Dissertations / Theses on the topic 'Standard Equilibrium Quantum Systems'
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Kasztelan, Christian. "Strongly Interacting Quantum Systems out of Equilibrium." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-124827.
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Lukkarinen, Jani. "Statistical analysis of finite equilibrium quantum systems." Helsinki : University of Helsinki, 2001. http://ethesis.helsinki.fi/julkaisut/mat/fysii/vk/lukkarinen/statisti.pdf.
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Dorner, Ross. "Non-equilibrium thermodynamics and dynamics of quantum systems." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/23916.
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This thesis is a study of non-equilibrium phenomena in quantum systems. Emphasis is given to the recently derived non-equilibrium fluctuation theorems, which relate the non-equilibrium response of a system to its equilibrium thermodynamic properties. We investigate the validity and importance of these theorems, from both a theoretical and experimental perspective, in systems ranging from a single atom to an ensemble of interacting particles. We also investigate the potential role of quantum dynamics in biological processes.
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Deesuwan, Tanapat. "Towards thermodynamics of quantum systems away from equilibrium." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/43379.
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A probability distribution encodes all the statistics of its corresponding random variable, hence it encodes all one can learn about the system via the random variable. In the theoretical part of this thesis, we discuss several equivalent representations of probability distributions in physics which establishes their roles as complete information measures in their own contexts. In particular, we show how Rényi entropies (as well as relative Rényi entropies) completely characterise the uncertainty of a system, hence implies the insufficiency of Shannon entropy (as well as relative entropy) in capturing the information in the presence of strong fluctuation. We also generalise Jarzynski equality in terms of relative Rényi entropies and show the equivalence between the generalised equality and the work distribution. As a consequence, an equivalence between a monotonic property of relative Rényi entropies and a kind of second law relations is revealed. In the experimental part, we study the non-equilibrium dynamics of an optically levitated nanosphere system in Knudsen regime and discover that, even though the system is not in equilibrium, the dynamics can still be treated as a Brownian motion with an effective temperature and an effective coefficient. Due to the Gaussian statistics of the levitated sphere, we show how some relevant non-equilibrium properties of the system, including several local temperatures, can be analysed from its power spectrum.
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Fusco, Lorenzo. "Non-equilibrium thermodynamics in quantum many-body systems." Thesis, Queen's University Belfast, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706680.
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Thermodynamics is one of the pillars of modern science. Understanding which are the boundaries for the applicability of a theory is fundamental for every science and thermodynamics makes no exception. This Thesis studied the implications of thermodynamic transformations applied to quantum systems, particularly discussing the limits of a proper thermodynamic interpretation of such a transformation for a quantum many-body system. First a framework is developed to give a physical meaning to the full statistics of the work distributions for a many-body system, with particular emphasis on the quantum Ising model. Signatures of criticality are found at any level of the statistics of the work distribution. Furthermore, a detailed study of cyclic work extraction protocols is reported, for the case of the Dicke model, analysing the interplay between entanglement and phase transition from the point of view of non-equilibrium thermodynamics. Afterwards, a study of non-equilibrium thermodynamics of open quantum systems is reported. The first experimental reconstruction of the irreversible entropy production for a critical quantum manybody system is demonstrated, showing an excellent agreement with the theoretical predictions. Finally, in the framework of thermodynamics of quantum jump trajectories, a novel approach to the resolution of the large-deviation function is derived. Using this method many studies on the thermodynamics of open quantum many-body systems can be realised in the future.
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Henriet, Loïc. "Non-equilibrium dynamics of many body quantum systems." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX036/document.
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Cette thèse porte sur l'étude de propriétés dynamiques de modèles quantiques portés hors équilibre. Nous introduisons en particulier des modèles généraux de type spin-boson, qui décrivent par exemple l'interaction lumière-matière ou certains phénomènes de dissipation. Nous contribuons au développement d'une approche stochastique exacte permettant de d'écrire la dynamique hors équilibre du spin dans ces modèles. Dans ce contexte, l'effet de l'environnement bosonique est pris en compte par l'intermédiaire des degrés de liberté stochastiques supplémentaires, dont les corrélations temporelles dépendent des propriétés spectrales de l'environnement bosonique. Nous appliquons cette approche à l'étude de phénomènes à N-corps, comme par exemple la transition de phase dissipative induite par un environnement bosonique de type ohmique. Des phénomènes de synchronisation spontanée, et de transition de phase topologique sont aussi identifiés. Des progrès sont aussi réalisés dans l'étude de la dynamique dans les réseaux de systèmes lumière-matière couplés. Ces développements théoriques sont motivés par les progrès expérimentaux récents, qui permettent d'envisager une étude approfondie de ces phénomènes. Cela inclut notamment les systèmes d'atomes ultra-froids, d'ions piégés, et les plateformes d'électrodynamique en cavité et en circuit. Nous intéressons aussi à la physique des systèmes hybrides comprenant des dispositifs à points quantiques mésoscopiques couplés à un résonateur électromagnétique. L'avènement de ces systèmes permet de mesures de la formation d'états à N-corps de type Kondo grâce au résonateur; et d'envisager des dispositifs thermoélectriquesThis thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We also investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introducethermoelectric applications in these devices
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MARCANTONI, STEFANO. "On the non-equilibrium thermodynamics of quantum systems." Doctoral thesis, Università degli Studi di Trieste, 2018. http://hdl.handle.net/11368/2917551.
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A consistent theory of non-equilibrium thermodynamics for Markovian open quantum systems has been developed in the late seventies in analogy with Classical Irreversible Thermodynamics. The time-evolution of these open systems is usually described by means of effective master equations in Lindblad form, that turn out to be reliable when there is a separation of time-scales between system and environment, such that memory effects are negligible and the so-called Markovian approximation is justified. In this framework, the variations of energy and entropy in the system are consistently described, distinguishing between heat and work contributions and providing a statement of the second law of thermodynamics as positivity of the entropy production.
However, there is empirical evidence that many physical systems like photosynthetic complexes,
opto-mechanical resonators and superconducting qubits, just to mention a few, experience more general non-Markovian dynamics. The formulation of the laws of thermodynamics in a non-Markovian setting is matter of current research and represents the main topic of the present work. As a first step, we show that the entropy production defined as in the Markovian case can be negative for a class of non-Markovian dynamics. We argue that this outcome should not be interpreted as a violation of the second law of thermodynamics because the environment must be explicitly taken into account in the balance of entropy in the non-Markovian setting. In order to justify this claim we adopt a more general point of view, studying a closed bipartite quantum system, such that each of the two subsystems plays the role of a finite environment out of equilibrium for the other one. We concentrate on the balance of energy first and construct an effective Hamiltonian for each subsystem using physically reasonable requirements; then we define heat and work as in the standard Markovian treatment, with the effective Hamiltonian replacing the free Hamiltonian. It turns out that, in our framework, the work power is perfectly balanced between subsystems, while the correlations can store a part of energy locally inaccessible and exchange it with both subsystems in the form of heat.
Concerning the balance of entropy, a quite general formulation of the second law of thermodynamics can be given as follows: under the assumption of a factorized initial state for the compound system, the sum of the total variations of the entropies in the two subsystems is always nonnegative. We show with an explicit example that this general formulation does not correspond to the statement presented in the framework of Markovian master equations, which should not be considered a priori the second law of thermodynamics.
In the last part of the thesis we concentrate of the so-called fluctuation relations, that are results extending the thermodynamic formalism beyond the behavior of average quantities. After reviewing the main theoretical outcomes, such as the Jarzynski equality and the Crooks fluctuation theorem, we describe a proposal to access experimentally the work performed on an ensemble of diatomic molecules by a time-dependent electric field coupled with their vibrational degree of freedom. This procedure could then be used to test the quantum Jarzynski equality. With respect to the results so far appeared in the literature, in which the left-hand side of the equality is inferred from an experiment and the right-hand side is computed according to a model, in our proposed setting we should be able to estimate from the experiment both the left-hand side and the right-hand side of the equality, independently.
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Holladay, Robert Tyler. "Steepest-Entropy-Ascent Quantum Thermodynamic Modeling of Quantum Information and Quantum Computing Systems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/94630.
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Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation.Doctor of Philosophy
Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.
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Scopa, Stefano. "Non-equilibrium dynamics of driven low-dimensional quantum systems." Thesis, Université de Lorraine, 2019. http://www.theses.fr/2019LORR0084/document.
