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A bstract Motivated by issues in the context of asymptotically flat spacetimes at null infinity, we discuss in the simplest example of a free massless scalar field in two dimensions several subtleties that arise when setting up the canonical formulation on a single or on two intersecting null hyperplanes with a special emphasis on the infinite-dimensional global and conformal symmetries and their canonical generators, the free data, a consistent treatment of zero modes, matching conditions, and implications for quantization of massless versus massive fields., info:eu-repo/semantics/published

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The single-channel Jost function is calculatedwith the computational R-matrix on a Lagrange-Jacobi mesh,in order to study its behaviour at complex wavenumbers.Three potentials derived from supersymmetric transforma-tions, two of which never previously studied, are used to testthe accuracy of the method. Each of these potentials, withs-wave or p-wave bound, resonance or virtual states, has asimple analytical expression for the Jost function, which iscompared with the calculated Jost function. Siegert statesand Siegert pseudostates are determined by finding the zerosof the calculated Jost function. Poles of the exact Jost func-tion are not present in the calculated Jost function due to thetruncation of the potential in the R-matrix method. Instead,Siegert pseudostates arise in the vicinity of the missing poles., SCOPUS: ar.j, info:eu-repo/semantics/published

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Les transformations de transformations, également appelées processus d'ordres supérieurs, forment un concept courant en informatique et en traitement de l'information. De tels processus apparaissent dès qu'il est question de manipulations sur l'opération à appliquer aux données, plutôt que sur les données elles-mêmes. Par exemple, lorsque l'on veut représenter un protocole informatique avec des boucles de rétroaction d'opérations, comme des boucles "for" imbriquées, ou lorsque l'on veut représenter un protocole de communication avec un contrôle dynamique des opérations, comme lorsqu'un adversaire agit sur les données d'entrée et de sortie d'une autre partie afin de la tromper, on utilisera des processus d'ordre supérieur.Ce paradigme appliqué à l'informatique quantique a récemment suscité un grand intérêt, tant au niveau pratique que fondamental. D'une part, il a été démontré que certains processus quantiques d'ordre supérieur permettaient de réduire le nombre d'opérations nécessaires à la réalisation de certains protocoles. D'autre part, ces processus présentent parfois des relations causales indéfinies au sens quantique du terme ;l'ordre des événements A et B peut se superposer entre A puis B et B puis A. Ce comportement est d'un grand intérêt fondamental car il remet en question certaines idées préconçues que d'aucun pensent incompatibles avec une théorie quantique de la gravité.Un cadre général pour représenter les transformations quantiques d'ordres supérieurs est dès lors nécessaire pour pleinement exploiter les améliorations qu'elles apportent et, en parallèle, pour étudier les relations causales quantiques singulières qu'elles présentent. Pareil cadre est développé dans cette thèse. Plus précisément, un ensemble d'outils pour caractériser les processus quantiques d'ordre supérieurs valides reposant sur la dualité canal-état ainsi que l'utilisation de projecteurs superopératoires est présenté. Il est montré que les manières possibles de définir un ensemble do, Transformations of transformations, also called higher-order processes, is a commonly occurring concept in computing and information processing. Such processes arise in situations involving manipulations of the operation applied to the data, rather than of the data itself. For example, when one wants to represent a computing protocol with feedback loops of operations, like nested 'for loops', or when one wants to represent a communication protocol with dynamical control over operations, like where an adversary party is acting on the input and output data of some other party so to deceive her, higher-order processes will be used. Applied to quantum computing, this paradigm has recently attracted significant interest both at the practical and fundamental levels. On the one hand, specific higher-order quantum processes were shown to decrease the number of operations needed to realize certain protocols. On the other hand, these processes sometimes feature causal relations that are ‘indefinite’ in the quantum sense; the ordering of events A and B can become superposed between A then B and B then A. This behavior is of great fundamental interest as it challenges some pre-conceived ideas some believe to be incompatible with a quantum theory of gravity. A general framework to represent higher-order quantum transformations is then necessary to fully harness the improvements they provide and, in parallel, to study the puzzling quantum causal relations they feature. Such a framework is developed in this thesis. Specifically, a set of tools for characterizing valid higher-order quantum processes relying on channel-state duality and the use of superoperator projectors is presented. It is shown that the possible ways to define a given set of higher-order transformations are homomorphic to an algebra of these superoperator projectors, which are in turn homomorphic to the signaling relations that the objects in this set may allow. Moreover, this algebra is shown to be very close to, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

A bstract We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent theory revealing a ’t Hooft anomaly in the space of coupling constants when suitable compact scalar background fields are activated. Furthermore, the gauging procedure also implies that our main example has infinitely many non-invertible global symmetries. These can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we comment on the holographic realization of both 2-group global symmetries and non-invertible symmetries discussed here by introducing a corresponding four-dimensional bulk description in terms of dynamical gauge fields., info:eu-repo/semantics/published

