Dans une série de travaux Zied Ammari et Francis Nier ont développé des méthodes pour étudier la dynamique de champ moyen bosonique pour des états quantiques généraux pouvant présenter des corrélations. Ils ont obtenu des formules pour décrire la dynamique des corrélations, ou plus généralement des matrices densité réduites d'ordre arbitraire. Cette thématique a été largement développée ces dernières années. Norbert Mauser en a été un des contributeurs, ainsi que sur la notion de mesure de Wigner qui est la clé de l'analyse développée par Z. Ammari et F. Nier. En général, il est admis que l'asymptotique de champ moyen est une bonne approximation du problème à N particules quand N dépasse la dizaine. Cela concerne l'asymptotique de la matrice densité réduite à une particule qui ne décrit pas la dynamique des corrélations. Un objectif est de tester la validité de la dynamique de champ moyen pour les matrices densité réduites à 2-particules. Pour des tests numériques, les modèles discrets qui n'ont pas été vraiment traités en détail dans les travaux précédents de Z. Ammari et F. Nier semblent bien adaptés. La thèse comprendra donc plusieurs étapes: adapter les résultats précédents de Z. Ammari et F. Nier à des modèles discrets , développer des méthodes numériques pour des systèmes simples mais pertinents, permettant de valider l'approximation de champ moyen et les formules pour la dynamique des corrélations. Au niveau numérique, on utilise des schémas numériques symplectiques, développés spécifiquement ces dernières années pour la discrétisation des équations hamiltoniennes. Une dernière étape concerne la combinaison des deux asymptotiques, champ moyen et approximation des modèles continus par les modèles discrets. / In a serie of works Z. Ammari and F. Nier developed methods to study the dynamics of bosonic mean field for general quantum states which can present correlations. They obtained formulas to describe the dynamics of the correlations, or more generally reduced density matrices with an arbitrary order. This topic was widely developed these last years. N.J. Mauser was one of contributors, as well as on the notion of Wigner measure which is the key of the analysis developed by Z. Ammari and F. Nier. Generally, the mean field asymptotic is admitted is a good approximation of the N-body problem when N exceed about ten. It concerns the asymptotics of the reduced density matrices for one particle which does not describe the dynamics of the correlations. An objective is to test the validity of the mean field dynamics for reduced density matrices for 2 particles. For numerical tests, the discrete models which were not really handled in detail in the previous works of Z. Ammari and F. Nier seem adapted well. The thesis will thus include several steps: adapt the previous results from Z. Ammari and F. Nier to discrete models , develop numerical methods, for simple but relevant systems, allowing to validate the approximation of mean field and the formulas for the dynamics of the correlations. About numerics, symplectic numerical scheme are used, developed specifically these last years for the discretization of the hamiltonian equations. A last possible step concerns the combination of both asymptotics, that is mean field and approximation of the continuous models by the discrete models.

No description available.

Quantum many-body phenomena have been a focal point of the physics community for the last several decades. From material science and chemistry to model systems and quantum computing, diverse problems share mathematical description and challenges. A key roadblock in many subfields is the exponential increase in problem size with increasing number of quantum constituents. Therefore, development of efficient compression and approximation methods is the only way to move forward. Parameterized models coming from the field of machine learning have successfully been applied to very large classical problems where data is abundant, leveraging recent advances in high-performance computing. In this thesis, state-of-the-art methods relying on such models are applied to the quantum many-body problem in two distinct ways: from first principles and data-driven, as described in chapter 1. In chapters 2 and 3, the framework of quantum Monte Carlo is used to efficiently manipulate variational approximations of many-body states, obtaining non-equilibrium states occurring in quantum circuits and real-time dynamics of large systems. In chapters 4 and 5, simulated synthetic data is used to train surrogate models that enhance original methods, allowing for computations that would otherwise be out of reach for conventional solvers. In all cases, a computational advantage is established when using machine learning methods to compress different versions of the quantum many-body problem. Each chapter is concluded by proposing extensions and novel applications of new compressed representation of the problem.