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Cette thèse analyse certains aspects de la dynamique hors équilibre de systèmes quantiques unidimensionnels lorsqu’ils sont soumis à des champs externes dépendant du temps. Nous considérons plus particulièrement le cas des forçages périodiques, et le cas d’une variation temporelle lente d’un paramètre de l’Hamiltonien qui permet de traverser une transition de phase quantique. La première partie contient une présentation des notions, des modèles et des outils nécessaires pour comprendre la suite de la thèse, avec notamment des rappels sur les modèles quantiques critiques (en particulier sur les chaines de spin et sur le modèle de Bose-Hubbard), le mécanisme de Kibble-Zurek, et la théorie de Floquet. Ensuite, nous étudions la dynamique hors équilibre des gaz de Tonks-Girardeau dans un potentiel harmonique dépendant du temps par différentes techniques : développements perturbatifs, diagonalisation numérique exacte et solutions analytiques exactes basées sur la théorie des invariants dynamiques d’Ermakov-Lewis. Enfin, nous analysons la dynamique hors équilibre des systèmes quantiques ouverts markoviens soumis à des variations périodiques des paramètres du système et de l’environnement. Nous formulons une théorie de Floquet afin d’obtenir des solutions exactes des équations de Lindblad périodiques. Ce formalisme de Lindblad-Floquet est utilisé pour obtenir une caractérisation exacte du fonctionnement en temps fini des machines thermiques quantiquesThis thesis analyzes some aspects regarding the dynamics of one-dimensional quantum systems which are driven out-of-equilibrium by the presence of time- dependent external fields. Among the possible kinds of driven systems, our focus is dedicated to the slow variation of a Hamiltonian’s parameter across a quantum phase transition and to the case of a time-periodic forcing. To begin with, we prepare the background and the tools needed in the following. This includes a brief introduction to quantum critical models (in particular to the xy spin chain and to the Bose-Hubbard model), the Kibble-Zurek mechanism and Floquet theory. Next, we consider the non-equilibrium dynamics of Tonks-Girardeau gases in time-dependent harmonic trap potentials. The analysis is made with different techniques: perturbative expansions, numerical exact diagonalization and exact methods based on the theory of Ermakov-Lewis dynamical invariants. The last part of the thesis deals instead with the non-equilibrium dynamics of markovian open quantum systems subject to time-periodic perturbations of the system parameters and of the environment. This has led to an exact formulation of Floquet theory for a Lindblad dynamics. Moreover, within the Lindblad-Floquet framework it is possible to have an exact characterization ofthe finite-time operation of quantum heat-engines
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PORTA, SERGIO. "Non-equilibrium control of quantum systems and their phases." Doctoral thesis, Università degli studi di Genova, 2019. http://hdl.handle.net/11567/987246.
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In the last years, one of the major aim of the condensed matter area of interest, at the same rate of fundamental research, is to produce new and substantial breakthrough innovations to be applied in the information technology world. Indeed, semiconductor-based devices have constantly improved their performances thanks to the ability of continually shrink the components inside chips. In this process, however, physical components cannot be reduced in size infinitely. All matter consists of atoms and, at the atomic level, particles behave according to the laws of quantum mechanics. With this respect, the control of quantum systems is becoming fundamental to go beyond the present technology and the engineering of powerful phases of matter, very hard to obtain in standard conditions, is one of the main goals people are trying to achieve. The realization of quantum computation devices, in this sense, strongly depends on these new ideas success. In this respect, researchers have faced the difficulty, both from the theoretical and the experimental points of view, to control the state of a quantum system. Quantum control, i.e. the control of quantum phenomena, is becoming one of the major concerns in condensed matter physics, even if results obtained in the recent past are mainly confined to static systems in equilibrium, due to the difficulty to experimentally manipulate out-of-equilibrium quantum systems and the absence of an efficient general theoretical framework to describe non-equilibrium dynamics. In this thesis, I address these currently open questions by inspecting several different condensed matter models, using various methods to drive the system out of equilibrium and focusing on its dynamical features as well as the properties of its equilibration towards a thermal or, more interestingly, non thermal steady state. I discuss the possibility to manipulate various systems to give rise to peculiar dynamical behaviors and corresponding steady states with properties not attainable in thermal equilibrium, ranging from quantum phase transitions and their dynamical counterparts to superconductivity.
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Hackl, Andreas. "Quantum criticality and non-equilibrium dynamics in correlated electron systems." Aachen Shaker, 2009. http://d-nb.info/1001216466/04.
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Shastry, Abhay, and Charles A. Stafford. "Temperature and voltage measurement in quantum systems far from equilibrium." AMER PHYSICAL SOC, 2016. http://hdl.handle.net/10150/621940.
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We show that a local measurement of temperature and voltage for a quantum system in steady state, arbitrarily far from equilibrium, with arbitrary interactions within the system, is unique when it exists. This is interpreted as a consequence of the second law of thermodynamics. We further derive a necessary and sufficient condition for the existence of a solution. In this regard, we find that a positive temperature solution exists whenever there is no net population inversion. However, when there is a net population inversion, we may characterize the system with a unique negative temperature. Voltage and temperature measurements are treated on an equal footing: They are simultaneously measured in a noninvasive manner, via a weakly coupled thermoelectric probe, defined by requiring vanishing charge and heat dissipation into the probe. Our results strongly suggest that a local temperature measurement without a simultaneous local voltage measurement, or vice versa, is a misleading characterization of the state of a nonequilibrium quantum electron system. These results provide a firm mathematical foundation for voltage and temperature measurements far from equilibrium.
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Menu, Raphaël. "Gaussian-state approaches to quantum spin systems away from equilibrium." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEN036.
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Que se passe-t-il quand un système quantique à N corps est brutalement amené loin de son état d’équilibre ? Vers quelle sorte d’état relaxe-t-il et quelle information peut-on extraire de sa dynamique ? Fournir des réponses à ses questions est un problème difficile qui a suscité l’intérêt de toute une communauté de physiciens. Cependant, le coût numérique important requis pour étudier le comportement de ces systèmes, en particulier pour de grandes tailles, a motivé le développement de méthodes numériques et théoriques de pointes. Cette thèse s’inscrit dans la continuité de ces efforts en proposant un ensemble de méthodes basées sur une représentation en termes d’une théorie de champs Gaussiens afin d’étudier l’évolution des systèmes de spins. Plus particulièrement,ces méthodes sont appliquées `a plusieurs modèles inspirés par les expériences d’atomes froids simulant le comportement de systèmes de spins avec un accent particulier sur l’étude des phénomènes de localisations. Cette thèse présente donc des résultats mettant en évidence l’émergence de la localisation dans des systèmes sans désordre par un effet d’interférence appelé cage d’Aharonov-Bohm ; ainsi qu’une dynamique explorant un riche spectre allant de la diffusion balistique`a la localisation, en passant par la diffusion anormale, cela dans un modèle d’Ising quantique avec désordre géométrique — ce dernier exemple présence un scénario bien plus riche que celui offert par la dynamique des particules libres dans un milieu désordonné. Enfin, nous avons exploré la possibilité pour les approches gaussiennes de décrire la dynamique de systèmes interagissant et leur relaxation vers des états thermiquesWhat happens when a quantum many-body system is brutally driven away fromequilibrium ? Toward which kind of states does it relax and what informationcan one extract from the resulting dynamics ? Providing answers to these questionsis a challenging problem that spured the interest of a whole community ofphysicists. However, the numerical cost required to investigate the behaviour ofthese systems, particularly for large system sizes, motivated the development ofcutting-edge numerical and theoretical techniques.This thesis aims at contributing to these efforts by proposing a set of methodsbased on a representation of the systems in terms of a Gaussian field theory, withthe purpose of studying the evolution of spin systems. More specifically, thesemethods are applied to several models inspired by cold-atoms experiments simulatingthe behaviour of spin systems, with a stress on the study of localizationphenomena. Therefore, this thesis highlights the emergence of localization in systemsdevoid of disorder due to an interference effect, the so-called Aharonov-Bohmcaging; as well as a geometrically disordered quantum Ising model displaying adynamics exploring a rich spectrum ranging from balistic diffusion to anomalousdiffusion, an then localization - this last example offers a scenario richer than theone exhibited by the dynamics of free particles in a disordered medium. Finally,we explored the possibility for Gaussian approaches to describe the dynamics ofinteracting systems and their relaxation toward thermal states
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GAMBETTA, FILIPPO MARIA. "Out-of-equilibrium dynamics of one-dimensional integrable quantum systems." Doctoral thesis, Università degli studi di Genova, 2018. http://hdl.handle.net/11567/930218.
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Friesdorf, Mathis [Verfasser]. "Closed quantum many-body systems out of equilibrium : A quantum information perspective / Mathis Friesdorf." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1099282829/34.
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Goihl, Marcel [Verfasser]. "Emergence of Thermodynamics For Quantum Systems Out Of Equilibrium / Marcel Goihl." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1203129017/34.
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Moraes, Eduardo Carlo Mascarenhas. "Collective and optical phenomena in equilibrium and nonequilibrium interacting quantum systems." Universidade Federal de Minas Gerais, 2014. http://hdl.handle.net/1843/BUOS-9TPHLT.