A bstract We study non-abelian gauge theories with fermions in a representation such that the surviving electric 1-form symmetry is ℤ 2 .This includes SU( N ) gauge theories with matter in the (anti)symmetric and N even, and USp(2 N ) with a Weyl fermion in the adjoint, i.e. $$ mathcal{N} $$ N = 1 SYM. We study the mixed ’t Hooft anomaly between the discrete axial symmetry and the 1-form symmetry and show that when it is non-trivial, it leads to non-invertible symmetries upon gauging the ℤ 2 .The TQFT dressing the non-invertible symmetry defects is universal to all the cases we study, namely it is always a U(1) 2 CS theory coupled to the ℤ 2 2-form gauge field. We uncover a pattern where the presence or not of non-invertible defects depends on the rank of the gauge group., info:eu-repo/semantics/published

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible codimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become codimension one non-invertible defects of a boundary theory with an ABJ anomaly., SCOPUS: ar.j, info:eu-repo/semantics/published

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We consider the prescribed mean curvature equation for entire spacelike hypersurfaces in the Lorentz-Minkowski space, namely -div(∇u1, SCOPUS: ar.j, info:eu-repo/semantics/published

This thesis investigates multiphoton quantum interference with a particular emphasis onphotonic partial distinguishability stemming from factors such as timelags or polarizationmismatches between the photons. We explore the gray area between the behaviour ofdistinguishable classical particles and ideally indistinguishable bosons in large linearinterferometers, with practical implications for photonic quantum computers – especiallyboson samplers – as well as fundamental consequences on the many-body physics ofbosonic systems.Our research leverages recent findings in the mathematical theory of matrix perma-nents to unravel new aspects of interference phenomena. In particular, we exhibit asurprising counterexample to the rule of thumb that "identical bosons bunch most",which can be observed with 7 photons in a 7-mode linear interferometer.We develop robust techniques to validate boson samplers – that is, to verify theincompatibility with classical samplers – by analyzing the photon distribution amongpartitions of the output modes. This innovative method extends existing validationtests, providing a comprehensive approach to assessing boson sampling experiments.An extra contribution of this thesis is the development of BosonSampling.jl, anopen-source, high-performance software package for multiphoton interferometry simula-tions, featuring versatile tools for boson sampling tasks and a suite of validation tools inorder to rigorously evaluate boson samplers in the presence of partial distinguishabilityand other noise sources., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Quantum gravity seeks to reconcile quantum mechanics and general relativity, the two pillars of modern physics, into a single consistent framework. One of the biggest achievements of quantum gravity is the discovery of the holographic principle (or holography). Holography suggests that the gravitational degrees of freedom in a region of space can be described by a quantum field theory on the boundary of that region. This thesis aims to study holography in the context of a three-dimensional gravity model, namely, topologically massive gravity (TMG) with a negative cosmological constant. It is a model of gravity with a topological term— gravitational Chern-Simons term—added to Einstein-Hilbert action. This term allows for the presence of a massive graviton in the theory.In this thesis, we develop holographic dictionary between warped black holes (WBHs) and warped conformal field theories (WCFTs). WBHs are three-dimensional rotating black holes that appear as solutions of TMG. WCFTs are two-dimensional non-relativistic field theories that share many similarities with two-dimensional CFTs. In addition to conventional holography, we develop WBH/WCFT correspondence in the near-extremal regime. This allows us to make contact with the holography for generic near-extremal black holes. Near-extremal black holes are black holes which have a very small Hawking temperature. We define and study their holographic counterparts—near-extremal WCFTs. We find strong support for WBH/WCFT correspondence. A central result of the thesis is: only non-unitary WCFTs can admit non-trivial holographic duals and are thus, the only ones interesting in a holographic context., Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Warped conformal field theories (WCFTs) are two-dimensional non-relativistic systems, with a chiral scaling and shift symmetry. We present a detailed derivation of the nearextremal limit for their torus partition function. This limit requires large values of the central charge, and is only consistent for non-unitary WCFT. We compare our analysis with previous studies of WCFT and its relation to a one-dimensional warped-Schwarzian theory. We discuss different ensembles of warped CFTs and contrast our results with analogous limits in two-dimensional CFTs., SCOPUS: ar.j, info:eu-repo/semantics/published

Gravitational waves are ripples in spacetime predicted by Einstein's theory of general relativity. Their first direct observational evidence came with the detection of a gravitational wave signal by the two LIGO interferometers in 2015, marking a historic event in gravitational physics. Accurate theoretical waveform templates are needed to detect the signals and to extract the information carried by gravitational waves. The space-based LISA interferometer, expected to fly in the mid-2030s, will be able to observe gravitational waves from sources that lie outside the sensitivity band of ground-based detectors. An example are extreme-mass-ratio inspirals (EMRIs), binary systems composed of a stellar-mass compact object (the "secondary") and a supermassive black hole (the "primary"). EMRIs can be modelled using gravitational self-force theory: the small body is treated as a perturbation to the background spacetime of the primary. The motion is driven by a self-force, which arises from the interaction of the secondary with its own gravitational field. Although originally designed to describe EMRIs, the self-force formalism was found to be applicable also for binaries with intermediate mass ratios and nearly comparable masses. A few such systems have already been observed by the ground-based detectors of the LIGO-Virgo-KAGRA Collaboration, and current modelling techniques struggle to accurately describe them. In this thesis, motivated by the prospect of detecting gravitational waves from binaries with small mass ratios, we study the motion of a non-spinning secondary in the spacetime of a supermassive primary. We restrict our analysis to quasi-circular orbits lying in the equatorial plane. The dissipative effect of the self-force leads to the secular decay of the orbit and to the final merger of the binary. The orbital motion can be divided into three stages. As long as the two bodies are at large orbital separations, the quasi-circular inspiral is characterized by two d, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