Au cours des dernières années, le domaine de l'interaction lumière-matière a fait un pas de plus en avant avec l'avènement des qubits supraconducteurs couplés ultra-fortement à des guides d'ondes ouverts. Dans ce contexte, un qubit devient simultanément couplé à de nombreux modes du guide d'onde, se transformant ainsi en un objet hybride lumière-matière hautement intriqué. L'étude de nouveaux phénomènes dynamiques qui émergent de la grande complexité de ces systèmes quantiques à N-corps est l'objectif principal de cette thèse.Dans une première étape cruciale, nous abordons l'évolution dans le temps d'un tel système en utilisant une nouvelle technique numérique basée sur un développement complet du vecteur d'état en termes d'états cohérents multimodes. Inspirée par des approches semi-classiques antérieures, cette technique numériquement exacte fournit un progrès important par rapport aux méthodes de pointe qui ont été utilisées jusqu'à présent pour étudier le régime de couplage ultra-fort à N-corps. Fondamentalement, cette approche préserve également le détail de la dynamique du système complet réunissant le guide d'onde et le qubit, permettant à la fois d'effectuer la tomographie et d'extraire la diffusion multi-particule des degrés de liberté du guide d'onde.Une exploration du régime de couplage ultra-fort multi-mode utilisant cette nouvelle technique a conduit aux deux prédictions théoriques fondamentales de cette thèse. La première démontre que le rayonnement émis spontanément par un qubit excité prend la forme d'un chat de Schrödinger de lumière, un résultat étonnamment différent de l'émission de photon unique habituelle en optique quantique. La seconde prédiction concerne la diffusion de signaux cohérents de faible puissance sur un qubit, un protocole expérimental très courant en laboratoire. De façon remarquable, il est montré que la non-linéarité du qubit, transférée au guide d'onde par l'interaction ultra-forte avec la lumière, est capable de diviser les photons du faisceau entrant en plusieurs photons de plus basse énergie, conduisant à l'émergence d'un continuum basse fréquence dans le spectre de puissance, qui domine le signal hors-résonant. En étudiant la fonction de corrélation de second ordre dans le champ rayonné, il est également démontré que l'émission en couplage ultra-fort présente des signatures caractéristiques de la production de particules.Dans la dernière partie de la thèse, la fonction de corrélation de second ordre est à nouveau étudiée, mais cette fois expérimentalement, et dans le régime du couplage modéré. Bien que les mesures soient encore préliminaires, cette partie de la thèse présente un compte-rendu instructif de la théorie de la mesure du signal et permet de comprendre en détail la procédure expérimentale impliquée dans la mesure des signaux quantiques. De plus, à l'avenir, les développements expérimentaux et les outils de simulation décrits pourraient être appliqués aux signaux émis par des qubits ultra-fortement couplés, afin d'observer les signatures de production de particules révélées par la fonction de corrélation du second ordre. / In the recent years, the field of light-matter interaction has made a further stride forward with the advent of superconducting qubits ultra-strongly coupled to open waveguides. In this setting, the qubit becomes simultaneously coupled to many different modes of the waveguide, thus turning into a highly intricate light-matter object. Investigating the wealth of new dynamical phenomena that emerge from the high complexity of these engineered quantum many-body systems is the main objective of this thesis.As a first crucial step, we tackle the time-evolution of such a non-trivial system using a novel numerical technique based on an expansion of the full state vector in terms of multi-mode coherent states. Inspired by earlier semi-classical approaches, this numerically exact method provides an important advance compared to the state-of-the-art techniques that have been used so far to study the many-mode ultra-strong coupling regime. Crucially, it also keeps track of every detail of the dynamics of the complete qubit-waveguide system, allowing both to perform the tomography and to extract multi-particle scattering of the waveguide degrees of freedom.An exploration of the many-mode ultra-strong coupling regime using this new technique led to the two core theoretical predictions of this thesis. The first demonstrates that the radiation spontaneously emitted by an excited qubit takes the form of a Schrödinger cat state of light, a result strikingly different from the usual single-photon emission known from standard quantum optics. The second prediction concerns the scattering of low-power coherent signals on a qubit, a very common experimental protocol performed routinely in laboratories. Most remarkably, it is shown that the qubit non-linearity, transferred to the waveguide through the ultra-strong light-matter interaction, is able to split photons from the incoming beam into several lower-energy photons, leading to the emergence of a low-frequency continuum in the scattered power spectrum that dominates the inelastic signal. By studying the second-order correlation function of the radiated field, it is also shown that emission at ultra-strong coupling displays characteristic signatures of particle production.In the final part of the thesis, the second-order correlation function is investigated again, but this time experimentally, and in the regime of moderate coupling. Although the results are still preliminary, this part of the thesis will provide an instructive account of signal measurement theory and will allow to understanding in-depth the experimental procedure involved in measuring quantum microwave signals. Moreover, the experimental developments and microwave simulations tools described in this section could be applied in the future to signals emitted by ultra-strongly coupled qubits, in order to observe the signatures of particle production revealed by the second-order correlation function.