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In this thesis we study collective, emergent and optical properties of interacting quantum systems both in equilibrium and nonequilibrium situations from a microscopic modelling. This orientation steams from both the fact there is a profound need to design, characterise and set up control strategies for realistic systems in which quantum technologies could be conceived and the interest to grasp and identify fundamental principles for the emergence of macroscopic behaviour. The thesis is divided into three parts: I Optical and Collective Phenomena; II Equilibrium many-body systems and III Nonequilibrium many-body systems. Part I includes four complementary contributions to the optics emerging from the collective behaviour of microscopic quantum systems. In part II (Equilibrium many-body systems) of the thesis I have addressed the physics of quantum phase transitions from the perspective of nonequilibrium thermodynamics. We have shown that such an approach captures the essential features of finite order transitions that have a strong connection to thermodynamical and energetic figures of merit, but does not capture infinite order transitions that are of a much more subtle nature. Motivated by these exotic infinite order transitions we have looked at quantum phases and phase transitions through an informational and operational perspective based on pure state conversions restricted by local operations. In the third and last part (Nonequilibrium many-body systems) of the thesis I have laid out a project on the closed evolution of quantum spin chains focussing on the emergent nonequilibrium laws that depart from equilibrium physics.
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Marcuzzi, Matteo. "A study on non-equilibrium dynamics in classical and quantum systems." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4805.
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The theory of statistical mechanics provides a powerful conceptual framework within which the relevant (macroscopic) features of systems at equilibrium can be described. As there is currently no equivalent capable of encompassing the much richer class of non-equilibrium phenomena, research in this direction proceeds mainly on an instance-by-instance basis. The aim of this Thesis is to
describe in some detail three such attempts, which involve different dynamical aspects of classical and quantum systems. As summarised below, each of the last three Chapters of this document delves into one of these different topics, while Chapter 2 provides a brief introduction on the study of non-equilibrium dynamics. In Chapter 3 we investigate the purely relaxational dynamics of classical critical ferromagnetic systems in the proximity of surfaces, paying particular attention to the effects that the latter induce on the early stages of the evolution following an abrupt change in the temperature of the sample.
When the latter ends close enough to the critical value which separates the paramagnetic from the ferromagnetic phase, it effectively introduces a temporal boundary which can be treated as if it were a surface. Within this picture, we highlight the emergence of novel effects near the effective edge formed by the intersection of the two spatial and temporal boundaries. Our findings are apparently in disagreement with previous predictions which were based on the assumption that the presence of such an edge would not affect the scaling behaviour of observables; in order to explain this discrepancy, we propose an alternative for the original power-counting argument which, at least, correctly predicts the emergence of novel field-theoretical divergences in our one-loop calculations. We show that said singularities are associated with the scaling at the edge. Moreover, by encoding our findings in a boundary renormalisation group framework, we argue that the new predicted behaviour represents a universal feature associated to the short-distance expansion of the order parameter of the transition near the edge; we also calculate explicitly its anomalous dimension at the first-order in a dimensional expansion. As a qualitative feature, this anomalous dimension depends on the type of phase transition occurring at the surface. We exploit this fact in order to provide numerical support to our predictions via Monte Carlo simulations of
the dynamical behaviour of a three-dimensional Ising model. The main results reported in Chap. 3 have appeared in Ref. [1]. In Chapter 4 we revisit the Euclidean mapping to imaginary times which has been recently
proposed [2, 3] as an alternative for approaching the problem of quantum dynamics following a quench. This is expected to allow one to reformulate the original problem as a static one confined in a film geometry. We show that this interpretation actually holds only if the initial state of the dynamics is pure. Statistical mixtures, instead, intertwine the effects due to the two boundaries,
which therefore cannot be regarded as being independent. We emphasize that, although the aforementioned reinterpretation as a confined static problem fails, one is still able, in principle, to write down and solve the corresponding equations. We also discuss in some detail the relation between this approach and the real-time field-theoretical one which makes use of the two-time Keldysh contour. For this purpose, we study the analytical structure of relevant observables — such as correlation functions — in the complex plane of times, identifying a subdivision of this domain into several sectors which depend on the ordering of the imaginary parts of the involved time coordinates.
Within each of these subdomains, the analytic continuation to the real axis provides in principle a different result. This feature allows one to reconstruct from the Euclidean formalism all possible non-time-ordered functions, which in particular include all those which can be calculated via the Keldysh two-time formalism. Moreover, we give a prescription on how to retrieve response
functions, discussing some simple examples and rationalising some recent numerical data obtained for one of these observables in a one-dimensional quantum Ising chain [4]. We also highlight the emergence of a light-cone effect fairly similar to the one previously found for correlation functions [2], which therefore provides further confirmation to the fact that information travels across the system in the form of the entanglement of quasi-particles produced by the quenching procedure. We have reported part of this analysis in Ref. [5].
Chapter 5 presents part of our recent work on effective relaxation in quantum systems following a quench and on the observed prethermalisation. We analyse the effects caused by the introduction of a long-range integrability-breaking interaction in the early stages of the dynamics of an otherwise integrable quantum spin chain following a quench in the magnetic field. By
employing a suitable transformation, we redefine the theory in terms of a fully-connected model of hard-core bosons, which allows us to exploit the (generically) low density of excitations for rendering our model exactly solvable (in a numerical sense, i.e., by numerically diagonalising an
exact matrix). We verify that, indeed, as long as the parameters of the quench are not too close to the critical point, the low-density approximation captures the dynamical features of the elementary operators, highlighting the appearance of marked plateaux in their dynamics, which we reinterpret
as the emergence of a prethermal regime in the original model. As expected, the latter behaviour is reflected also on extensive observables which can be constructed as appropriate combinations of the mode populations. For these quantities, the typical approach to the quasi-stationary value is algebraic with exponent a ≈ 3, independently of the size of the system, the strength of the interaction and the amplitude of the magnetic field (as long as it is kept far from the critical point). The plateaux mentioned above last until a recurrence time — which can be approximately identified with tR ≈ N/2 for single modes and t′R ≈ N/4 for extensive quantities — after which quantum oscillations due to the finite size of the chain reappear. Our procedure allows us to shed some light over prethermal features without having to considerably limit the size of the system, which we can choose to be quite large, as we discuss in Ref. [6].
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Franchetti, Guido. "Pattern-forming in non-equilibrium quantum systems and geometrical models of matter." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/245145.
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This thesis is divided in two parts. The first one is devoted to the dynamics of polariton condensates, with particular attention to their pattern-forming capabilities. In many configurations of physical interest, the dynamics of polariton condensates can be modelled by means of a non-linear PDE which is strictly related to the Gross-Pitaevskii and the complex Ginzburg-Landau equations. Numerical simulations of this equation are used to investigate the robustness of the rotating vortex lattice which is predicted to spontaneously form in a non-equilibrium trapped condensate. An idea for a polariton-based gyroscope is then presented. The device relies on peculiar properties of non-equilibrium condensates - the possibility of controlling the vortex emission mechanism and the use of pumping strength as a control parameter - and improves on existing proposals for superfluid-based gyroscopes. Finally, the important rôle played by quantum pressure in the recently observed transition from a phase-locked but freely flowing condensate to a spatially trapped one is discussed. The second part of this thesis presents work done in the context of the geometrical models of matter framework, which aims to describe particles in terms of 4-dimensional manifolds. Conserved quantum numbers of particles are encoded in the topology of the manifold, while dynamical quantities are to be described in terms of its geometry. Two infinite families of manifolds, namely ALF gravitational instantons of types A_k and D_k, are investigated as possible models for multi-particle systems. On the basis of their topological and geometrical properties it is concluded that A_k can model a system of k+1 electrons, and D_k a system of a proton and k-1 electrons. Energy functionals which successfully reproduce the Coulomb interaction energy, and in one case also the rest masses, of these particle systems are then constructed in terms of the area and Gaussian curvature of preferred representatives of middle dimension homology. Finally, an idea for constructing multi-particle models by gluing single-particle ones is discussed.
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Hackl, Andreas [Verfasser]. "Quantum criticality and non-equilibrium dynamics in correlated electron systems / Andreas Hackl." Aachen : Shaker, 2010. http://d-nb.info/1122546815/34.
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Buchhold, Michael. "Thermalization and Out-of-Equilibrium Dynamics in Open Quantum Many-Body Systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-181786.
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Thermalization, the evolution of an interacting many-body system towards a thermal Gibbs ensemble after initialization in an arbitrary non-equilibrium state, is currently a phenomenon of great interest, both in theory and experiment. As the time evolution of a quantum system is unitary, the proposed mechanism of thermalization in quantum many-body systems corresponds to the so-called eigenstate thermalization hypothesis (ETH) and the typicality of eigenstates. Although this formally solves the contradiction of thermalizing but unitary dynamics in a closed quantum many-body system, it does neither make any statement on the dynamical process of thermalization itself nor in which way the coupling of the system to an environment can hinder or modify the relaxation dynamics.