La non-classicalité d'un état monomode de la lumière et l'intrication d'états photoniques bipartites sont des phénomènes quantiques centraux composant deux des différences les plus essentielles entre les domaines classique et quantique. Depuis leur découverte, ces propriétés ont suscité un intérêt considérable et constant de la part de la communauté des physiciens, dans le but de développer des protocoles basés sur ces phénomènes et qui n'ont pas d'équivalent classique. Pour prendre un seul exemple, l'intrication de deux photons peut être utilisée comme ressource pour effectuer de la cryptographie quantique, c'est-à-dire pour distribuer une clé secrète de manière sécurisée entre deux parties qui n'ont même pas besoin de faire confiance à leurs dispositifs quantiques. Afin d'exploiter ces propriétés et de développer des sources optiques d'états non-classiques ou intriqués, il est crucial de pouvoir détecter si l'état émis par la source est effectivement non-classique ou intriqué. Dans cette optique, de nombreux témoins (conditions suffisantes) de non-classicalité ou d'intrication ont été conçus au fil des années.Dans cette thèse, nous nous intéressons particulièrement à une hiérarchie de critères qui a été développée par Shchukin, Richter et Vogel au début des années 2000. Le témoin le plus courant de l'intrication est le critère PPT de "positive partial transpose", qui stipule que tout état séparable doit rester physique après avoir subi une transposition partielle. Si cette condition n'est pas remplie, cela signifie que l'état est intriqué. Sur cette base, un ensemble complet de critères a été exprimé par ces auteurs à partir d'une matrice de moments des opérateurs de mode (création et annihilation). De même, un ensemble de critères a été construit sur la base d'une matrice de moments dans l'ordre normal afin d'exprimer la non-négativité de la fonction P de Glauber, donnant lieu à une hiérarchie de témoins de non-classicalité.La principale difficulté dans la détect, The so-called nonclassicality of a single-mode state of light and the entanglement of bipartite photonic states are central quantum phenomena which underlie two of the most essential differences between the classical and the quantum. Since their discovery, these properties have attracted a tremendous, constant interest from the quantum physics community, with the goal of developing protocols that take advantage of them and have no classical counterpart. To take a single example, the entanglement of two photons can be used as a resource to perform quantum cryptography in a device-independent manner, that is, to distribute a secret key in a secure way between two parties who do not even need to trust their quantum devices. In order to exploit these properties and develop optical sources of nonclassical or entangled states, it is crucial to be able to detect whether the state emitted by the source is effectively nonclassical or entangled. Along this way, numerous witnesses (sufficient conditions) for nonclassicality or entanglement have been conceived over the years.In this thesis, we are especially interested in a hierarchy of criteria that has been developed by Shchukin, Richter, and Vogel in the early 2000s. The most common witness of entanglement is the PPT criterion for "positive partial transpose'', which states that any separable state must remain physical after undergoing a partial transpose. If this condition is not met, it means that the state is entangled. Based on this, a complete set of criteria was expressed by these authors based on a matrix of moments of the mode (creation and annihilation) operators. Similarly, a set of criteria was built based on a matrix of normally-ordered moments in order to express the non-negativity of the Glauber-Sudarshan P-function, giving rise to a hierarchy of nonclassicality witnesses.The main difficulty in the practical detection of nonclassicality or entanglement is the measurement of the quantities that are needed to app, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

We investigate the vacuum structure of the dyonic [SO(1, 1) × SO(6)] ⋉ R12 gaugedmaximal supergravity in four dimensions and find new families of AdS4 solutionswith residual N = 0, 1 or 2 supersymmetry, extending the known N = 4 solution.Using techniques from Exceptional Field Theory (ExFT), we uplift these solutions toType IIB supergravity on AdS4 × S1 × S5 .The resulting backgrounds are referredto as S-folds because they feature an S-duality monodromy induced by an hyperbolicelement of SL(2, Z) around the S1.S-folds are conjectured to be the holographic duals of new strongly coupled CFT3’sclosely related to localised interfaces in SYM4. In order to characterise the low-lyingoperator content and explore the possible existence of a conformal manifold of suchCFT3’s, we study the mass spectrum and moduli space of the S-fold solutions. Weprove that all S-folds with continuous residual symmetries admit exactly marginaldeformations breaking some, or all, of the residual (super)symmetries. These deformationsare generated in four dimensions by turning on axionic fields which we dub“flat deformations”.The Type IIB uplift of these deformations are classified in terms of mapping toriand shown to encode a geometric monodromy of the S5 over the S1. Focussing on theflat deformations of the original N = 4 S-fold, we establish the existence of a modulispace of non-supersymmetric, yet perturbatively stable, solutions. We also examinethe non-perturbative stability of the non-supersymmetric solutions and do not findany decay channel. These results challenge the non-SUSY AdS conjecture existing inthe literature.Next, we consider holographic RG-flows ending, in the IR, at the S-fold solutionsusing both numerical and semi-analytical techniques. We show that the S-folds arethe IR fixed points of anisotropic deformations of SYM4 placed on S1, in line withthe interface interpretation of their CFT duals. Moreover, we present an RG-flowconnecting the N = 1 solution in the UV to the N = 2 sol, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