Ce travail de thèse s'inscrit dans le cadre du développement de la méthode de mélange de configurations multiparticules-multitrous visant à décrire les propriétés de structure des noyaux atomiques. Basée sur un double principe variationnel, cette approche permet de déterminer simultanément les coefficients d'expansion de la fonction d'onde et les orbitales individuelles.Dans ce manuscrit, le formalisme complet méthode de mélange de configurations multiparticules-multitrous auto-cohérente est pour la première fois appliqué à la description de quelques noyaux des couches p et sd, avec l'interaction de Gogny D1S.Un première étude du 12C est effectuée afin de tester et comparer le double processus de convergence lorsque différents types de critères sont appliqués pour sélectionner les configurations à N-corps inclues dans la fonction d'onde du noyau. Une analyse détaillée de l'effet induit par l'optimisation des orbitales est conduite. En particulier, son impact sur la densité à un corps et sur la fragmentation de la fonction d'onde de l'état fondamental, est analysé.Une étude systématique de noyaux de la couche sd est ensuite conduite. Une analyse précise du contenu en corrélation de l'état fondamental est effectuée, et quelques quantités observables telles que les énergies de liaison et de séparation, ainsi que les rayons de charge, sont calculées et comparées à l'expérience. Les résultats obtenus sont satisfaisants. La spectroscopie de basse énergie est ensuite étudiée. Les énergies d'excitation théoriques sont en très bon accord avec les données expérimentales, et les caractéristiques dipolaires magnétiques sont également satisfaisantes. Les propriétés quadripolaires électriques, et en particulier les probabilités de transition B(E2), sont par contre largement sous-estimée par rapport aux valeurs expérimentales, et révèle un manque important de collectivité dans la fonction d'onde, dû à l'espace de valence restreint considéré. Si la renormalisation des orbitales induit une importante fragmentation de la fonction d'onde de l'état fondamental, seul un effet très faible est obtenu sur les probabilités de transition B(E2). Une tentative d'explication est donnée.Enfin, les informations de structure fournies par la méthode de mélange de configurations multiparticules-multitrous sont utilisées comme ingrédient de base pour des calculs de réactions telles que la diffusion inélastique de protons et d'électrons sur noyaux de la couche sd. Si les résultats révèlent aussi un manque de collectivité, les tendances expérimentales sont bien reproduites et sont améliorées par l'optimisation des orbitales. / This thesis project takes part in the development of the multiparticle-multihole configuration mixing method aiming to describe the structure of atomic nuclei. Based on a double variational principle, this approach allows to determine the expansion coefficients of the wave function and the single-particle states at the same time. In this work we apply for the first time the fully self-consistent formalism of the mp-mh method to the description of a few p- and sd-shell nuclei, using the D1S Gogny interaction.A first study of the 12C nucleus is performed in order to test the doubly iterative convergence procedure when different types of truncation criteria are applied to select the many-body configurations included in the wave-function. A detailed analysis of the effect caused by the orbital optimization is conducted. In particular, its impact on the one-body density and on the fragmentation of the ground state wave function is analyzed.A systematic study of sd-shell nuclei is then performed. A careful analysis of the correlation content of the ground state is first conducted and observables quantities such as binding and separation energies, as well as charge radii are calculated and compared to experimental data. Satisfactory results are found. Spectroscopic properties are also studied. Excitation energies of low-lying states are found in very good agreement with experiment, and the study of magnetic dipole features are also satisfactory. Calculation of electric quadrupole properties, and in particular transition probabilities B(E2), however reveal a clear lack of collectivity of the wave function, due to the reduced valence space used to select the many-body configurations. Although the renormalization of orbitals leads to an important fragmentation of the ground state wave function, only little effect is observed on B(E2) probabilities. A tentative explanation is given.Finally, the structure description of nuclei provided by the multiparticle-multihole configuration mixing method is utilized to study reaction mechanisms such as electron and proton inelastic scattering on sd-shell nuclei. Although the results also suffer from the lack of collectivity, the experimental trends are well reproduced and improved by the orbital optimization.