In this thesis, we address both the question whether or not a quantum system driven away from equilibrium is able to relax to a thermal state, which fulfills detailed balance, and if one can identify universal behavior in the non-equilibrium relaxation dynamics.
As a first realization of driven quantum systems out of equilibrium, we investigate a system of Ising spins, interacting with the quantized radiation field in an optical cavity. For multiple cavity modes, this system forms a highly entangled and frustrated state with infinite correlation times, known as a quantum spin glass. In the presence of drive and dissipation, introduced by coupling the intra-cavity radiation field to the photon vacuum outside the cavity via lossy mirrors, the quantum glass state is modified in a universal manner. For frequencies below the photon loss rate, the dissipation takes over and the system shows the universal behavior of a dissipative spin glass, with a characteristic spectral density $\\mathcal{A}(\\omega)\\sim\\sqrt{\\omega}$. On the other hand, for frequencies above the loss rate, the system retains the universal behavior of a zero temperature, quantum spin glass. Remarkably, at the glass transition, the two subsystems of spins and photons thermalize to a joint effective temperature, even in the presence of photon loss. This thermalization is a consequence of the strong spin-photon interactions, which favor detailed balance in the system and detain photons from escaping the cavity. In the thermalized system, the features of the spin glass are mirrored onto the photon degrees of freedom, leading to an emergent photon glass phase. Exploiting the inherent photon loss of the cavity, we make predictions of possible measurements on the escaping photons, which contain detailed information of the state inside the cavity and allow for a precise, non-destructive measurement of the glass state.
As a further set of non-equilibrium systems, we consider one-dimensional quantum fluids driven out of equilibrium, whose universal low energy theory is formed by the so-called Luttinger Liquid description, which, due to its large degree of universality, is of intense theoretical and experimental interest. A set of recent experiments in research groups in Vienna, Innsbruck and Munich have probed the non-equilibrium time-evolution of one-dimensional quantum fluids for different experimental realizations and are pushing into a time regime, where thermalization is expected. From a theoretical point of view, one-dimensional quantum fluids are particular interesting, as Luttinger Liquids are integrable and therefore, due to an infinite number of constants of motion, do not thermalize. The leading order correction to the quadratic theory is irrelevant in the sense of the renormalization group and does therefore not modify static correlation functions, however, it breaks integrability and will therefore, even if irrelevant, induce a completely different non-equilibrium dynamics as the quadratic Luttinger theory alone. In this thesis, we derive for the first time a kinetic equation for interacting Luttinger Liquids, which describes the time evolution of the excitation densities for arbitrary initial states. The resonant character of the interaction makes a straightforward derivation of the kinetic equation, using Fermi\'s golden rule, impossible and we have to develop non-perturbative techniques in the Keldysh framework. We derive a closed expression for the time evolution of the excitation densities in terms of self-energies and vertex corrections. Close to equilibrium, the kinetic equation describes the exponential decay of excitations, with a decay rate $\\sigma^R=\\mbox\\Sigma^R$, determined by the self-energy at equilibrium. However, for long times $\\tau$, it also reveals the presence of dynamical slow modes, which are the consequence of exactly energy conserving dynamics and lead to an algebraic decay $\\sim\\tau^$ with $\\eta_D=0.58$. The presence of these dynamical slow modes is not contained in the equilibrium Matsubara formalism, while they emerge naturally in the non-equilibrium formalism developed in this thesis.
In order to initialize a one-dimensional quantum fluid out of equilibrium, we consider an interaction quench in a model of interacting, dispersive fermions in Chap.~\\ref. In this scenario, the fermionic interaction is suddenly changed at time $t=0$, such that for $t>0$ the system is not in an eigenstate and therefore undergoes a non-trivial time evolution. For the quadratic theory, the stationary state in the limit $t\\rightarrow\\infty$ is a non-thermal, or prethermal, state, described by a generalized Gibbs ensemble (GGE). The GGE takes into account for the conservation of all integrals of motion, formed by the eigenmodes of the Hamiltonian. On the other hand, in the presence of non-linearities, the final state for $t\\rightarrow\\infty$ is a thermal state with a finite temperature $T>0$. . The spatio-temporal, dynamical thermalization process can be decomposed into three regimes: A prequench regime on the largest distances, which is determined by the initial state, a prethermal plateau for intermediate distances, which is determined by the metastable fixed point of the quadratic theory and a thermal region on the shortest distances. The latter spreads sub-ballistically $\\sim t^$ in space with $0<\\alpha<1$ depending on the quench. Until complete thermalization (i.e. for times $t<\\infty$), the thermal region contains more energy than the prethermal and prequench region, which is expressed in a larger temperature $T_{t}>T_$, decreasing towards its final value $T_$. As the system has achieved local detailed balance in the thermalized region, energy transport to the non-thermal region can only be performed by the macroscopic dynamical slow modes and the decay of the temperature $T_{t}-T_\\sim t^$ again witnesses the presence of these slow modes. The very slow spreading of thermalization is consistent with recent experiments performed in Vienna, which observe a metastable, prethermal state after a quench and only observe the onset of thermalization on much larger time scales. As an immediate indication of thermalization, we determine the time evolution of the fermionic momentum distribution after a quench from non-interacting to interacting fermions. For this quench scenario, the step in the Fermi distribution at the Fermi momentum $k\\sub$ decays to zero algebraically in the absence of a non-linearity but as a stretched exponential (the exponent being proportional to the non-linearity) in the presence of a finite non-linearity. This can serve as a proof for the presence or absence of the non-linearity even on time-scales for which thermalization can not yet be observed.
Finally, we consider a bosonic quantum fluid, which is driven away from equilibrium by permanent heating. The origin of the heating is atomic spontaneous emission of laser photons, which are used to create a coherent lattice potential in optical lattice experiments. This process preserves the system\'s $U(1)$-invariance, i.e. conserves the global particle number, and the corresponding long-wavelength description is a heated, interacting Luttinger Liquid, for which phonon modes are continuously populated with a momentum dependent rate $\\partial_tn_q\\sim\\gamma |q|$. In the dynamics, we identify a quasi-thermal regime for large momenta, featuring an increasing time-dependent effective temperature. In this regime, due to fast phonon-phonon scattering, detailed balance has been achieved and is expressed by a time-local, increasing temperature. The thermal region emerges locally and spreads in space sub-ballistically according to $x_t\\sim t^{4/5}$. For larger distances, the system is described by an non-equilibrium phonon distribution $n_q\\sim |q|$, which leads to a new, non-equilibrium behavior of large distance observables. For instance, the phonon decay rate scales universally as $\\gamma_q\\sim |q|^{5/3}$, with a new non-equilibrium exponent $\\eta=5/3$, which differs from equilibrium. This new, universal behavior is guaranteed by the $U(1)$ invariant dynamics of the system and is insensitive to further subleading perturbations. The non-equilibrium long-distance behavior can be determined experimentally by measuring the static and dynamic structure factor, both of which clearly indicate the exponents for phonon decay, $\\eta=5/3$ and for the spreading of thermalization $\\eta_T=4/5$.
Remarkably, even in the presence of this strong external drive, the interactions and their aim to achieve detailed balance are strong enough to establish a locally emerging and spatially spreading thermal region.
The physical setups in this thesis do not only reveal interesting and new dynamical features in the out-of-equilibrium time evolution of interacting systems, but they also strongly underline the high degree of universality of thermalization for the classes of models studied here. May it be a system of coupled spins and photons, where the photons are pulled away from a thermal state by Markovian photon decay caused by a leaky cavity, a one-dimensional fermionic quantum fluid, which has been initialized in an out-of-equilibrium state by a quantum quench or a one-dimensional bosonic quantum fluid, which is driven away from equilibrium by continuous, external heating, all of these systems at the end establish a local thermal equilibrium, which spreads in space and leads to global thermalization for $t\\rightarrow\\infty$. This underpins the importance of thermalizing collisions and endorses the standard approach of equilibrium statistical mechanics, describing a physical system in its steady state by a thermal Gibbs ensemble.
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Bertini, Bruno. "Non-equilibrium dynamics of interacting many-body quantum systems in one dimension." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:1e2c50b9-73b3-4ca0-a5f3-276f967c3720.