We use holography and four-dimensional N = 4 gauged supergravity to collect evidence for a large class of interconnected three-dimensional N = 2 conformal field theories. On the gravity side, we construct a one-parameter family of ISO(3) × ISO(3) gaugings of half-maximal supergravity containing a rich structure of N = 2 AdS_4 solutions at fixed radius. By looking at excitations around these AdS_4 solutions, the spectrum of low lying operators in the dual N = 2 CFT_3’s is computed and further arranged into osp(2, info:eu-repo/semantics/published

This thesis aims to explore the properties of the motion of finite size, compact test bodies around a Kerr black hole in the small mass-ratio approximation. The small body is modelled as a perturbation of Kerr geometry, neglecting its gravitational back-reaction but including deviations from a purely geodesic motion by allowing it to possess a non-trivial internal structure. Such a body can be accurately described by a worldline endowed with a collection of multipole moments. Hereafter, we shall always consider the multipole expansion truncated at quadrupole order. Moreover, only spin-induced quadrupole moment will be taken into account, thus discarding the presence of any tidal-type deformation. For astrophysically realistic objects, this approximation is consistent with expanding the equations of motion up to second order in the body's spin magnitude.The text is structured as follows. The first part is devoted to an extended review of geodesic motion in Kerr spacetime, including Hamiltonian formulation and classification of timelike geodesics, with a particular emphasis put on near-horizon geodesics of high spin black holes. The second part introduces the equations of motion for extended test bodies in generic curved spacetime, also known as Mathisson-Papapetrou-Dixon (MPD) equations. They are derived from a generic action principle, and their physical significance and mathematical consistency is examined in details. The third part discusses conserved quantities for the MPD equations in Kerr spacetime, restricting to the aforementioned quadrupole approximation. The conservation is required to hold perturbatively in the test body's spin magnitude, and the related conserved quantities are build through the explicit resolution of the conservation constraint equations. Finally, the covariant Hamiltonian formulation of test body motion in curved spacetime is presented, and an Hamiltonian reproducing the spin-induced quadrupole MPD equations is derived. Two applications, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schrödinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic densities associated with the fundamentally conserved quantities and other slow modes possibly emerging from continuous symmetry breaking, as well as macrofields conjugated to these densities. Functional identities can be deduced, allowing us to identify the reversible and dissipative parts of the mean current densities, to obtain general equations for the time evolution of the conjugate macrofields, and to establish the relationship to projection-operator methods. The entropy production is shown to be nonnegative by applying the Peierls-Bogoliubov inequality to a quantum integral fluctuation theorem. Using the expansion in the gradients of the conjugate macrofields, the transport coefficients are given by Green-Kubo formulas and the entropy production rate can be expressed in terms of quantum Einstein-Helfand formulas, implying its nonnegativity in agreement with the second law of thermodynamics. The results apply to multicomponent fluids and can be extended to condensed matter phases with broken continuous symmetries., SCOPUS: ar.j, info:eu-repo/semantics/published

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A partially hinged, partially free rectangular plate is considered, with the aim of addressing the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal stretching active in the spanwise direction. The wind-flow in the chordwise direction is modeled through a piston-theoretic approximation, which provides both weak (frictional) dissipation and nonconservative forces. The long-time behavior of solutions is analyzed from various points of view. Compact global attractors, as well as fractal exponential attractors, are constructed using the recent quasi-stability theory. The nonconservative nature of the dynamics requires the direct construction of a uniformly absorbing ball, and this relies on the superlinearity of the stretching. For some parameter ranges, the nontriviality of the attractor is shown through the spectral analysis of the stationary linearized (non-self-adjoint) equation and the existence of multiple unimodal solutions is shown. Several stability results, obtained through energy estimates under various smallness conditions and/or assumptions on the equilibrium set, are also provided. Finally, the existence of a finite set of determining modes for the dynamics is demonstrated, justifying the usual modal truncation in engineering for the study of the qualitative behavior of suspension bridge dynamics., SCOPUS: ar.j, info:eu-repo/semantics/published

We provide the first holographic evidence for the existence of a nonsupersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter nonsupersymmetric deformation of a supersymmetric AdS nongeometric background in type IIB string theory. We prove that the nonsupersymmetric backgrounds are perturbatively stable and also do not suffer from various nonperturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections., SCOPUS: ar.j, info:eu-repo/semantics/published

