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Nesse trabalho, são investigadas as propriedades dinâmicas de modelos da mecânica estatística na criticalidade. Inicialmente, trabalhando com modelos de spin e utilizando os conceitos de persistência global e de dimensão anômala da magnetização inicial, mostramos que o modelo de Baxter-Wu não está na mesma classe de universalidade dos modelos de Potts com quatro estados e de Ising com interação de três spins em uma direção, todos bidimensionais. Na segunda parte da tese, estudamos o fenômeno de crescimento da superfície gerada pela deposição segundo as regras que definem os autômatos celulares probabilísticos propostos por Grassberger (modelos A e B). Esses dois autômatos não pertencem à classe de universalidade de Domany-Kinzel e apresentam novos expoentes críticos, cuja origem se deve à conservação de paridade. Determinamos o expoente de crescimento beta w, válido em tempos curtos, assim como os outros expoentes críticos associados ao crescimento de superfície (alfa e z). Nossas estimativas se comparam bem com os resultados obtidos a partir de razões de inteiros propostas por Jensen para os expoentes beta, ni paralelo e ni perpendicular. Finalmente, investigamos a transição de fase entre o estado helicoidal e o estado desordenado (random coil) da polialanina e do fragmento peptídico PTH(1-34), que corresponde aos resíduos 1 a 34 da região aminoterminal do hormônio das paratireóides. Nosso cálculo, que leva em conta as interações entre todos os átomos da molécula, está baseado em uma abordagem de tempos curtos. Os resultados dessa análise indicam que a transição helix-coil das polialaninas e do PTH(1-34) é de segunda ordem e apontam para uma classe de universalidade para a transição helix-coil em homopolímeros e proteínas (partindo de um estado helicoidal). / In this work we investigated dynamic properties of statistical mechanical models at criticality. At first, using the concepts of global persistence and anomalous dimension of initial magnetization, we showed that the Baxter-Wu model does not belong to the same universality class as 4-state Potts model and Ising with multispin interaction in one direction. In the sequence, we studied the roughening behavior generated by deposition governed by rules defined by probabilistic cellular automata proposed by Grassberger (A and B models). Those models are known do not belong to the Domany-Kinzel universality class. They are characterized by different exponents which are related to the parity conserving (PC). We estimated the growth exponent beta w, in short-time regimen, such as, other critical exponents associated to the surface growth (alpha and z). Our results are in good agreement with those expected for parity conserving universality class. At last we studied the phase transition between the completely helical state and the random coil of the polyalanine, such as, for the 34-residue human parathyroid fragment PTH(1-34). Our short-time simulations of the helix-coil transition are based on a detailed all-atom representation of proteins. The results indicate that helix-coil transition in polyalanine and PTH(1-34) is a second-order phase transition and suggest a universality class to the helix-coil transition in homopolymer and (helical) proteins.