Mean-field approaches successfully reproduce nuclear bulk properties like masses and radii within the Energy Density Functional (EDF) framework. However, complex correlations are missing in mean-field models and several observables related to single-particle and collective nuclear properties cannot be predicted accurately. The necessity to provide a precise description of the available data as well as reliable predictions in the exotic regions of the nuclear chart motivates the use of more sophisticated beyond-mean-field models. Correlations and higher-order corrections (beyond the leading mean-field order) are introduced. A crucial aspect in these calculations is the choice of the effective interaction to be used when one goes beyond the leading order (available effective interactions are commonly adjusted at the mean-field level). In the first part, we deal with the equation of state of nuclear matter evaluated up to the second order with the phenomenological Skyrme force. We analyze the ultraviolet divergence that is related to the zero range of the interaction and we introduce Skyrme-type regularized interactions that can be used at second order for matter. Cutoff regularization and dimen- sional regularization techniques are explored and applied. In the latter case, connections are naturally established between the EDF framework and some techniques employed in Effective Field Theories. In the second part, we check whether the regularized interactions introduced for nuclear matter can be employed also for finite nuclei. As an illustration, this analysis is performed within the particle- vibration model that represents an example of beyond mean-field models where an ultraviolet divergence appears if zero-range forces are used. These first applications suggest several directions to be explored to finally provide regularized interactions that are specially tailored for beyond- mean-field calculations for finite nuclei. Conclusions and perspectives are finally illustrated.

Orientadores: Aurea Rosas Vasconcellos, Roberto Luzzi / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-06T02:30:23Z (GMT). No. of bitstreams: 1 AndradeNeto_AntonioVieirade_D.pdf: 580703 bytes, checksum: 8cd331112c8a9047f3815f8b9238e984 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho realizamos um estudo pormenorizado das propriedades ópticas de semicondutores polares de gap direto dopado tipo n.Em particular nos concentramos nos efeitos de muitos corpos (interação coulombiana)e na in .uência da interação elétron fônon LO (potencial de Fröhlich)sobre as propriedades ópticas do sistema. Para tanto,inicialmente,calculamos a função dielétrica longitudinal do sistema recorrendo ao elegante,prático e poderoso método das Funções de Green Termodinâmicas de Tempo Duplo. Obtivemos expressões analíticas para as partes real e imaginária da função dielétrica onde estão incorporados efeitos dinâmicos. Foi evidenciado o inter-relacionamento entre os efeitos coletivos ¿gerados pela interação coulombiana ¿e a interação polar.Isto se manifesta claramente nas expressões obtidas para a renormalização das energias de excitação bem como nas funções de relaxação dinâmicas associadas com os efeitos dissipativos no sistema.Tais características se mostram fundamentais para que os resultados numéricos,obtidos a partir da teoria,quando comparados com as curvas experimentais forneçam um muito bom acordo em posição e forma das bandas de espalhamento Raman por modos híbridos de plasmons-fônons LO e o espectros de re .etividade do GaN, inclusive é evidenciada e interpretada,uma banda anômala