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This thesis lies in the framework of the spontaneous symmetry breaking mechanism. When such a mechanism occurs, Goldstone's theorem predicts the existence of massless modes, called Nambu-Goldstone modes (NG modes). The current knowledge on NG modes is classified following the types of symmetries involved in the considered breaking pattern. Spacetime symmetries are the ones for which most of the analysis remains to be done. From a perturbative approach, we separately and concomitantly study the breaking of dilatation symmetry and of spatial translation symmetry. It allows us to comment on the present-day conjectures concerning the counting of NG modes associated to breaking patterns involving spacetime symmetries. Moreover, we get closer to standard laboratory conditions by investigating the situation in presence of a chemical potential. The considered Landau-Ginzburg's like models constitute plausible effective field theories to describe superfluids. The higher derivative terms required to spontaneously break translations lead to emergent subsystem symmetries. A connection between NG modes and fractonic modes, i.e. excitations with reduced mobility, is then made. Non-relativistic systems are less constrained by the symmetries compared to Lorentz invariant systems which make the former more general. Even for non-spacetime symmetries, some uncertainties on the physics of NG modes remain when dealing with non-relativistic models. One of them is the critical dimension of Minkowski spacetime under which no spontaneous symmetry breaking can occur. This dimension has been conjectured and we propose an explicit computation in order to attest this conjecture. However, through a holographic analysis, we discuss some way out for large N field theories. All along the dissertation, concrete future research perspectives on the above-mentioned discussions are provided., Cette thèse porte sur le mécanisme de la brisure spontanée de symétrie. Lorsqu’un tel mécanisme se produit, le théorème de Goldstone prédit l’existence de modes non-massifs, appelés modes de Nambu-Goldstone (modes NG). Nos connaissances actuelles sur les modes NG sont classifiées suivant le type de symétries impliquées dans le motif de brisure considéré. Les symétries d’espace-temps sont les symétries pour lesquelles la majorité de l’analyse reste encore à faire. A travers une approche perturbative, nous étudions séparément et de façon concomitante la brisure de la symétrie de dilatation et la brisure de la symétrie de translation spatiale. Cela nous permet de commenter les conjectures actuelles portant sur le comptage des modes NG associés au motif de brisure faisant intervenir des symétries d’espace-temps. De plus, nous nous rapprochons des conditions expérimentales en investiguant la situation en présence d’un potentiel chimique. Les modèles de type Landau-Ginzburg considérés constituent des théories effectives plausibles pour la description de superfluides. Les termes de dérivées supérieures nécessaires à la brisure des translations mènent à l’émergence de symétries de sous-systèmes. Un lien entre les modes NG et les modes fractoniques, c-à-d. des excitations à mobilité réduite, est alors établi.Les systèmes non-relativistes sont moins contraints par les symétries comparés aux systèmes invariants de Lorentz, ce qui rend les premiers plus généraux. Ainsi, même pour des symétries qui ne sont pas d’espace-temps, certaines incertitudes sur la physique des modes NG subsistent lorsque nous considérons des modèles non-relativistes. L’une d’entre elles est la dimension critique de l’espace-temps de Minkowski en-dessous de laquelle aucune brisure spontanée de symétrie ne peut se produire. Cette dimension a été conjecturée et nous proposons un calcul explicite en vue de valider cette conjecture. Cependant, à travers une analyse holographique, nous discutons d’une échappat, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

In recent years, the direct detection of gravitational waves and the appearance of the black hole picture directly proved the correctness of the general relativity in the strong field regime. The future mission of the ground-based and space-based observatories on the detection of potential signals from the intermediate mass-ratio coalescences and extreme mass ratio inspirals requires further development of the gravitational waveform models. Accurate modeling of their waveforms within general relativity can be achieved within black hole perturbation theory including self-force and finite size effects. The finite size effects, whose first effects are the spin effects, deviate the extended object away from its geodesic motion. The self force effects can also be seen as the perturbation of the timelike geodesics. Therefore, to develop these models, a deeper understanding about the geodesic motion is required as well.This thesis starts with the investigation of non-equatorial geodesic motion in Kerr spacetime. We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime, the ergoregion, and the near-horizon extreme Kerr, by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation, using a novel compact notation and by implementing the constraints from polar, time, and azimuthal motion. We derive the explicit phase space of all such root systems and classify whether each corresponding radial geodesic motion is allowed or disallowed from the existence of polar, time, and azimuthal motion. We explicitly parameterize the separatrix describing root systems with double roots as well.Furthermore, we investigate the spin and self force effects in near-horizon extreme Kerr. For simplicity, we discuss them separately. We present analytic results to the Teukolsky perturbation of equatorial orbits in the near horizon region of an extremely high spin black hole including spin coupling and finite size effects at leading order in t, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