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In this thesis we study three examples of interacting many-body systems undergoing a non equilibrium time evolution. Firstly we consider the time evolution in an integrable system: the sine-Gordon field theory in the repulsive regime. We will focus on the one point function of the semi-local vertex operator eiβφ(x)/2 on a specific class of initial states. By analytical means we show that the expectation value considered decays exponentially to zero at late times and we determine the decay time. The method employed is based on a form-factor expansion and uses the "Representative Eigenstate Approach" of Ref. [73] (a.k.a. "Quench Action"). In a second example we study the time evolution in models close to "special" integrable points characterised by hidden symmetries generating infinitely many local conservation laws that do not commute with one another, in addition to the infinite commuting family implied by integrability. We observe that both in the case where the perturbation breaks the integrability and when it breaks only the additional symmetries maintaining integrability, the local observables show a crossover behaviour from an initial to a final quasi stationary plateau. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin-1/2 chain with additional perturbations that break integrability. Finally, we study the effects of integrability breaking perturbations on the non-equilibrium evolution of more general many-particle quantum systems, where the unperturbed integrable model is generic. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalisations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalisation group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalisation plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalisation plateaux towards thermal behaviour. We identify a time scale characterising this crossover.
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Kleinert, Philipp Thomas. "Gauge/gravity duality and non-equilibrium dynamics of strongly coupled quantum systems." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:6f5de56f-8efa-4caf-a9bc-4ec951bfc69d.
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This thesis explores applications of gauge/gravity duality to strongly coupled quantum field theories out of equilibrium. Within the framework of holography, it addresses both small deviations from equilibrium accessible via the effective theory of hydrodynamics, as well as far-from-equilibrium dynamics, which are studied using a first-principles approach. After an introduction into the duality and a presentation of the two approaches to out-of-equilibrium physics, we present our results on holographic fluids in the first part of the thesis. We derive new Kubo formulae for five second-order transport coefficients of relativistic non-conformal fluids and apply them to a class of non-conformal holographic field theories at infinite coupling. We find strong evidence that the Haack-Yarom identity, which is known to hold for conformal holographic fluids at infinite coupling, is universally satisfied by strongly coupled fluids regardless of conformal symmetry. We prove analytically that the identity is obeyed when taking into account leading non-conformal corrections and provide numerical evidence that the result holds beyond these leading corrections. In the second part of the thesis, we examine two proposals for the holographic dictionary for correlation functions in out-of-equilibrium states. We show that these proposals are equivalent on the level of two-point functions of operators dual to free scalar bulk fields. We then use one of the two non-equilibrium dictionaries to study the thermalisation of two-point functions of scalar operators and effective occupation numbers in a holographic model of quantum quenches. We find that both thermalise with a rate set by the lowest quasinormal mode of the final-state black hole in the gravitational dual.
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Chiocchetta, Tomelleri Alessio. "A study on non-equilibrium dynamics in isolated and open quantum systems." Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/4909.
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Grujic, Thomas. "Non-equilibrium strongly-correlated quantum dynamics in photonic resonator arrays." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:6ca48890-b5ab-4572-9430-c3c0c7bd8d72.
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Strong effective photon-photon interactions mediated by atom-photon couplings have been routinely achievable in QED setups for some time now. Recently, there have been several proposals to push the physics of interacting photons into many- body distributed architectures. The essential idea is to coherently couple together arrays of QED resonators, such that photons can hop between resonators while interacting with each other inside each resonator. These proposed structures have attracted intense theoretical attention while simultaneously inspiring experimental efforts to realise this novel regime of strongly-correlated many-body states of light. A central challenge of both theoretical and practical importance is to understand the physics of such coupled resonator arrays (CRAs) beyond equilibrium, when unavoidable (or sometimes even desired) photon loss processes are accounted for. This thesis presents several studies whose purpose can roughly be divided in two aims. The first part studies just what constitutes a valid physical and computational representation of non-equilibrium driven-dissipative CRAs. Addressing these ques- tions constitutes essential groundwork for further investigations of CRA phenomena, as numerical experiments are likely to guide and interpret near-future experimen- tal array observations. The relatively small body of existing work on CRAs out of equilibrium has often truncated their full, rich physics. It is important to establish the effects and validity of these approximations. To this end we introduce powerful numerical algorithms capable of efficiently simulating the full dynamics of CRAs, and use them to characterise the non-equilibrium steady states of arrays reached under the combined influence of dissipation and pumping. Having established the rigour necessary to realistically describe CRAs, we exam- ine two novel phenomena observable in near-future small arrays. Firstly we relate a counter-intuitive ‘super bunching’ in the statistics of photons emitted from arrays engineered to demonstrate strong effective photon-photon repulsion at the single and two-photon level, to an interplay between the underlying eigen-structure and details of the non-equilibrium operation. Secondly we characterise a dynamical phenomenon in which domains of ‘frozen’ photons remain trapped in sufficiently nonlinear arrays. Finally we present a preliminary characterisation of a previously unexplored phase diagram of arrays under coherent two-photon pumping. Com- petition between the coherence injected by the pumping, photon interactions and delocalisation processes lead to interesting new physical signatures.
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Gagel, Pia [Verfasser], and J. [Akademischer Betreuer] Schmalian. "Universal non-equilibrium dynamics in quantum critical systems / Pia Gagel ; Betreuer: J. Schmalian." Karlsruhe : KIT-Bibliothek, 2018. http://d-nb.info/1174252197/34.
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Cevolani, Lorenzo. "Out-Of-Equilibrium Dynamics and Locality in Long-Range Many-Body Quantum Systems." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLO011/document.
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Cette thèse présente une étude des propagations des corrélations dans les systèmes avec interaction de longue portée. La dynamique des observables locales ne peut pas être décrite avec les méthodes utilisées pour la physique statistique à l’équilibre et les approches complètement nouvelles doivent être développées. Différentes bornes sur l’évolution temporelle des corrélations ont été dérivées, mais la dynamique réelle trouvée dans des données expérimentales et numériques est beaucoup plus compliquée avec différents régimes de propagation. Une approche plus spécifique est donc nécessaire pour comprendre ces phénomènes. Nous présentons une méthode analytique pour décrire l’évolution temporelle d’observables génériques dans des systèmes décrits par des hamiltoniens quadratiques avec interactions de courte et longue portée. Grâce ces expressions, la propagation des observables peut être interprétée comme la propagation des excitations du système. Nous appliquons cette méthode générique à un modèle de spins et on obtient trois régimes différents. Ils peuvent être directement expliqués qualitativement et quantitativement par les divergences du spectre des excitations. Le résultat le plus important est le fait que la propagation, là où elle n’est pas instantanée, est au plus balistique, voir plus lente, alors les bornes permettent une propagation significativement plus rapide. On applique les mêmes expressions analytiques à un système de bosons sur un réseau avec interaction de longue et courte portée. Nous étudions les corrélations à deux corps qui ont un comportement toujours balistique et les corrélations à un corps qui ont un comportement plus riche. Cet effet peut être expliqué en calculant la contribution aux deux observables des différentes excitations qui déterminent les parties du spectre contribuant à l’observable. Ces résultats démontrent que la propagation des observables n’est pas déterminée uniquement par le spectre des excitations mais également par des quantités qui dépendent de l’observable et qui peuvent changer complètement le régime de propagationIn this thesis we present our results on the propagation of correlations in long-range interacting quantum systems. The dynamics of local observables in these systems cannot be described with the standard methods used in equilibrium statistical physics and completely new methods have to be developed. Several bounds on the time evolution of correlations have been derived for these systems. However the propagation found in experimental and numerical results is completely different and several regimes are present depending on the long-range character of the interactions. Here we present analytical expressions to describe the time evolution of generic observables in systems where the Hamiltonian takes a quadratic form with long- and short-range interactions. These expressions describe the spreading of local observables as the spreading of the fundamental excitations of the system. We apply these expressions to a spin model finding three different propagation regimes. They can be described qualitatively et quantitatively by the divergences in the energy spectrum. The most important result is that the propagation is at most ballistic, but it can be also significantly slower, where the general bounds predict a propagation faster than ballistic. This points out that the bounds are not able to describe properly the propagation, but a more specific approach is needed. We then move to a system of lattice bosons interacting via long-range interactions. In this case we study two different observables finding completely different results for the same interactions: the spreading of two-body correlations is always ballistic while the one of the one-body correlations ranges from faster-than-ballistic to ballistic. Using our general analytic expressions we find that different parts of the spectrum contribute differently to different observables determining the previous differences. This points out that an observable-dependent notion of locality, missing in the general bounds, have to be developed to correctly describe the time evolution
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LEGGIO, Bruno. "Quantum fluctuations and correlations in equilibrium and nonequilibrium thermodynamics." Doctoral thesis, Università degli Studi di Palermo, 2014. http://hdl.handle.net/10447/90914.
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Faye), Morris Jennifer F. (Jennifer. "Combining a renewable portfolio standard with a cap-and-trade policy : a general equilibrium analysis." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/53062.
