of intestinal digestion, 0404 agricultural biotechnology, medicine, FOS: Mathematics, Water holding capacity, Animals, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Dry matter, Physics - Biological Physics, modélisation, soluble dietary fiber, General Immunology and Microbiology, water holding capacity, Quantitative Biology - Tissues and Organs, Intestinal digestion, Physics - Medical Physics, Small intestine, insoluble dietary fiber, solubilité, FOS: Biological sciences, Dietary fiber, Medical Physics (physics.med-ph), [SDV.AEN]Life Sciences [q-bio]/Food and Nutrition
Abstract

International audience; In this work, we continue the modelling of the digestion in the small intestine, started in a previous article, by investigating the effects of dietary fibre. We recall that this model aims at taking into account the three main phenomena of the digestion, namely the transit of the bolus, the degradation of feedstuffs and the absorption through the intestinal wall. In order to study the role of dietary fibre on digestion, we model their two principal physiochemical characteristics which interact with the function of the small intestine, i.e. viscosity and water holding capacity. This leads us to consider some features of digestion which have not been taken into account previously, in particular the interrelationship between the evolution of dry matter and water in the bolus. The numerical results are in agreement with the positive effect of insoluble dietary fibre on the velocity of bolus along the small intestine and on its degradation. These results highlight the negative effect of soluble dietary fibre on digestion. Although, this model is generic and contains a large number of parameters, to our knowledge, it is among the first qualitative dynamical modelling of fibre influence on intestinal digestion.

Published
2014
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31. Large Time Behavior of Periodic Viscosity Solutions for Uniformly Parabolic Integro-Differential Equations

Author

Adina Ciomaga, Cyril Imbert, Emmanuel Chasseigne, Guy Barles, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Department of Mathematics, University of Chicago, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)

Subjects
35B40, 35R09, 35D40, 35D10, Differential equation, media_common.quotation_subject, Ergodic problem, 01 natural sciences, Parabolic nonlinear integro-differential equations, Mathematics - Analysis of PDEs, FOS: Mathematics, Applied mathematics, Initial value problem, Ergodic theory, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Long time behavior, Lipschitz estimates, media_common, Mathematics, Variable (mathematics), Applied Mathematics, 010102 general mathematics, Order (ring theory), Infinity, Lipschitz continuity, 010101 applied mathematics, Nonlinear system, Analysis, Analysis of PDEs (math.AP), Strong maximum principle
Abstract

International audience; In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem}(or cell problem), i.e. we construct solutions of the form $\lambda t + v(x)$. We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (i) the fact that we handle the case of ''mixed operators'' for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (ii) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis.

Published
2014
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32. Regularity Results and Large Time Behavior for Integro-Differential Equations with Coercive Hamiltonians

Author

Guy Barles, Shigeaki Koike, Erwin Topp, Olivier Ley, Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Mathematical Institute, Tohoku University [Sendai], Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Departamento de Ingenieria Matematica, Centro Modelamiento Matematico, Universidad de Santiago de Chile [Santiago] (USACH)-Centro Modelamiento Matematico (CMM), Shigeaki Koike is supported by Grant-in-Aid for Scientific Research (No. 23340028) of Japan Society for the Promotion of Science. Erwin Topp was partially supported by CONICYT, Grants Capital Humano Avanzado, Cotutela en el Extranjero and Ayuda Realización Tesis Doctoral., ANR-12-BS01-0020,WKBHJ,KAM faible au-delà de Hamilton-Jacobi(2012), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université de Tours-Centre National de la Recherche Scientifique (CNRS), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Comparison Principles, Differential equation, Applied Mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Strong Maximum Principles, 16. Peace & justice, Lipschitz continuity, Regularity, Large Time Behavior, Maximum principle, Mathematics - Analysis of PDEs, Linearization, Bounded function, FOS: Mathematics, Ergodic theory, A priori and a posteriori, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 35R09, 35B51, 35B65, 35D40, 35B10, 35B40, Parabolic Integro-Differential Equations, Analysis, Analysis of PDEs (math.AP), Mathematics
Abstract

International audience; In this paper we obtain regularity results for elliptic integro-differential equations driven by the stronger effect of coercive gradient terms. This feature allows us to construct suitable strict supersolutions from which we conclude Hölder estimates for bounded subsolutions. In many interesting situations, this gives way to a priori estimates for subsolutions. We apply this regularity results to obtain the ergodic asymptotic behavior of the associated evolution problem in the case of superlinear equations. One of the surprising features in our proof is that it avoids the key ingredient which are usually necessary to use the Strong Maximum Principle: linearization based on the Lipschitz regularity of the solution of the ergodic problem. The proof entirely relies on the Hölder regularity.

