Tesis sobre el tema "Nonequilibrim steady statte"

Cette thèse porte sur la mécanique statistique hors équilibre des réseaux d'oscillateurs harmoniques, et plus particulièrement sur la statistique des fluctuations des flux d'énergie dans ces réseaux. C'est un travail original qui s'intéresse à la théorie mathématique du transport sur des réseaux de systèmes mécaniques. Ces modèles jouent un rôle important dans les développements actuels de la mécanique statistique hors équilibre, aussi bien, au niveau de la théorie que des expériences. En effet, contrairement à la mécanique statistique de l'équilibre qui est une discipline bien établie sur des bases universellement acceptées, la mécanique statistique des systèmes hors équilibre est une théorie naissante dont les bases théoriques sont encore fragiles. Une des avancées les plus marquantes dans son développement durant les dernières décennies est la découverte de relations de fluctuations universelles pour la production d'entropie et de leurs implications pour la théorie de la réponse linéaire.Ce travail consiste à mettre en œuvre l'approche axiomatique des relations de fluctuations des systèmes dynamiques classiques dans le cas des réseaux harmoniques. Il présente une poursuite des travaux de [JPS], où des Principes de Grandes Déviations et des Relations de fluctuations ont été démontrés pour la production d'entropie. Nous visons les statistiques des fluctuations des flux de chaleurs de ces réseaux d'oscillateurs. En une première étape, nous décrivons une condition de contrôlabilité du système d'oscillateurs pour un Principe de Grandes Déviations local et les Relations de fluctuations associées. Ensuite, nous étalons notre discussion et nous dérivons un Principe de Grandes Déviations global en imposant certaines conditions sur le réseau
This thesis focuses on the non-equilibrium statistical mechanics of harmonic oscillator networks, and more particularly on the statistics of fluctuations of energy fluxes in these networks. It is an original work that is related to the mathematical theory of transport on networks of mechanical systems. These models play an important role in the current developments of non-equilibrium statistical mechanics, both in theory and in experiments. Indeed, unlike the statistical mechanics of equilibrium, which is a discipline well established on universally accepted bases, the statistical mechanics of non-equilibrium systems, is a nascent theory whose theoretical bases are still fragile. One of the most significant advance in its development during the recent decades is the discovery of universal fluctuation relationships for the production of entropy and their implications for linear response theory.This work consists in implementing the axiomatic approach of the fluctuation relationships of classical dynamic systems in the case of harmonic networks. It presents a continuation of [JPS], where a Large Deviation Principles and Fluctuation Relations were demonstrated for the entropy production. We aim for statistics of the fluctuations of heat fluxes of these oscillator networks. In a first step, we describe a condition of controllability of the oscillator system to obtain a local Large Deviation Principle and associated Fluctuation Relations. Then, we develop our discussion and derive a global Large Deviation Principle by imposing some condition on the network

We conduct a comprehensive and systematic study of the temporal asymmetries of the fluctuations in properties of nonequilibrium, deterministic and reversible systems. Our motivation stems from the theories that predict asymmetry of fluctuation paths in stochastic dynamics. However, stochastic descriptions are an approximation in the sense that real systems obey deterministic reversible dynamics (at the classical level). In order to understand if the predicted asymmetry is an artifact of the stochastic model, we consider the results from studies of deterministic reversible systems composed of many particles. In order to examine these systems we used molecular dynamics simulations. We thoroughly investigate the presence of temporal asymmetry in the fluctuations of various properties in nonequilibrium, microscopic simulated systems, which are reversible and deterministic. We consider systems undergoing steady state Couette shear flow, and colour diffusion. For the first time we provide light on the particular path by which irreversibility emerges from microscopic reversible dynamics out of equilibrium. Asymmetry appears to be more accentuated in the larger the fluctuations. To assess the generality of temporal asymmetries in such deterministic systems, we consider identification of temporal asymmetries using differences of cross correlation functions: we establish from theoretical arguments and numerical evidence that a microscopic system undergoing colour diffusion exhibits asymmetry in a number of cross correlation functions. Furthermore we prove that some particular cross correlation functions have necessarily to be symmetric for a reversible and deterministic system to be regarded as “physical”. We then demonstrate how to mathematically express the fluctuation paths as a correlation function. We verify with strong numerical evidence that this equivalence holds for a simulated system. In light of this link between the asymmetry of correlation functions and that of fluctuation paths, we explain the presence of asymmetry in fluctuation paths via the transient time correlation formalism. We therefore give the first theoretical justification of the emergence of asymmetry in the fluctuations of microscopic deterministic and reversible systems. In this manner we are able to provide a sound theory to explain and characterize asymmetries in the fluctuations of mesoscopic systems. Finally we briefly outline possible future research directions.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Biomolecular and Physical Sciences
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We investigate the nonequilibrium steady state of driven magnetic flux lines in type-II superconductors subject to strong point or columnar pinning centers and the aging dynamics of nonequilibrium relaxation process in the presence of weak point pinning centers. We employ a three-dimensional elastic line model and Metropolis Monte Carlo simulations. For the first part, we characterize the system by means of the force-velocity / current-voltage curve, static structure factor, mean vortex radius of gyration, number of double-kink and half-loop excitations, and velocity / voltage noise features. We compare the results for the above quantities for randomly distributed point and columnar defects. Most of both numerical works have been done in two-dimensional systems such as thin film in which the structure of flux lines is treated as a point-like particle. Our main point of investigation in this paper is to demonstrate that the vortex structure and its other transport properties may exhibit a remarkable variety of complex phenomena in three-dimensional or bulk superconductors. The second part devotes to the study of aging phenomena in the absence of a driving force in disordered superconductors with much weaker point disorder. By investigating the density autocorrelation function, we observe all three crucial properties of the aging phenomena; slow power-law relaxation, breaking of time-translation invariance, and the presence of the dynamical scaling. We measure the dynamical exponents b and lambda_c/z and compare to other work. We find exponent values increase for increasing pinning strength, smaller interaction range, lower temperature, and denser defect density while the exponents measured in other approach tend to decrease.
Ph. D.