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Thesis (S.M. in Technology and Policy)--Massachusetts Institute of Technology, Engineering Systems Division, Technology and Policy Program, 2009.Includes bibliographical references (p. 68-71).
Most economists see incentive-based measures such a cap-and-trade system or a carbon tax as cost effective policy instruments for limiting greenhouse gas emissions. In actuality, many efforts to address GHG emissions combine a cap-and-trade system with other regulatory instruments. This raises an important question: What is the effect of combining a cap-and-trade policy with policies targeting specific technologies? To investigate this question I focus on how a renewable portfolio standard (RPS) interacts with a cap-and-trade policy. An RPS specifies a certain percentage of electricity that must come from renewable sources such as wind, solar, and biomass. I use a computable general equilibrium (CGE) model, the MIT Emissions Prediction and Policy Analysis (EPPA) model, which is able to capture the economy-wide impacts of this combination of policies. I have represented renewables in this model in two ways. At lower penetration levels renewables are an imperfect substitute for other electricity generation technologies because of the variability of resources like wind and solar. At higher levels of penetration renewables are a higher-cost prefect substitute for other generation technologies, assuming that with the extra cost the variability of the resource can be managed through backup capacity, storage, long range transmissions and strong grid connections. To represent an RPS policy, the production of every kilowatt hour of electricity from non-renewable sources requires an input of a fraction of a kilowatt hour of electricity from renewable sources.
(cont.) The fraction is equal to the RPS target. I find that adding an RPS requiring 25 percent renewables by 2025 to a cap that reduces emissions by 80% below 1990 levels by 2050 increases the welfare cost of meeting such a cap by 27 percent over the life of the policy, while reducing the CO2-equivalent price by about 8 percent each year.
by Jennifer F. Morris.
S.M.in Technology and Policy
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Hild, Sebastian [Verfasser], and Immanuel [Akademischer Betreuer] Bloch. "Microscopy of quantum many-body systems out of equilibrium / Sebastian Hild ; Betreuer: Immanuel Bloch." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2016. http://d-nb.info/111747416X/34.
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Klöckner, Christian Friedrich [Verfasser]. "Functional Renormalization Group Approach to Correlated Quantum Systems Far from Equilibrium / Christian Friedrich Klöckner." Berlin : Freie Universität Berlin, 2019. http://d-nb.info/1192755561/34.
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Klöckner, Christian [Verfasser]. "Functional Renormalization Group Approach to Correlated Quantum Systems Far from Equilibrium / Christian Friedrich Klöckner." Berlin : Freie Universität Berlin, 2019. http://d-nb.info/1192755561/34.
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Scarlatella, Orazio. "Driven-Dissipative Quantum Many-Body Systems." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS281/document.
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Ma thèse de doctorat était consacrée à l'étude des systèmes quantiques à plusieurs corps dissipatifs et pilotés. Ces systèmes représentent des plateformes naturelles pour explorer des questions fondamentales sur la matière dans des conditions de non-équilibre, tout en ayant un impact potentiel sur les technologies quantiques émergentes. Dans cette thèse, nous discutons d'une décomposition spectrale de fonctions de Green de systèmes ouverts markoviens, que nous appliquons à un modèle d'oscillateur quantique de van der Pol. Nous soulignons qu’une propriété de signe des fonctions spectrales des systèmes d’équilibre ne s’imposait pas dans le cas de systèmes ouverts, ce qui produisait une surprenante "densité d’états négative", avec des conséquences physiques directes. Nous étudions ensuite la transition de phase entre une phase normale et une phase superfluide dans un système prototype de bosons dissipatifs forcés sur un réseau. Cette transition est caractérisée par une criticité à fréquence finie correspondant à la rupture spontanée de l'invariance par translation dans le temps, qui n’a pas d’analogue dans des systèmes à l’équilibre. Nous discutons le diagramme de phase en champ moyen d'une phase isolante de Mott stabilisée par dissipation, potentiellement pertinente pour des expériences en cours. Nos résultats suggèrent qu'il existe un compromis entre la fidélité de la phase stationnaire à un isolant de Mott et la robustesse d'une telle phase à taux de saut fini. Enfin, nous présentons des développements concernant la théorie du champ moyen dynamique (DMFT) pour l’étude des systèmes à plusieurs corps dissipatifs et forcés. Nous introduisons DMFT dans le contexte des modèles dissipatifs et forcés et nous développons une méthode pour résoudre le problème auxiliaire d'une impureté couplée simultanément à un environnement markovien et à un environnement non-markovien. À titre de test, nous appliquons cette nouvelle méthode à un modèle simple d’impureté fermioniqueMy PhD was devoted to the study of driven-dissipative quantum many-body systems. These systems represent natural platforms to explore fundamental questions about matter under non-equilibrium conditions, having at the same time a potential impact on emerging quantum technologies. In this thesis, we discuss a spectral decomposition of single-particle Green functions of Markovian open systems, that we applied to a model of a quantum van der Pol oscillator. We point out that a sign property of spectral functions of equilibrium systems doesn't hold in the case of open systems, resulting in a surprising ``negative density of states", with direct physical consequences. We study the phase transition between a normal and a superfluid phase in a prototype system of driven-dissipative bosons on a lattice. This transition is characterized by a finite-frequency criticality corresponding to the spontaneous break of time-translational invariance, which has no analog in equilibrium systems. Later, we discuss the mean-field phase diagram of a Mott insulating phase stabilized by dissipation, which is potentially relevant for ongoing experiments. Our results suggest that there is a trade off between the fidelity of the stationary phase to a Mott insulator and robustness of such a phase at finite hopping. Finally, we present some developments towards using dynamical mean field theory (DMFT) for studying driven-dissipative lattice systems. We introduce DMFT in the context of driven-dissipative models and developed a method to solve the auxiliary problem of a single impurity, coupled simultaneously to a Markovian and a non-Markovian environment. As a test, we applied this novel method to a simple model of a fermionic, single-mode impurity
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Ozaki, Junichi. "Dynamical quantum effects in cluster dynamics of Fermi systems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199083.
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Cavina, Vasco. "Thermodynamics of open quantum systems: from a critical study to the optimization of non-equilibrium heat engines." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85921.
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One of the most relevant aspects of thermodynamics is its universality. Its prescriptions
are ubiquitous in the characterizaton of the energy transfer between systems
at equilibrium, even at the nanoscale, where quantum effects start to become important.
In these models the energy balance is completely described in terms of universal
quantities, like the Helmoltz free energy and the Boltzmann entropy, while the probabilistic
fluctations of work, heat end particle number are tipically negligible making
equilibirum thermodynamics essentially a deterministic theory. There are, however,
plenty of fields in which the equilibrium approach is too limiting, for instance when
dealing with steady state and driven heat engines, researching efficient quantum probes
in metrology and even studying decoherence phenomena in quantum computation. In
the non equilibrium scenario many specific details, usually negligible in the standard
approach, become relevant and a more accurate knowledge of the dynamics is necessary
to improve the capacity of controlling, measuring and manipulating energy, whose puctuations also become larger and larger making the theory intrinsecally stochastic.
The characterization of out of equilibrium quantum system is the principal aim
of this manuscript, which encompasses several aspects of the field. A perturbative
expansion for slowly driven master equations is derived, reproducing the quasi static
equilibrium trajectory for infinitely slow modulations and providing a compact formula
for calculating the deviations on such a behavior. The expansion turns also
to be succesful for the description of low dissipation heat engines, providing interesting
connections between some celebrated efficiencies at maximum power (like the
Schmiedl Seifert and Curzon Ahlborn ones [34, 37]) and the spectral density of the
baths inducing thermalization.
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Leyton, Ortega Vicente Ancelmo [Verfasser], and Michael [Akademischer Betreuer] Thorwart. "Quantum noise in nonlinear nanoscale systems out of equilibrium / Vicente Ancelmo Leyton Ortega. Betreuer: Michael Thorwart." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1030366446/34.
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Ceballos, Russell R. "G-CONSISTENT SUBSETS AND REDUCED DYNAMICAL QUANTUM MAPS." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1434.
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A quantum system which evolves in time while interacting with an external environ- ment is said to be an open quantum system (OQS), and the influence of the environment on the unperturbed unitary evolution of the system generally leads to non-unitary dynamics. This kind of open system dynamical evolution has been typically modeled by a Standard Prescription (SP) which assumes that the state of the OQS is initially uncorrelated with the environment state. It is here shown that when a minimal set of physically motivated assumptions are adopted, not only does there exist constraints on the reduced dynamics of an OQS such that this SP does not always accurately describe the possible initial cor- relations existing between the OQS and environment, but such initial correlations, and even entanglement, can be witnessed when observing a particular class of reduced state transformations termed purity extractions are observed. Furthermore, as part of a more fundamental investigation to better understand the minimal set of assumptions required to formulate well defined reduced dynamical quantum maps, it is demonstrated that there exists a one-to-one correspondence between the set of initial reduced states and the set of admissible initial system-environment composite states when G-consistency is enforced. Given the discussions surrounding the requirement of complete positivity and the reliance on the SP, the results presented here may well be found valuable for determining the ba- sic properties of reduced dynamical maps, and when restrictions on the OQS dynamics naturally emerge.