Published
2014
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33. On the exit time from a cone for Brownian motion with drift

Author

Rodolphe Garbit, Kilian Raschel, Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Université de Tours-Centre National de la Recherche Scientifique (CNRS), and Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
Statistics and Probability, 60G50, Polynomial, Geometry, Exit time, 01 natural sciences, 010104 statistics & probability, 60J05, Position (vector), FOS: Mathematics, 60J65, 0101 mathematics, Heat kernel, Brownian motion, Mathematics, 010102 general mathematics, Probability (math.PR), Brownian motion with drift, Function (mathematics), Exponential function, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Distribution (mathematics), 60F17, 60G50, 60J05, 60J65, Cone (topology), 60F17, Statistics, Probability and Uncertainty, Cone, Mathematics - Probability
Abstract

We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in particular that its exponential decreasing rate is a function of the distance between the drift and the cone, whereas the polynomial part in the asymptotics depends on the position of the drift with respect to the cone and its polar cone, and reflects the local geometry of the cone at the point where the drift is orthogonally projected.

Published
2013
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34. Identification of the twisting function for the dynamic Schrödinger operator in a quantum waveguide

Author

Bellassoued, Mourad, Cristofol, Michel, Soccorsi, Eric, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), and Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematics - Analysis of PDEs, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

In this paper we examine the inverse problem of determining the twisting function for the dynamicSchrodinger operator in a quantum waveguide from some suitable localized, either interior or boundary.

Published
2012

35. Symmetries, currents and holography of higher spin

Author

Meunier, Elisa, Meunier, Elisa, gravitation, Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Physique Théorique (LMPT), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Université François Rabelais - Tours, and Xavier BEKAERT(xavier.bekaert@lmpt.univ-tours.fr)

Subjects
AdS/CFT correspondence, [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], Symétries, espace-temps de cour- bure constante, conserved currents, formalisme ambiant, correspondance AdS/CFT, spins élevés, ambient formalism, ideal/unitary Fermi gas, gaz parfait/unitaire de Fermi, Noether method, méthode de Noether, spacetime of constant curvature, courants conservés, holography, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], holographie, higher spin, Symmetries
Abstract

The higher spin theory is the field of theoretical physics at the center of this thesis. Besides an introduction presenting the general context of the birth of this theory, this PhD thesis consists of three recent studies in this area. Particular attention will be paid to symmetries, currents and holography. The first part focuses on the ingredients for the construction of cubic vertices between a scalar matter field and a higher spin gauge field in a constant curvature space-time. Noether's method describes how to build the interactions from conserved currents, whose writing may be condensed using generating functions. Ambient formalism is the main aspect of this calculation since it allows simplification. In a second step, we prepare the around for a future test of the holographic correspon- dence in the cubic or quartic order in the coupling constant. More specifically, we review in detail the computation of some propagators, which leads us to calculate three-point functions involving two scalar fields. The last part, although always on the higher spin holography, deals with non-relativistic physics. Symmetries and currents of an ideal or unitary Fermi gas are studied. In particular, we prove that the maximal symmetry algebra of Schrödinger equation is the Weyl alge- bra. The link between relativistic and non-relativistic physics is obtained by Bargmann's dimensional reduction. The higher spin nonrelativistic holography is also discussed., La théorie des spins élevés est le domaine de la physique théorique au centre de cette thèse. Outre une introduction présentant le contexte général de la naissance de cette théo- rie, ce manuscrit de thèse regroupe trois études récentes dans ce domaine. Une attention particulière sera portée aux symétries, aux courants et à l'holographie. La première partie est axée sur les ingrédients permettant la construction de vertex cubiques entre un champ scalaire de matière et un champ de jauge de spin élevé dans un espace-temps à courbure constante. La méthode de Noether indique comment construire ces interactions à partir des courants conservés, dont on peut condenser l'écriture en utili- sant les fonctions génératrices. Le formalisme ambiant est le principal aspect de ce calcul puisqu'il le facilite et en permet la simplification. Dans un second temps, nous préparons les éléments pour un futur test de la correspon- dance holographique à l'ordre cubique voire quartique en la constante de couplage. Plus précisément, nous révisons en détail le calcul de certains propagateurs, ce qui nous mène à calculer les fonctions à trois points impliquant deux champs scalaires. La dernière partie, bien que concernant toujours l'holographie des spins élevés, traite de la physique non-relativiste. Les symétries et les courants d'un gaz parfait/unitaire de Fermi y sont étudiés. En particulier, nous prouvons que l'algèbre maximale de symétrie de l'équation de Schrödinger est l'algèbre de Weyl. Le lien entre physiques relativiste et non-relativiste est obtenu grâce à la réduction dimensionnelle de Bargmann. L'holographie des spins élevés non relativistes est également évoquée.