Nesse trabalho, são investigadas as propriedades dinâmicas de modelos da mecânica estatística na criticalidade. Inicialmente, trabalhando com modelos de spin e utilizando os conceitos de persistência global e de dimensão anômala da magnetização inicial, mostramos que o modelo de Baxter-Wu não está na mesma classe de universalidade dos modelos de Potts com quatro estados e de Ising com interação de três spins em uma direção, todos bidimensionais. Na segunda parte da tese, estudamos o fenômeno de crescimento da superfície gerada pela deposição segundo as regras que definem os autômatos celulares probabilísticos propostos por Grassberger (modelos A e B). Esses dois autômatos não pertencem à classe de universalidade de Domany-Kinzel e apresentam novos expoentes críticos, cuja origem se deve à conservação de paridade. Determinamos o expoente de crescimento beta w, válido em tempos curtos, assim como os outros expoentes críticos associados ao crescimento de superfície (alfa e z). Nossas estimativas se comparam bem com os resultados obtidos a partir de razões de inteiros propostas por Jensen para os expoentes beta, ni paralelo e ni perpendicular. Finalmente, investigamos a transição de fase entre o estado helicoidal e o estado desordenado (random coil) da polialanina e do fragmento peptídico PTH(1-34), que corresponde aos resíduos 1 a 34 da região aminoterminal do hormônio das paratireóides. Nosso cálculo, que leva em conta as interações entre todos os átomos da molécula, está baseado em uma abordagem de tempos curtos. Os resultados dessa análise indicam que a transição helix-coil das polialaninas e do PTH(1-34) é de segunda ordem e apontam para uma classe de universalidade para a transição helix-coil em homopolímeros e proteínas (partindo de um estado helicoidal). / In this work we investigated dynamic properties of statistical mechanical models at criticality. At first, using the concepts of global persistence and anomalous dimension of initial magnetization, we showed that the Baxter-Wu model does not belong to the same universality class as 4-state Potts model and Ising with multispin interaction in one direction. In the sequence, we studied the roughening behavior generated by deposition governed by rules defined by probabilistic cellular automata proposed by Grassberger (A and B models). Those models are known do not belong to the Domany-Kinzel universality class. They are characterized by different exponents which are related to the parity conserving (PC). We estimated the growth exponent beta w, in short-time regimen, such as, other critical exponents associated to the surface growth (alpha and z). Our results are in good agreement with those expected for parity conserving universality class. At last we studied the phase transition between the completely helical state and the random coil of the polyalanine, such as, for the 34-residue human parathyroid fragment PTH(1-34). Our short-time simulations of the helix-coil transition are based on a detailed all-atom representation of proteins. The results indicate that helix-coil transition in polyalanine and PTH(1-34) is a second-order phase transition and suggest a universality class to the helix-coil transition in homopolymer and (helical) proteins.

Probing nonequilibrium dynamics in a trapped, inhomogeneous atomic quantum gas can be a challenging task because coexisting mass transport and spreading of quantum correlations often make the problem intractable. By removing density inhomogeneity in an atomic quantum gas and employing local control of chemical potential as well as interaction parameters, it is possible to perform quasi-particle control, initiate and probe collective quantum dynamics without or with a controlled mass flow. We report our experimental results toward quasi-particle control and nonequilibrium dynamics in a homogeneous two-dimensional quantum gas.

Nous étudions les propriétés des états stationnaires et de dynamiques hors-équilibre, d’un point de vue théorique et numérique. Ces dynamiques sont obtenues en perturbant la dynamique d’équilibre par forçage mécanique et/ou thermique. Dans l’approche théorique, le système considéré évolue selon une dynamique de Langevin à laquelle on ajoute une force extérieure. Nous étudions la convergence de la loi de la dynamique vers la mesure stationnaire, en donnant des estimations quantitatives du taux, dans les régimes Hamiltonien et sur amorties. Dans l’approche numérique, nous considérons une chaîne de rotateurs soumise aux deux forçages et une chaîne d’oscillateurs de Toda soumise à un forçage thermique et à une perturbation stochastique. Nous étudions les caractéristiques de l’état stationnaire et les propriétés de transport. Dans le cas de la chaîne de rotateurs nous observons en particulier que le courant d’énergie moyen est dans certains cas accru par un gradient de température opposé. / We study the properties of stationary states associated with nonequilibrium dynamics from a theoretical and a numerical point of view. These dynamics are obtained by perturbing equilibrium dynamics with mechanical and / or thermal forcings. In the theoretical approach, the system considered evolves according to a Langevin dynamics perturbed by a torque. In this framework, we study the convergence of the law of dynamics to the stationary measure, giving quantitative estimates of the exponential rate, both in the Hamiltonian and `` overdamped '' regimes.By a numerical approach, we consider a chain of rotors subjected to both forcings and a chain of Toda oscillators subject to a thermal forcing and a stochastic perturbation. We study the features of the stationary state and analyze its transport properties. In particular, in the case of the rotor chain, contrary to what is naively expected, we observe that the average energy current is in some cases increased by an opposite temperature gradient.

