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6 results on '"Instituto de Ciencias Matemàticas [Madrid] (ICMAT)"'

1. On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

Author

Ivan Bardet, Cambyse Rouzé, David Pérez-García, Angelo Lucia, Angela Capel, Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), California Institute of Technology (CALTECH), Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Ivan Bardet is supported by French A.N.R. grant: ANR-14-CE25-0003 'StoQ'. Angela Capel is partially supported by a La Caixa-Severo Ochoa grant (ICMAT Severo Ochoa project SEV-2011-0087, MINECO) and Angela Capel and David Perez Garcia acknowledge support from MINECO (grant MTM2017-88385-P) and from Comunidad de Madrid (grantQUITEMAD-CM, ref. P2018/TCS-4342). Angelo Lucia acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1733907), and from the BBVA Fundation.This project has received funding from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation programme (grant agreementNo 648913). Cambyse Rouzé acknowledges financial support from the TUM university Foundation Fellowship and by the DFG cluster of excellence 2111 (Munich Center for Quantum Science and Technology)., Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Security, Cryptology and Transmissions (SECRET), Instituto de Ciencias Matemàticas [Madrid], Consejo Superior de Investigaciones Científicas [Spain] (CSIC), Universidad Complutense de Madrid [Madrid] (UCM), and Technische Universität München [München] (TUM)

Subjects
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Gibbs state, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Entropy (classical thermodynamics), symbols.namesake, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, 0101 mathematics, Gibbs measure, Mixing (physics), Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematical physics, Mathematics, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 010102 general mathematics, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Sobolev space, symbols, Dissipative system, 010307 mathematical physics, Constant (mathematics), Quantum Physics (quant-ph), Hamiltonian (control theory)
Abstract

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular we show that for the heat-bath dynamics for 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy., 28 pages, 4 figures. Included some additional comments and updated results in light of recent advances in the literature

Published
2021
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2. Parabolic subgroups acting on the additional length graph

Author

Yago Antolín, María Cumplido, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), University of Sevilla, Spanish GovernmentEuropean CommissionMTM2014-53810-C2-01MTM2017-82690-PMTM2016-76453-C2-1-PSpanish Government through the 'Severo Ochoa Programme for Centres of Excellence in RD'SEV-2015-0554European CommissionMTM2016-76453-C2-1-P, Universidad de Sevilla. Departamento de Álgebra, and Universidad de Sevilla. FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía

Subjects
Pure mathematics, media_common.quotation_subject, Braid group, Garside groups, artin-tits groups, Group Theory (math.GR), acylindrically hyperbolic groups, parabolic subgroups, 01 natural sciences, Mathematics::Group Theory, Álgebra, 0103 physical sciences, relative growth, FOS: Mathematics, Uniform boundedness, braid groups, 0101 mathematics, [MATH]Mathematics [math], Mathematics, media_common, growth of groups, Grupos (Matemáticas), Sequence, Group (mathematics), 010102 general mathematics, Infinity, 20F36, 20F65, Artin groups, Generating set of a group, Graph (abstract data type), 010307 mathematical physics, Geometry and Topology, Element (category theory), Mathematics - Group Theory
Abstract

Let $A\neq A_1, A_2, I_{2m}$ be an irreducible Artin--Tits group of spherical type. We show that periodic elements of $A$ and the elements preserving some parabolic subgroup of $A$ act elliptically on the additional length graph $\mathcal{C}_{AL}(A)$, an hyperbolic, infinite diameter graph associated to $A$ constructed by Calvez and Wiest to show that $A/Z(A)$ is acylindrically hyperbolic. We use these results to find an element $g\in A$ such that $\langle P,g \rangle\cong P* \langle g \rangle$ for every proper standard parabolic subgroup $P$ of $A$. The length of $g$ is uniformly bounded with respect to the Garside generators, independently of $A$. This allows us to show that, in contrast with the Artin generators case, the sequence $\{\omega(A_n,\mathcal{S})\}_{n\in \mathbb{N}}$ of exponential growth rates of braid groups with respect to the Garside generating set, goes to infinity., Comment: 19 pages, 2 figures

Published
2021
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3. Mapping properties of operator-valued pseudo-differential operators

Author

Runlian Xia, Xiao Xiong, Laboratoire de Mathématiques (LM-Brest), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Institute for Advanced Study [Tsinghua], Tsinghua University [Beijing] (THU), School of Mathematics and Statistics, and University of New South Wales [Sydney] (UNSW)