L’entropie de Bekenstein d’un trou noir est donnée par son aire divisée par 4. Gibbons et Hawking ont retrouvé ce résultat en évaluant la fonction de partition d’un trou noir par la méthode euclidienne, c’est-à-dire en évaluant à l’extremum de l’exponentielle incluse dans l’intégrale de chemin euclidienne. Le but du projet pendant ma thèse était de s’attaquer plutôt à la fonction de partition sous forme de trace du facteur de Boltzmann, en espérant que ce calcul fasse automatiquement ressortir les degrés de liberté de la théorie qui donneraient lieu à l’entropie. Afin de procéder par petites étapes, on a étudié le calcul de la fonction de partition de l’électromagnétisme dans un condensateur. L’électromagnétisme et la gravitation sont en effet deux théories assez proches dans leur formulation, puisque ce sont des théories de jauge. D’autre part, un condensateur sphérique est proche d’un description géométrique simple d’un trou noir de Schwarzschild. L’avantage du condensateur électromagnétique est que c’est un sujet bien connu et maîtrisé, dont la fonction de partition est calculée dans le cadre de l’effet Casimir. Nous nous sommes concentrés dans le cas du condensateur plan dans un premier temps. Dans ce contexte, le champ électromagnétique peut être reformulé en terme de deux champs scalaires, grâce aux vecteurs de polarisation à nombre d’onde fixé. On retrouve donc les deux polarisations de l’espace infini, à la différence près que ces polarisations ont dans ce cas une condition aux bords (l’une est Dirichlet, l’autre est Neumann). En utilisant des tenseurs de polarisation adaptés, le champ gravitationnel linéarisé et la 2-forme peuvent aussi être reformulés en terme de champs scalaires. Ces équivalences avec des champs scalaires nous ont menés à étudier le calcul de fonctions de partition de champs scalaires, en prenant certaines de ces dimensions infiniment grandes et en gardant d’autres finies. Nous avons étudié les trois principales méthodes de calcul : la mé, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

The present thesis aims at providing a unified description of radiative phase spaces in General Relativity for any value of the cosmological constant using covariant phase space methods. We start by considering generic asymptotically locally (A)dS spacetimes with leaky boundary conditions in the Starobinsky/Fefferman-Graham gauge and in arbitrary dimensions. The boundary structure is allowed to fluctuate and plays the role of source yielding some flux of gravitational radiation at the boundary. The holographic renormalization procedure is employed to remove divergences from the presymplectic structure, which leads to finite surface charges for the whole class of boundary diffeomorphisms and Weyl rescalings. The charge algebra represents this asymptotic symmetry algebra under the Barnich-Troessaert bracket, up to a field-dependent 2-cocycle in odd spacetime dimensions. We then propose a boundary gauge fixing isolating the radiative components among the boundary degrees of freedom without constraining the Cauchy problem in asymptotically de Sitter spacetimes. This additional gauge fixing reduces the set of allowed boundary diffeomorphisms to the infinite-dimensional $\Lambda$-BMS algebroid, which is the counterpart to the Generalized BMS algebra of smooth supertranslations and super-Lorentz transformations in the flat limit. In a second round, the analysis is repeated in the Bondi gauge, which is better suited to discuss radiative phenomena as well as construct a flat limit process at the level of the solution space. Thanks to a diffeomorphism we translate the results previously obtained in the Starobinsky/Fefferman-Graham coordinates and identify the analogues of the Bondi news, mass and angular momentum aspects in the presence of a non-vanishing cosmological constant. We give a prescription to perform the flat limit at the level of the phase space and demonstrate how to use this connection to renormalize the corresponding phase space of asymptotically locally flat s, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

We write the field equations of torsion gravity theories and the Noether identity they obey directly in terms of metric and contorsion tensor components expressed with respect to natural coordinates, i.e. without using vierbien but Lagrange multipliers. Then we obtain explicit solutions of these equations, under specific ansätze for the contorsion field, by assuming the metric to be respectively of the Bertotti-Robinson, pp-wave, Friedmann-Lemaître-Robertson-Walker or static spherically symmetric type. Among these various solutions we obtain some of them have their contorsion tensor depending on arbitrary functions that did not influence their geometry. This raises questions about the predictability of the theory., SCOPUS: ar.j, info:eu-repo/semantics/published

Type IIB S-folds of the form AdS4 × S1 × S5 are conjectured to correspond to new strongly coupled three-dimensional CFT’s on a localised interface of SYM4. In this work we construct holographic RG flows on the D3-brane that generically connect anisotropic deformations of SYM4 in the UV to various S-fold CFT’s in the IR with different amounts of supersymmetry and flavour symmetries. Examples of holographic RG flows between S-fold CFT’s are also presented. Lastly a geometric interpretation of axion deformations is provided in terms of monodromies on the internal S5 when moving around the S1. Special attention is paid to the monodromy-induced patterns of symmetry breaking as classified by the mapping torus Th(S5)., SCOPUS: ar.j, info:eu-repo/semantics/published