Lattice gauge theories are crucial for our understanding of many physical phenomena ranging from fundamental particle interactions in high-energy physics to frustration and topological order in condensed matter. Hence, many equilibrium aspects of these theories have been studied intensively over the past decades. Recent developments, however, have shown that the study of nonequilibrium dynamics in lattice gauge theories also provides a very fertile ground for interesting phenomena. This thesis is devoted to the study of two particular dynamical processes in lattice gauge theories and related quantum spin models. First, we show that an interacting two-dimensional lattice gauge theory can exhibit disorder-free localization: a mechanism for ergodicity breaking due to local constraints imposed by gauge invariance. This result is particularly remarkable as the stability in two dimensions of the more conventional (disorder-induced) many-body localization is still debated. Concretely, we show this type of nonergodic behavior in the quantum link model. Our central result is based on a bound on the localization-delocalization transition, which is established through a concomitant classical percolation problem. Further, we develop a numerical method dubbed “variational classical networks”, to study the quantum dynamics in this system. This technique provides an efficient and perturbatively controlled representation of the wave function in terms of networks of classical spins akin to artificial neural networks. This allows us to identify distinguishing transport properties in the localized and ergodic phases, respectively. In the second problem, we study the dynamics of string breaking, a key process in confining gauge theories, where a string connecting two charges decays due to the creation of new particle-antiparticle pairs. Our main result here is that string breaking can also be observed in quantum Ising chains, in which domain walls get confined either by a symmetry-breaking field or by long-range interactions. We identify, in general, two distinct stages in this process. While at the beginning the initial charges remain stable, the string can exhibit complex dynamics with strong quantum correlations. We provide an effective description of this string motion, and find that it can be highly constrained. In the second stage, the string finally breaks at a timescale that depends sensitively on the initial separation of domain walls. We observe that the second stage can be significantly delayed as a consequence of the dynamical constraints appearing in the first stage. Finally, we discuss the generalization of our results to low-dimensional confining gauge theories. As a general aspect of this work, we discuss how the phenomena studied here could be realized experimentally with current and future technologies in quantum simulation. Furthermore, the methods developed in this thesis can also be applied to other lattice gauge theories and constrained quantum many-body models, not only to address purely theoretical questions but also to provide a theoretical description of experiments in quantum simulators. / Gittereichtheorien sind ein wichtiger Bestandteil im Verständnis vieler physikalischer Phänomene und Grundlage verschiedener Theorien, welche sich von der elementaren Wechselwirkungen in der Hochenergiephysik, Frustration in Spinmodellen bis hin zu topologischer Ordnung in der Festkörperphysik erstrecken. Die Eigenschaften von Eichtheorien im Gleichgewicht waren in den letzten Jahrzehnten ein zentraler Punkt der Forschung. Obwohl sich Untersuchungen der Dynamik jenseits des Gleichgewichs als eine große Herausfordung dargestellt haben, haben kürzliche Erkenntnisse gezeigt, dass die Dynamik in Gittereichtheorien überraschende und interessante Entdeckungen bereithält. Diese Dissertation behandelt zwei zentrale dynamische Prozesse in Gittereichtheorien und verwandten Spinmodellen. Einerseits soll die Dynamik von zweidimensionalen und wechselwirkenden Gittereichtheorien untersucht werden im Falle des sogenan- nten Quanten-Link-Modells untersucht werden. Entgegen der Ergodenhypothese zeigt das System Lokalisierung ohne Unordnung aufgrund lokaler Zwangsbedingungen durch Eininvarianz. Dieses