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Wald, Sascha Sebastian. "Thermalisation and Relaxation of Quantum Systems." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0129/document.
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Cette thèse traite la dynamique hors équilibre des systèmes quantiques ouverts couplés à un réservoir externe. Un modèle spécifique exactement soluble, le modèle sphérique, sert comme exemple paradigmatique. Ce modèle se résout exactement en toute dimension spatiale et pour des interactions très générales. Malgré sa simplicité technique, ce modèle est intéressant car ni son comportement critique d’équilibre ni celui hors équilibre est du genre champ moyen. La présentation débute avec une revue sur la mécanique statistique des transitions de phases classique et quantique, et sur les propriétés du modèle sphérique. Sa dynamique quantique ne se décrit point à l’aide d’une équation de Langevin phénoménologique. Une description plus complète à l’aide de la théorie de l’équation de Lindblad est nécessaire. Les équations de Lindblad décrivent la relaxation d’un système quantique vers son état d’équilibre. En tant que premier exemple, le diagramme de phases dynamique d’un seul spin sphérique quantique est étudié. Réinterprétant cette solution en tant qu’une approximation champ moyen d’un problème de N corps, le diagramme de phases quantique est établi et un effet « congeler en réchauffant » quantique est démontré. Ensuite, le formalisme de Lindblad est généralisé au modèle sphérique quantique de N particules: primo, la forme précise de l’équation de Lindblad est obtenue des conditions que (i) l’état quantique d’équilibre exacte est une solution stationnaire de l’équation de Lindblad et (ii) dans le limite classique, l’équation Langevin de mouvement est retrouvée. Secundo, le modèle sphérique permet la réduction exacte du problème de N particules à une seule équation intégro-différentielle pour le paramètre sphérique. Tertio, en résolvant pour le comportement asymptotique des temps longs de cette équation, nous démontrons que dans la limite semi-classique, la dynamique quantique effective redevient équivalente à une dynamique classique, à une renormalisation quantique de la température T près. Quarto, pour une trempe quantique profonde dans la phase ordonnée, nous démontrons que la dynamique quantique dépend d’une manière non triviale de la dimension spatiale. L’émergence du comportement d’échelle dynamique et des corrections logarithmiques est discutée en détail. Les outils mathématiques de cette analyse sont des nouveaux résultats sur le comportement asymptotique de certaines fonctions hypergéométriques confluentes en deux variablesThis study deals with the dynamic properties of open quantum systems far from equilibrium in d dimensions. The focus is on a special, exactly solvable model, the spherical model (SM), which is technically simple. The analysis is of interest, since the critical behaviour in and far from equilibrium not of mean-field type. We begin with a résumé of the statistical mechanics of phase transitions and treat especially the quantum version of the SM. The quantum dynamics (QD) of the model cannot be described by phenomenological Langevin equation and must be formulated with Lindblad equations.First we examine the dynamic phase diagram of a single spherical quantum spin and interpret the solution as a mean-field approximation of the N-body problem. Hereby, we find a quantum mechanical ‘freezing by heating’ effect. After that, we extend the formalism to the N-body problem, determining first the form of the Lindblad equation from consistency conditions. The SM then allows the reduction to a single integro-differential equation whose asymptotic solution shows, that the effective QD in the semi-classical limit is fully classical. For a deep quench in the ordered phase, we show that the QD strongly and non-trivially depends on d and derive the dynamic scaling behaviour and its corrections. The mathematical tools for this analysis are new results on the asymptotic behaviour of certain confluent hypergeometric functions in two variables
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Karevski, Dragi. "Ising Quantum Chains." Habilitation à diriger des recherches, Université Henri Poincaré - Nancy I, 2005. http://tel.archives-ouvertes.fr/hal-00113500.
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The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical properties of the quantum chain. The remaining part is devoted to the nonequilibrium dynamical behaviour of such quantum chains relaxing from a nonequilibrium pure initial state. In particular, a special attention is made on the relaxation of transverse magnetization. Two-time linear response functions and correlation functions are also considered, giving insights on the nature of the final nonequilibrium stationnary state. The possibility of aging is also discussed.
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Al-Abbasi, Omar Abdulaziz. "Modeling the Non-Equilibrium Behavior of Chemically Reactive Atomistic Level Systems Using Steepest-Entropy-Ascent Quantum Thermodynamics." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/24069.
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Predicting the kinetics of a chemical reaction is a challenging task, particularly for systems in states far from equilibrium. This work discusses the use of a relatively new theory known as intrinsic quantum thermodynamics (IQT) and its mathematical framework steepest-entropy-ascent quantum thermodynamics (SEA-QT) to predict the reaction kinetics at atomistic levels of chemically reactive systems in the non-equilibrium realm. IQT has emerged over the last three decades as the theory that not only unifies two of the three theories of physical reality, namely, quantum mechanics (QM), and thermodynamics but as well provides a physical basis for both the entropy and entropy production. The SEA-QT framework is able to describe the evolution in state of a system undergoing a dissipative process based on the principle of steepest-entropy ascent or locally-maximal-entropy generation. The work presented in this dissertation demonstrates for the first time the use of the SEA-QT framework to model the evolution in state of a chemically reactive system as its state relaxes to stable equilibrium. This framework brings a number of benefits to the field of reaction kinetics. Among these is the ability to predict the unique non-equilibrium (kinetic) thermodynamic path which the state of the system follows in relaxing to stable equilibrium. As a consequence, the reaction rate kinetics at every instant of time is known as are the chemical affinities, the reaction coordinates, the direction of reaction, the activation energies, the entropy, the entropy production, etc. All is accomplished without any limiting assumption of stable or pseudo-stable equilibrium. The objective of this work is to implement the SEA-QT framework to describe the chemical reaction process as a dissipative one governed by the laws of quantum mechanics and thermodynamics and to extract thermodynamic properties for states that are far from equilibrium. The F+H2-->HF+H and H+F2-->HF+F reaction mechanisms are used as model problems to implement this framework.Ph. D.
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Minganti, Fabrizio. "Out-of-Equilibrium Phase Transitions in Nonlinear Optical Systems." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC004/document.
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Dans cette thèse nous étudions théoriquement de systèmes dissipatifs pompés,décrits par une équation maîtresse de Lindblad. En particulier, nous adressons les problématiques liés à l’émergence de phénomènes critiques. Nous présentons une théorie générale reliant les transitions de phase du premier et deuxième ordres aux propriétés spectrales du superopérateur liouvillien. Dans la région critique, nous déterminons la forme générale de l’état stationnaire et de la matrice propre du liouvillien associée à son gap spectral. Nous discutons aussi l’utilisation de trajectoires quantiques individuelles afin de révéler l’apparition des transitions de phase. En ayant dérivé une théorie générale, nous étudions le modèle de Kerr en présence de pompage à un photon (cohérent) et à deux photons (paramétrique) ainsi que de dissipation. Nous explorons les propriétés dynamiques d’une transition de phase du premier ordre dans un modèle de Bose-Hubbard dissipatif et d’une de second ordre dans un modèle XYZ dissipatif d’Heisenberg. Enfin, nous avons considéré la physique des cavités soumises à de la dissipation à un et deux photons ainsi qu’un pompage à deux photons, obtenu par ingénierie de réservoirs. Nous avons démontré que l’état stationnaire unique est un mélange statistique de deux états chats de Schrödinger, malgré de fortes pertes à un photon.Nous proposons et étudions un protocole de rétroaction pour la génération d’états chat pursIn this thesis we theoretically study driven-dissipative nonlinear systems, whosedynamics is capture by a Lindblad master equation. In particular, we investigate theemergence of criticality in out-of-equilibrium dissipative systems. We present a generaland model-independent spectral theory relating first- and second-order dissipative phasetransitions to the spectral properties of the Liouvillian superoperator. In the critical region,we determine the general form of the steady-state density matrix and of the Liouvillianeigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We discuss the relevanceof individual quantum trajectories to unveil phase transitions. After these general results,we analyse the inset of criticality in several models. First, a nonlinear Kerr resonator in thepresence of both coherent (one-photon) and parametric (two-photon) driving and dissipation.We then explore the dynamical properties of the coherently-driven Bose-Hubbard and of thedissipative XYZ Heisenberg model presenting a first-order and a second-order dissipativephase transition, respectively. Finally, we investigate the physics of photonic Schrödingercat states in driven-dissipative resonators subject to engineered two-photon processes andone-photon losses. We propose and study a feedback protocol to generate a pure cat-likesteady state
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Robinson, Neil Joe. "Pairing, paramagnetism and prethermalization in strongly correlated low-dimensional quantum systems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:167d164c-e318-49b3-83ea-69b54ec531e0.