Type IIB S-folds of the form AdS4× S1× S5 have been shown to contain axion-like deformations parameterising flat directions in the 4D scalar potential and corresponding to marginal deformations of the dual S-fold CFT’s. In this note we present a group-theoretical characterisation of such flat deformations and provide a 5D interpretation thereof in terms of s(6) -valued duality twists inducing a class of Cremmer-Scherk-Schwarz flat gaugings in a reduction from 5D to 4D. In this manner we establish the existence of two flat deformations for the N = 4 and SO(4) symmetric S-fold causing a symmetry breaking down to its U(1)2 Cartan subgroup. The result is a new two-parameter family of non-supersymmetric S-folds which are perturbatively stable at the lower-dimensional supergravity level, thus providing the first examples of such type IIB backgrounds., SCOPUS: ar.j, info:eu-repo/semantics/published

Motivated by the long-time transport properties of quantum waves in weakly disordered media, the present work puts random Schrödinger operators into a new spectral perspective. Based on a stationary random version of a Floquet type fibration, we reduce the description of the quantum dynamics to a fibered family of abstract spectral perturbation problems on the underlying probability space. We state a natural resonance conjecture for these fibered operators: in contrast with periodic and quasiperiodic settings, this would entail that Bloch waves do not exist as extended states but rather as resonant modes, and this would justify the expected exponential decay of time correlations. Although this resonance conjecture remains open, we develop new tools for spectral analysis on the probability space, and in particular, we show how ideas from Malliavin calculus lead to rigorous Mourre type results: we obtain an approximate dynamical resonance result and the first spectral proof of the decay of time correlations on the kinetic timescale. This spectral approach suggests a whole new way of circumventing perturbative expansions and renormalization techniques., SCOPUS: ar.j, info:eu-repo/semantics/published

This note is concerned with the global well-posedness of nonlinear Schrödinger equations in the continuum with spatially homogeneous random initial data., SCOPUS: ar.j, info:eu-repo/semantics/published

We consider the distribution of secret keys, both in a bipartite and a multipartite (conference) setting, via a quantum network and establish a framework to obtain bounds on the achievable rates. We show that any multipartite private state - the output of a protocol distilling secret key among the trusted parties - has to be genuinely multipartite entangled. In order to describe general network settings, we introduce a multiplex quantum channel, which links an arbitrary number of parties where each party can take the role of sender only, receiver only, or both sender and receiver. We define asymptotic and nonasymptotic local quantum operations and classical communication-assisted secret-key-agreement (SKA) capacities for multiplex quantum channels and provide strong and weak converse bounds. The structure of the protocols we consider, manifested by an adaptive strategy of secret-key and entanglement [Greenberger-Horne-Zeilinger (GHZ) state] distillation over an arbitrary multiplex quantum channel, is generic. As a result, our approach also allows us to study the performance of quantum key repeaters and measurement-device-independent quantum key distribution (MDI-QKD) setups. For teleportation-covariant multiplex quantum channels, we get upper bounds on the SKA capacities in terms of the entanglement measures of their Choi states. We also obtain bounds on the rates at which secret key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. We are able to determine the capacities for MDI-QKD setups and rates of GHZ-state distillation for some cases of interest., SCOPUS: ar.j, info:eu-repo/semantics/published

This thesis is centered on a novel approach to quantum uncertainty based on applying the theory of continuous majorization to quantum phase-space distributions. Majorization theory is a powerful mathematical framework that is aimed at comparing distributions with respect to intrinsic disorder. It is particularly significant in the sense that establishing a majorization relation between two distributions amounts to proving that every (Shur-concave) measure of disorder will categorize one distribution as more ordered than the other. Although this is less known, the distributions here do not need to be normalized nor positive for majorization theory to apply, so the latter even extends beyond probability distributions. Further, a majorization relation can rigorously be defined for both discrete and continuous distributions over a finite-size domain, as well as for (discrete and continuous) distributions that are positive over an infinite-size domain.The central thrust of this thesis is to characterize quantum uncertainty in phase space by applying the tools of majorization theory to the Wigner function, which is the most common (quasi)distribution that embodies a quantum state in phase space. Wigner functions are in general positive and negative, putting them beyond the reach of most information-theoretical measures but perfect candidates for the theory of majorization. We start our manuscript with a succinct overview of the basics of quantum optics in phase space, which are a prerequisite for the characterization of disorder in phase space. This gives us the occasion to present a secondary achievement of the thesis consisting in establishing a resource theory for local Gaussian work extraction, which exploits the symplectic formalism within quantum thermodynamics. In this context, work can be defined as the difference between the trace and symplectic trace of the covariance matrix of the state, and it displays a number of interesting properties. Back to our primary in, Cette thèse est centrée sur une nouvelle approche de l'incertitude quantique basée sur l'application de la théorie de la majorisation continue aux distributions de l'espace des phases quantique. La théorie de la majorisation est un cadre mathématique puissant qui vise à comparer des distributions par rapport à leur désordre intrinsèque. Elle est particulièrement importante dans le sens où établir une relation de majorisation entre deux distributions revient à prouver que toute mesure (Shur-concave) du désordre classera une distribution comme plus ordonnée que l'autre. Bien que cela soit moins connu, les distributions ici n'ont pas besoin d'être normalisées ni positives pour que la théorie de la majorisation s'applique, de sorte que cette dernière s'étend même au-delà des distributions de probabilité. De plus, une relation de majorisation peut être rigoureusement définie pour les distributions discrètes et continues sur un domaine de taille finie, ainsi que pour les distributions (discrètes et continues) qui sont positives sur un domaine de taille infinie. L'idée maîtresse de cette thèse est de caractériser l'incertitude quantique dans l'espace des phases en appliquant les outils de la théorie de la majorisation à la fonction de Wigner, qui est la (quasi-)distribution la plus commune qui incarne un état quantique dans l'espace des phases. Les fonctions de Wigner sont en général positives et négatives, ce qui les place hors de portée de la plupart des mesures de la théorie de l'information mais en fait des candidats parfaits pour la théorie de la majorisation. Nous commençons notre manuscrit par un aperçu succinct des bases de l'optique quantique dans l'espace de phase, qui sont une condition préalable à la caractérisation du désordre dans l'espace des phases. Cela nous donne l'occasion de présenter une réalisation secondaire de la thèse consistant à établir une théorie des ressources pour l'extraction du travail gaussien local, qui exploite le formalisme symplectique, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality of this sort is whether or not the predictions of a given operational theory can be explained by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-measure scenarios. We first show that, when mapping an operational theory to a GPT by quotienting relative to operational equivalences, the constraint of explainability by a generalized-noncontextual ontological model is mapped to the constraint of explainability by an ontological model. We then show that, under the additional assumption that the ontic state space is of finite cardinality, this constraint on the GPT can be expressed as a geometric condition which we term simplex embeddability. Whereas the traditional notion of classicality for a GPT is that its state space be a simplex and its effect space be the dual of this simplex, simplex embeddability merely requires that its state space be embeddable in a simplex and its effect space in the dual of that simplex. We argue that simplex embeddability constitutes an intuitive and freestanding notion of classicality for GPTs. Our result also has applications to witnessing nonclassicality in prepare-measure experiments., SCOPUS: ar.j, info:eu-repo/semantics/published