Published
2012

36. Short Time Uniqueness Results for Solutions of Nonlocal and Non-monotone Geometric Equations

Author

Hiroyoshi Mitake, Olivier Ley, Guy Barles, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Department of Applied Mathematics, Fukuoka University, Research Fellowship (20-5332, 22-1725) for Young Researcher from JSPS and Excellent Young Researchers Overseas Visit Program of JSPS, ANR-06-BLAN-0082,MICA,Mouvements d'interfaces, calcul et applications(2006), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)

Subjects
35K15, 34A12, 35A02, 49L25, 45K05, 53C44, Viscosity Solution, General Mathematics, Lower Gradient Estimate, Short Time Uniqueness, Type (model theory), 01 natural sciences, Nonlocal Hamilton-Jacobi Equations, Viscosity, Mathematics - Analysis of PDEs, Simultaneous equations, FOS: Mathematics, Initial value problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, Nonlinear Sciences::Pattern Formation and Solitons, Mathematics, Lebesgue measure, Independent equation, 010102 general mathematics, Mathematical analysis, Non-Fattening Condition, Front (oceanography), Dislocation Dynamics, 010101 applied mathematics, Nonlocal Front Propagation, Analysis of PDEs (math.AP), Fitzhugh-Nagumo System
Abstract

International audience; We describe a method to show short time uniqueness results for viscosity solutions of general nonlocal and non-monotone second-order geometric equations arising in front propagation problems. Our method is based on some lower gradient bounds for the solution. These estimates are crucial to obtain regularity properties of the front, which allow to deal with nonlocal terms in the equations. Applications to short time uniqueness results for the initial value problems for dislocation type equations, asymptotic equations of a FitzHugh-Nagumo type system and equations depending on the Lebesgue measure of the fronts are presented.

Published
2012
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37. Unbounded solutions of the nonlocal heat equation

Author

Emmanuel Chasseigne, Cristina Brändle, Raúl Ferreira, Departamento de Matematicas, Universidad Carlos III de Madrid [Madrid] (UC3M), Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Departamento de Matematica Aplicada [Madrid], Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Universidad Carlos III de Madrid [Madrid], Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours, Universidad Complutense de Madrid [Madrid] (UCM), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pure mathematics, Class (set theory), Polynomial, Trace (linear algebra), Matemáticas, Matemáticas aplicadas, Probability density function, optimal classes of data, Space (mathematics), 01 natural sciences, Mathematics - Analysis of PDEs, Non-local diffusion, FOS: Mathematics, Initial value problem, 45A05, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, initial trace, Mathematics, 35A01, Applied Mathematics, 010102 general mathematics, 35A02, 010101 applied mathematics, Heat equation, Analysis, Analysis of PDEs (math.AP)
Abstract

We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: $ u_t = J\ast u -u, $ where $J$ is a symmetric continuous probability density. Depending on the tail of $J$, we give a rather complete picture of the problem in optimal classes of data by: $(i)$ estimating the initial trace of (possibly unbounded) solutions; $(ii)$ showing existence and uniqueness results in a suitable class; $(iii)$ proving blow-up in finite time in the case of some critical growths; $(iv)$ giving explicit unbounded polynomial solutions.