observada experimentalmente / Abstract: A detailed analysis of the in fluence of the polar and Coulomb interactions, and brief comments on impurities,on the optical properties of III-Nitrides is presented.Raman scattering by coupled plasmon-LO phonon modes is considered in particular.Numerical calculations are done in the case of n-doped GaN obtaining excellent agreement with the experimental data and,in the process,the explanation of certain observed so-called anomalies is done.A brief study of re .ectivity spectra is also included / Doutorado / Física da Matéria Condensada / Doutor em Ciências

As a degree project in Theoretical Physics, the variational MCMC-scheme aided by neural network quantum states was examined for the purpose ofsolving the nuclear pairing model. The method entailed minimization of the local energy sampled via the Born distribution obtained through the neural network output.Both the ground and excited states' energies were computed, where the latter case used an extended loss function which included the overlap to the former.The NNQS-ansatz worked well when emulating the ground state, in which case the Stochastic Reconfiguration optimization method was particularly effective. This optimization method resulted in relative fast convergence to low variance states, and did not require a large number of hyperparameter modifications. Ultimately, all resulting energy intervals encompassed the exact ground state solutions, and had relative errors equal to or near zero.For the excited states, the VMC-NNQS was less effective, as each individual occupation number state investigated required considerable hyperparameter testing before reasonably low lying energy eigenstates could be obtained. Moreover, the convergence properties were less distinguished than for the ground state, as the optimization struggled to maintain orthogonality to the ground state. Nonetheless, the final results included the nearest solutions of the first excited states for several systems and indicated correlation energies similar to those of the ground state. / Som examensarbete inom teoretisk fysik undersöktes den variationella MCMC-metoden tillsammans med neurala nätverk i syfte att lösa kärnparsmodellen. Metoden innebar minimering av den lokala energin som samplades via Born-fördelningen erhållen genom utdata från neurala nätverksapproximationer. Både grundtillståndets och exciterade tillstånds energier beräknades, där det senare fallet använde en utökad kostnadsfunktion som inkluderade överlappet med det förnämnda. NNQS-ansatsen fungerade väl vid emulering av grundtillståndet, i vilket fall optimeringsmethoden stokastisk omkonfigurering (Stochastic Reconfiguration) var särskilt effektivt. Denna optimeringsmetod resulterade i relativt snabb konvergens till lågvarianstillstånd och krävde inte ett stort antal hyperparametriska modifieringar. De slutliga energiintervallen innefattade de exakta lösningarna för grundtillstånden med en relativ felmarginal lika med eller nära noll. För exciterade tillstånd var VMC-NNQS mindre effektivt, eftersom varje enskilt ockupationstillstånd som undersöktes krävde en ansenlig mängd hyperparametrisk testning innan rimligt låga egentillstånd kunde erhållas. Dessutom var konvergensensegenskaperna mycket mindre särspäglade än för grundtillståndet, eftersom optimeringen inte fullt kunde upprätthålla ortogonaliteten mot grundtillståndet. Likväl inkluderade de slutliga resultaten de närmaste lösningarna av de första exciterade energierna för ett flertal system, och visade på korrelationsenergier liknande de för grundtillståndet.