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Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum circuits, also called quantum combs. A systematic understanding of the physical interpretation of more general types of quantum supermaps - in particular, those incompatible with a definite causal structure - is however lacking. In this paper, we identify two types of circuits that naturally generalize the fixed-order case and that likewise correspond to distinct classes of quantum supermaps, which we fully characterize. We first introduce "quantum circuits with classical control of causal order,"in which the order of operations is still well defined, but not necessarily fixed in advance: it can, in particular, be established dynamically, in a classically controlled manner, as the circuit is being used. We then consider "quantum circuits with quantum control of causal order,"in which the order of operations is controlled coherently. The supermaps described by these classes of circuits are physically realizable, and the latter encompasses all known examples of physically realizable processes with indefinite causal order, including the celebrated "quantum switch."Interestingly, it also contains other examples arising from the combination of dynamical and coherent control of causal order, and we detail explicitly one such process. Nevertheless, we show that quantum circuits with quantum control of causal order can only generate "causal"correlations, compatible with a well-defined causal order. We furthermore extend our considerations to probabilistic circuits that produce also classical outcomes, and we demonstrate by an example how the characterizations derived in this work allow us to identify advantages for quantum information processing tasks that could be demonstrated in practice., SCOPUS: ar.j, info:eu-repo/semantics/published

In this paper, we introduce the resource theory of unextendibility as a relaxation of the resource theory of entanglement. The free states in this resource theory are the -extendible states, associated with the inability to extend quantum entanglement in a given quantum state to multiple parties. The free channels are -extendible channels, which preserve the class of -extendible states. We define several quantifiers of unextendibility by means of generalized divergences and establish their properties. By utilizing this resource theory, we obtain nonasymptotic upper bounds on the rate at which quantum communication or entanglement preservation is possible over a finite number of uses of an arbitrary quantum channel assisted by -extendible channels at no cost. These bounds are significantly tighter than previously known bounds for both the depolarizing and erasure channels. Finally, we revisit the pretty strong converse for the quantum capacity of antidegradable channels and establish an upper bound on the nonasymptotic quantum capacity of these channels., SCOPUS: ar.j, info:eu-repo/semantics/published

This thesis is devoted to the study of orientifolds and dynamical supersymmetry breaking in configurations of D-branes on toric Calabi-Yau singularities, through the lens of dimer models. We first review the basic ingredients of string theory that led to the formulation of gauge/gravity dualities in terms of dimers. Then, we discuss the non-abelian anomaly cancellation conditions for the supersymmetric gauge theories arising on D-branes and provide necessary geometric criteria to determine whether an orientifold projection can be safely introduced. We also find a new realization of orientifold projection without fixed loci in dimer models and expand on its physical features. We argue that it exhausts the possibilities of orientifolding dimer models. In the subsequent part of the thesis, we investigate dynamical supersymmetry breaking vacua in the same class of models and their typical instability along N=2 Coulomb branches. This leads us to formulate a no-go theorem against their stability based on geometrical features of the singularity, and then to establish a precise way to circumvent it. We eventually find the first instance of stable dynamical supersymmetry breaking vacuum in string theory from D-branes on a toric Calabi-Yau singularity, the Octagon., Doctorat en Sciences, info:eu-repo/semantics/nonPublished