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Quasi-one-dimensional quantum models are ideal for theoretically exploring the physical phenomena associated with strong correlations. In this thesis we study three examples where strong correlations play an important role in the static or dynamic properties of the system. Firstly, we examine the behaviour of a doped fermionic two-leg ladder in which umklapp interactions are present. Such interactions arise at special band fillings and can be induced by the formation of charge density wave order in an array of two-leg ladders with long-range (three-dimensional) interactions. For the umklapp which arises from the half-filling of one of the bands, we show that the low-energy theory has a number of phases, including a strong coupling regime in which the dominant fluctuations are superconducting in nature. These superconducting fluctuations carry a finite wave vector – they are the one-dimensional analogue of Fulde-Ferrell-Larkin-Ovchinnikov superconductivity. In a second example, we consider a quantum spin model which captures the essential one-dimensional physics of CoNb2O6, a quasi-one-dimensional Ising ferromagnet. Motivated by high-resolution inelastic neutron scattering experiments, we calculate the dynamical structure in the paramagnetic phase and show that a small misalignment of the transverse field can lead to quasi-particle breakdown – a surprising broadening in the single particle mode observed in experiment. Finally, we study the out-of-equilibrium dynamics of a model with tuneable integrability breaking. When integrability is broken by the presence of weak interactions, we show that the system relaxes to a non-thermal state on intermediate time scales, the so-called “prethermalization plateau”. We describe the approximately stationary behaviour in this regime by constructing a generalised Gibbs ensemble with charges deformed to leading order in perturbation theory. Expectation values of these charges are time-independent, but interestingly the charges do not commute with the Hamiltonian to leading order in perturbation theory. Increasing the strength of the integrability breaking interactions leads to behaviour compatible with thermalisation. In each case we use a combination of perturbative analytical calculations and non-perturbative numerical computations to study the problem at hand.
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Erne, Sebastian Anton [Verfasser], and Thomas [Akademischer Betreuer] Gasenzer. "Far-From-Equilibrium Quantum Many-Body Systems: From Universal Dynamics to Statistical Mechanics / Sebastian Anton Erne ; Betreuer: Thomas Gasenzer." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177252805/34.
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Younis, Aimen M. "Modeling the Non-equilibrium Phenomenon of Diffusion in Closed and Open Systems at an Atomistic Level Using Steepest-Entropy-Ascent Quantum Thermodynamics." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/55127.
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Intrinsic quantum Thermodynamics (IQT) is a theory that unifies thermodynamics and quantum mechanics into a single theory. Its mathematical framework, steepest-entropy-ascent quantum thermodynamics (SEAQT), can be used to model and describe the non-equilibrium phenomenon of diffusion based on the principle of steepest-entropy ascent. The research presented in this dissertation demonstrates the capability of this framework to model and describe diffusion at atomistic levels and is used here to develop a non-equilibrium-based model for an isolated system in which He3 diffuses in He4. The model developed is able to predict the non-equilibrium and equilibrium characteristics of diffusion as well as capture the differences in behavior of fermions (He3) and bosons (He4). The SEAQT framework is also used to develop the transient and steady-state model for an open system in which oxygen diffuses through a tin anode. The two forms of the SEAQT equation of motion are used. The first, which only involves a dissipation term, is applied to the state evolution of the isolated system as its state relaxes from some initial non-equilibrium state to stable equilibrium. The second form, the so-called extended SEAQT equation of motion, is applied to the transient state evolution of an open system undergoing a dissipative process as well mass-interactions with two mass reservoirs. In this case, the state of the system relaxes from some initial transient state to steady state. Model predictions show that the non-equilibrium thermodynamic path that the isolated system takes significantly alters the diffusion data from that of the equilibrium-based models for isolated atomistic-level systems found in literature. Nonetheless, the SEAQT equilibrium predications for He3 and He4 capture the same trends as those found in the literature providing a point of validation for the SEAQT framework. As to the SEAQT results for the open system, there is no data in the literature with which to compare since the results presented here are completely original to this work.Ph. D.
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Inkaya, Ugur Yigit. "Ratchet Effect In Mesoscopic Systems." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606929/index.pdf.
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Rectification phenomena in two specific mesoscopic systems are reviewed. The phenomenon
is called ratchet effect, and such systems are called ratchets. In this thesis,
particularly a rocked quantum-dot ratchet, and a tunneling ratchet are considered.
The origin of the name is explained in a brief historical background. Due to rectification,
there is a net non-vanishing electronic current, whose direction can be reversed
by changing rocking amplitude, the Fermi energy, or applying magnetic field
to the devices (for the rocked ratchet), and tuning the temperature (for the tunneling
ratchet). In the last part, a theoretical examination based on the Landauer-Büttiker formalism of mesoscopic quantum transport is presented.
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Buchhold, Michael [Verfasser], Sebastian [Akademischer Betreuer] Diehl, and Walter [Akademischer Betreuer] Hofstetter. "Thermalization and Out-of-Equilibrium Dynamics in Open Quantum Many-Body Systems / Michael Buchhold. Betreuer: Sebastian Diehl. Gutachter: Sebastian Diehl ; Walter Hofstetter." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://d-nb.info/1078205078/34.
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Droenner, Leon Janek [Verfasser], Alexander [Akademischer Betreuer] Carmele, Andreas [Akademischer Betreuer] Knorr, Andreas [Gutachter] Knorr, and Peter [Gutachter] Rabl. "Out-of-equilibrium dynamics of open quantum many-body systems / Leon Janek Droenner ; Gutachter: Andreas Knorr, Peter Rabl ; Alexander Carmele, Andreas Knorr." Berlin : Technische Universität Berlin, 2019. http://d-nb.info/1177881233/34.
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Schmitt, Markus [Verfasser], Stefan [Akademischer Betreuer] Kehrein, Stefan [Gutachter] Kehrein, Reiner [Gutachter] Kree, and Martin [Gutachter] Eckstein. "Dynamics of isolated quantum many-body systems far from equilibrium / Markus Schmitt ; Gutachter: Stefan Kehrein, Reiner Kree, Martin Eckstein ; Betreuer: Stefan Kehrein." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2018. http://d-nb.info/1151398926/34.
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Schmitt, Markus Verfasser], Stefan [Akademischer Betreuer] [Kehrein, Stefan [Gutachter] Kehrein, Reiner [Gutachter] Kree, and Martin [Gutachter] Eckstein. "Dynamics of isolated quantum many-body systems far from equilibrium / Markus Schmitt ; Gutachter: Stefan Kehrein, Reiner Kree, Martin Eckstein ; Betreuer: Stefan Kehrein." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2018. http://d-nb.info/1151398926/34.
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Schiulaz, Mauro. "Ideal quantum glass transitions: many-body localization without quenched disorder?" Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4908.
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In this work the role of disorder, interaction and temperature in the physics of quantum non-ergodic systems is discussed. I first review what is meant by thermalization in closed quantum systems, and how ergodicity is violated in the presence of strong disorder, due to the phenomenon of Anderson localization. I explain why localization can be stable against the addition of weak dephasing interactions, and how this leads to the very rich phenomenology associated with many-body localization. I also briefly compare localized systems with their closest classical analogue, which are glasses, and discuss their similarities and differences, the most striking being that in quantum systems genuine non ergodicity can be proven in some cases, while in classical systems it is a matter of debate whether thermalization eventually takes place at very long times.
Up to now, many-body localization has been studies in the region of strong disorder and weak interaction. I show that strongly interacting systems display phenomena very similar to localization, even in the absence of disorder. In such systems, dynamics starting from a random inhomogeneous initial condition are non-perturbatively slow, and relaxation takes place only in exponentially long times. While in the thermodynamic limit ergodicity is ultimately restored due to rare events, from the practical point of view such systems look as localized on their initial condition, and this behavior can be studied experimentally. Since their behavior shares similarities with both many-body localized and classical glassy systems, these models are termed “quantum glasses”.
Apart from the interplay between disorder and interaction, another important issue concerns the role of temperature for the physics of localization. In non-interacting systems, an energy threshold separating delocalized and localized states exist, termed “mobility edge”. It is commonly believed that a mobility edge should exist in interacting systems, too. I argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile baths that induce global delocalization. I conclude that true non-ergodicity can be present only if the whole spectrum is localized. Therefore, the putative transition as a function of temperature is reduced to a sharp crossover. I numerically show that the previously reported mobility edges can not be distinguished from finite size effects. Finally, the relevance of my results for realistic experimental situations is discussed.