In the wake of the Big Data phenomenon, the computing world has seen a number of computational paradigms developed in response to the sudden need to process ever-increasing volumes of data. Most notably, MapReduce has proven quite successful in scaling out an extensible class of simple algorithms to even hundreds of thousands of nodes. However, there are some tasks---even embarrassingly parallelizable ones---that neither MapReduce nor any existing automated parallelization framework is well-equipped to perform. For instance, any computation that (naively) requires consideration of all pairs of inputs becomes prohibitively expensive even when parallelized over a large number of worker nodes. Many of the most desirable methods in machine learning and statistics exhibit these kinds of all-pairs or, more generally, all-tuples computations; accordingly, their application in the Big Data setting may seem beyond hope. However, a new algorithmic strategy inspired by breakthroughs in computational physics has shown great promise for a wide class of computations dubbed generalized N-body problems (GNBPs). This strategy, which involves the simultaneous traversal of multiple space-partitioning trees, has been applied to a succession of well-known learning methods, accelerating each asymptotically and by orders of magnitude. Examples of these include all-k-nearest-neighbors search, k-nearest-neighbors classification, k-means clustering, EM for mixtures of Gaussians, kernel density estimation, kernel discriminant analysis, kernel machines, particle filters, the n-point correlation, and many others. For each of these problems, no overall faster algorithms are known. Further, these dual- and multi-tree algorithms compute either exact results or approximations to within specified error bounds, a rarity amongst fast methods. This dissertation aims to unify a family of GNBPs under a common framework in order to ease implementation and future study. We start by formalizing the problem class and then describe a general algorithm, the generalized fast multipole method (GFMM), capable of solving all problems that fit the class, though with varying degrees of speedup. We then show O(N) and O(log N) theoretical run-time bounds that may be obtained under certain conditions. As a corollary, we derive the tightest known general-dimensional run-time bounds for exact all-nearest-neighbors and several approximated kernel summations. Next, we implement a number of these algorithms in a commercial database, empirically demonstrating dramatic asymptotic speedup over their conventional SQL implementations. Lastly, we implement a fast, parallelized algorithm for kernel discriminant analysis and apply it to a large dataset (40 million points in 4D) from the Sloan Digital Sky Survey, identifying approximately one million quasars with high accuracy. This exceeds the previous largest catalog of quasars in size by a factor of ten and has since been used in a follow-up study to confirm the existence of dark energy.

On considère généralement que la fonction d’onde macroscopique décrivant un condensat de paires de fermions possède une phase parfaitement définie et immuable. En réalité, il n’existe que des systèmes de taille finie, préparés à température non nulle ; le condensat possède alors un temps de cohérence fini, même lorsque le système est isolé. Cet effet fondamental, crucial pour les applications qui exploitent la cohérence macroscopique, restait très peu étudié.Dans cette thèse, nous relions le temps de cohérence à la dynamique de phase du condensat, et nous montrons par une approche microscopique que la dérivée temporelle de l’opérateur phase ˆθ0 est proportionnelle à un opérateur potentiel chimique qui inclut les deux branches d’excitations du gaz : celle, fermionique, de brisure des paires et celle, bosonique, de mise en mouvement de leur centre de masse. Pour une réalisation donnée de l’énergie E et du nombre de particules N, la phase évolue aux temps longs comme −2μmc(E,N)t/~ où μmc(E,N) est le potentiel chimique microcanonique ; les fluctuations de E et de N d’une réalisation à l’autre conduisent alors à un brouillage balistique de la phase, et à une décroissance gaussienne de la fonction de cohérence temporelle avec un temps caractéristique ∝ N1/2. En l’absence de telles fluctuations, la décroissance est au contraire exponentielle avec un temps de cohérence qui diverge linéairement en N à cause du mouvement diffusif de ˆθ0 dans l’environnement des modes excités. Nous donnons une expression explicite de ce temps caractéristique à bassetempérature dans le cas d’une branche d’excitation bosonique convexe lorsque les phonons interagissent via les processus 2 ↔ 1 de Beliaev-Landau. Enfin, nous proposons des méthodes permettant de mesurer avec un gaz d’atomes froids chaque contribution au temps de cohérence / It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature ; the condensate has then a finite coherence time, even when the system is isolated. This fundamental effect, crucial for applicationsusing macroscopic coherence, was scarcely studied. Here, we link the coherence time to the condensate phase dynamics, and show using a microscopic theory that the time derivative of the condensate phase operator ˆθ0 is proportional to a chemical potential operator which includes both the fermionic pair-breaking and the bosonic pair-motion excitation branches.For a given realization of the number of particle N and of the energy E, the phase evolves at long times as −2μmc(E,N)t/~ where μmc(E,N) is the microcanonical chemical potential ; fluctuations of N and E from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristictime ∝ N1/2. On the contrary, in the absence of energy and number fluctuations, the decay of the temporal coherence function is exponential with a characteristic time scaling as N due to the diffusive motion of ˆθ0 in the environnement created by the excited modes. We give an explict expression of this characteristic time at low temperature in the case where the bosonicbranch is convex and the phonons undergo 2 ↔ 1 Beliaev-Landau process. Finally, we propose methods to measure each contribution to the coherence time using ultracold atoms.