Subjects
010102 general mathematics, Mathematics - Operator Algebras, Torus, Differential operator, 01 natural sciences, Functional Analysis (math.FA), Combinatorics, Sobolev space, Mathematics - Functional Analysis, Atomic decomposition, Operator (computer programming), Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Primary: 46L52, 42B30. Secondary: 46L07, 47L65, Computer Science::Symbolic Computation, 010307 mathematical physics, 0101 mathematics, [MATH]Mathematics [math], Operator Algebras (math.OA), Analysis, Mathematics
Abstract

In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces $F_1^{\alpha,c}(\mathbb{R}^d,\mathcal{M})$ obtained in our previous paper, we establish the $F_1^{\alpha,c}$-regularity of regular symbols for every $\alpha\in \mathbb{R}$, and the $F_1^{\alpha,c}$-regularity of forbidden symbols for $\alpha>0$. As applications, we obtain the same results on the usual and quantum tori., Comment: 37 pages

Published
2018
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4. Self-improving properties for abstract Poincaré type inequalities

Author

José María Martell, Frédéric Bernicot, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Ministerio de Economía y Competitividad (España), Martell, José María, and Martell, José María [0000-0001-6788-4769]

Subjects
Generalized Poincar e-Sobolev inequalities, Computer Science::Machine Learning, General Mathematics, Dyadic cubes, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Computer Science::Digital Libraries, 01 natural sciences, semigroups, Statistics::Machine Learning, symbols.namesake, 0103 physical sciences, 46E35, John-Nirenberg inequalities, Direct proof, 0101 mathematics, Lp space, Self-improving properties, Mathematics, BMO and Lipschitz spaces, Conjecture, Euclidean space, Applied Mathematics, 010102 general mathematics, 1. No poverty, Lipschitz continuity, pseudo-Poincaré inequalities, Algebra, Elliptic operator, Pseudo-Poincare inequalities, Mathematics - Classical Analysis and ODEs, Poincaré conjecture, Computer Science::Mathematical Software, symbols, generalized Poincaré-Sobolev inequalities, 010307 mathematical physics
Abstract

We study self-improving properties in the scale of Lebesgue spaces of generalized Poincar e inequalities in the Euclidean space. We present an abstract setting where oscillations are given by certain operators (e.g., approximations of the identity, semigroups or mean value operators) that have o -diagonal decay in some range. Our results provide a uni ed theory that is applicable to the classical Poincar e inequalities and furthermore it includes oscillations de ned in terms of semigroups associated with second order elliptic operators as those in the Kato conjecture. In this latter situation we obtain a direct proof of the John-Nirenberg inequality for the associated BMO and Lipschitz spaces of [HMay, HMM], The second author was supported by MINECO Grant MTM2010-16518 and ICMAT Severo Ochoa project SEV-2011-0087

Published
2014
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5. Vertical versus conical square functions

Author

José María Martell, Pascal Auscher, Steve Hofmann, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), University of Missouri [Columbia] (Mizzou), University of Missouri System, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
elliptic operators, Applied Mathematics, General Mathematics, 010102 general mathematics, Mathematical analysis, extrapolation, MSC 2010: 42B25, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Conical surface, 01 natural sciences, Vertical square functions, Square (algebra), Elliptic operator, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 010307 mathematical physics, 0101 mathematics, conical square functions, Analysis of PDEs (math.AP), Mathematics
Abstract

We study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator., Comment: 21 pages

Published
2012
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6. On Euler’s decomposition formula for $$q$$ q MZVs

Author

Kurusch Ebrahimi-Fard, Dominique Manchon, Jaime Castillo Medina, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
Pure mathematics, Algebra and Number Theory, Mathematics - Number Theory, Generalization, Mathematics::Number Theory, 010102 general mathematics, Jackson integral, Rota–Baxter algebra, 01 natural sciences, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], symbols.namesake, Number theory, Fourier analysis, 0103 physical sciences, FOS: Mathematics, Decomposition (computer science), Euler's formula, symbols, Number Theory (math.NT), 010307 mathematical physics, 0101 mathematics, [MATH]Mathematics [math], Mathematics
Abstract

We derive a $$q$$ -generalization of Euler’s decomposition formula for the $$q$$ MZVs recently introduced by Y. Ohno, J. Okuda, and W. Zudilin. This answers a question posed by these authors in J Number Theory 132, 144–155 (2012).

Published
2015
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