Published
2011

38. Einstein constraints on a characteristic cone

Author

Yvonne Choquet-Bruhat, Piotr T. Chruściel, Jose M. Martin-Garcia, Université Pierre et Marie Curie - Paris 6 (UPMC), Institut des Hautes Etudes Scientifiques (IHES), IHES, Fédération de recherche Denis Poisson (FDP), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Laboratoire Univers et Théories (LUTH (UMR_8102)), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7), Institut d'Astrophysique de Paris (IAP), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut des Hautes Études Scientifiques (IHES), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, High Energy Physics::Lattice, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Gauge (firearms), General Relativity and Quantum Cosmology, High Energy Physics::Theory, symbols.namesake, Cone (topology), Einstein equations, Vertex (curve), symbols, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Initial value problem, Einstein, Mathematical physics
Abstract

We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation., Comment: 10 pages, to be published in the Proceedings of the 15th International Conference on Waves and Stability in Continuous Media, held in Palermo, 28th June to 1st July 2009

Published
2010

39. The light-cone theorem

Author

Yvonne Choquet-Bruhat, Jose M. Martin-Garcia, Piotr T. Chrusciel, Université Pierre et Marie Curie - Paris 6 (UPMC), Institut des Hautes Etudes Scientifiques (IHES), IHES, Fédération de recherche Denis Poisson (FDP), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Laboratoire Univers et Théories (LUTH (UMR_8102)), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7), Institut d'Astrophysique de Paris (IAP), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Institut des Hautes Études Scientifiques (IHES), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Université d'Orléans (UO)-Université de Tours-Centre National de la Recherche Scientifique (CNRS), and PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Physics and Astronomy (miscellaneous), 010308 nuclear & particles physics, 010102 general mathematics, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 01 natural sciences, General Relativity and Quantum Cosmology, De Sitter universe, Light cone, 0103 physical sciences, Minkowski space, Domain (ring theory), Metric (mathematics), [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], 0101 mathematics, Energy (signal processing), Mathematical physics
Abstract

We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light-cone., 24 pages, 1 figure. Minor changes to match published version

Published
2009

40. Un résultat d' homogénéisation pour une équation de Hamilton-Jacobi périodique sur un réseau hétérogéne

Author

Ariela Briani, Guy Barles, Emmanuel Chasseigne, Nicoletta Tchou, Fédération de recherche Denis Poisson ( FRDP ), Université d'Orléans ( UO ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques et Physique Théorique ( LMPT ), Université de Tours-Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), ANR-12-BS01-0008,HJnet,Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux ( 2012 ), Fédération de recherche Denis Poisson (FDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANR-12-BS01-0008,HJnet,Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux(2012), Briani, Ariela, BLANC - Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux - - HJnet2012 - ANR-12-BS01-0008 - BLANC - VALID, Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours

Subjects
contrôle optimale, équations de Bellman, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Homogénéisation, solution de viscosité, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; On considère ici, dans le cas simple de R^N partagé en deux ouverts complémentaires périodiques Ω1 et Ω2 , le probìème d' homogénéiser les équations de type Hamilton-Jacobi. On suppose les données limitées ,régulìères et ZN-périodiques en y, (pour tous x et α i). Pour ce probìème dans [5, 6] nous avons montré que l'on peut définir plusieurs solutions (et donc fonctions valeurs), selon le type de trajectoires qu'on accepte pour le probìème de contrôle optimal correspondant. Ici on décrit le comportement asymptotique de solutions minimale et maximale U- , U+ et on etudier les probìème d' homogénéisation dans les deux cas. C'est important de remarquer que si pour traiter U− on peut utiliser des méthodes style EDP a la Lions-Papanicolau-Varadan, dans le cas de U+ il faut s'appuyer sur sa caractérisation contrôle optimal.

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