Ergebnis ist insofern bemerkenswert, als die gewöhnliche, durch Unordnung induzierte, Vielteilchenlokalisierung in zwei Dimensionen umstritten ist. Als ein Hauptergebnis finden wir einen Übergang zwischen einer lokalisierten und ergodischen Phase, dessen Existenz durch ein zugehöriges klassisches Perkolationsproblem gezeigt werden konnte. Die quantenmechanischen Transporteigenschaften, elementar verschieden in der lokalisierten und ergodischen Phase, werden charakterisiert und untersucht. Die Lösung der quantenmechanischen Zeitentwicklung wird durch eine methodische Weiterentwicklung der sogenannten „variationellen klassischen Netzwerke“ erreicht Diese Methode stellt eine perturbative, aber kontrollierte Repräsentation von zeitentwickelten quantenmechanischen Wellenfunktionen dar in Form von Netzwerken klassischer Spins, ähnlich wie bei einem künstlichen neuronalen Netz. Im zweiten Teil untersuchen wir die Dynamik eines Schlüsselprozesses in Eichtheorien mit Confinement, welcher als „String-Breaking“ bezeichnet wird In diesem Prozess zerfällt der der Strang, der zwei elementare Ladungen verbindet, durch die Bildung neuer Teilchen-Antiteilchen-Paare. Ein Hauptresultat dieser Arbeit ist die Beobachtung dieses dynamischen Phänomens in Quantum-Ising-Ketten und damit in Systemen ohne Eichinvarianz. Das Confinement entsteht dabei zwischen Domänenwänden entweder durch eine langreichweitige Wechselwirkung zwischen den beteiligten Spins oder durch symmetriebrechende Magnetfelder. Es wird gezeigt, dass während des „String-breaking“ Prozesses das Modell zwei Phasen durchläuft: Während zu Beginn die Anfangsladungen stabil bleiben, weist der Strang eine komplexe Dynamik mit starken Quantenkorrelationen auf. Für diese erste Phase wird eine effektive Beschreibung eingeführt, um die verschiedenen Aspekte zu analysieren und zu verstehen. Die Zeitskalen zur Destabilisierung des Strangs innerhalb einer zweiten Phase zeigen eine starke Abhängigkeit von der anfänglichen Trennung der Domänenwände. Es wird gezeigt, dass die zweite Phase als Konsequenz der dynamischen Beschränkungen der ersten Phase signifikant verzögert werden kann. Diese Resultate können in niedrigdimensionalen Eichtheorien verallgemeinert werden. Weiterführend sollen die Ergebnisse als Grundlage einer experimentellen Realisierung durch Quantensimulationen dienen. Die entwickelten Methoden können auf andere Eichtheorien und verwandten Vielteilchenmodellen angewendet werden und bieten eine Plattform für weitere Ansätze.

Les systèmes quantiques unidimensionnels à N corps présentent des comportements particuliers et intrigants liés à leur dimensionnalité réduite, qui amplifie l’effet des fluctuations et des corrélations. Les expériences de gaz d’atomes ultra-froids permettent d’isoler et de contrôler efficacement les paramètres du système et de simuler des systèmes modèles pour lesquels il existe de nombreux outils théoriques. Je présenterai ici les résultats des études réalisées pendant ma thèse de Doctorat, visant à explorer le comportement de gaz de Bose unidimensionnels (gaz de Lieb-Liniger) à l’équilibre et hors équilibre. Je donnerai notamment un aperçu de la boite à outils aujourd’hui disponible permettant de caractériser les propriétés thermodynamiques d’un gaz de Lieb-Liniger, et présenterai une étude détaillée du mode de respiration d’un tel système. / One-dimensional quantum many-body systems exhibit peculiar and intriguing behaviors as a consequence of the reduced dimensionality, which enhances the effect of fluctuations and correlations. The high degree of isolation and controllability of experiments manipulating ultra-cold atomic gases allows for the experimental simulation of text-book models, for which many theory tools are available for quantitative comparison. I will present instances of such efforts carried out during my PhD thesis, namely, the studies performed to investigate the behavior of 1D Bose gas (Lieb-Liniger gas) at equilibrium and beyond. An overview of the toolbox available to date to characterize the equilibrium thermodynamics of a Lieb-Liniger gas will be shown, followed by a detailed study of the breathing mode of such a system.

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