This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.

Bose-Einstein condensation is a collective quantum phenomenon where a macroscopic number of bosons occupies the lowest quantum state. For fixed temperature, bosons condense above a critical particle density. This phenomenon is a consequence of the Bose-Einstein distribution which dictates that excited states can host only a finite number of particles so that all remaining particles must form a condensate in the ground state. This reasoning applies to thermal equilibrium. We investigate the fate of Bose condensation in nonisolated systems of noninteracting Bose gases driven far away from equilibrium. An example of such a driven-dissipative scenario is a Floquet system coupled to a heat bath. In these time-periodically driven systems, the particles are distributed among the Floquet states, which are the solutions of the Schrödinger equation that are time periodic up to a phase factor. The absence of the definition of a ground state in Floquet systems raises the question, whether Bose condensation survives far from equilibrium. We show that Bose condensation generalizes to an unambiguous selection of multiple states each acquiring a large occupation proportional to the total particle number. In contrast, the occupation numbers of nonselected states are bounded from above. We observe this phenomenon not only in various Floquet systems, i.a. time-periodically-driven quartic oscillators and tight-binding chains, but also in systems coupled to two baths where the population of one bath is inverted. In many cases, the occupation numbers of the selected states are macroscopic such that a fragmented condensation is formed according to the Penrose-Onsager criterion. We propose to control the heat conductivity through a chain by switching between a single and several selected states. Furthermore, the number of selected states is always odd except for fine-tuning. We provide a criterion, whether a single state (e.g., Bose condensation) or several states are selected. In open systems, which exchange also particles with their environment, the nonequilibrium steady state is determined by the interplay between the particle-number-conserving intermode kinetics and particle-number-changing pumping and loss processes. For a large class of model systems, we find the following generic sequence when increasing the pumping: For small pumping, no state is selected. The first threshold, where the stimulated emission from the gain medium exceeds the loss in a state, is equivalent to the classical lasing threshold. Due to the competition between gain, loss and intermode kinetics, further transitions may occur. At each transition, a single state becomes either selected or deselected. Counterintuitively, at sufficiently strong pumping, the set of selected states is independent of the details of the gain and loss. Instead, it is solely determined by the intermode kinetics like in closed systems. This implies equilibrium condensation when the intermode kinetics is caused by a thermal environment. These findings agree well with observations of exciton-polariton gases in microcavities. In a collaboration with experimentalists, we observe and explain the pump-power-driven mode switching in a bimodal quantum-dot micropillar cavity
Die Bose-Einstein-Kondensation ist ein Quantenphänomen, bei dem eine makroskopische Zahl von Bosonen den tiefsten Quantenzustand besetzt. Die Teilchen kondensieren, wenn bei konstanter Temperatur die Teilchendichte einen kritischen Wert übersteigt. Da die Besetzungen von angeregten Zuständen nach der Bose-Einstein-Statistik begrenzt sind, bilden alle verbleibenden Teilchen ein Kondensat im Grundzustand. Diese Argumentation ist im thermischen Gleichgewicht gültig. In dieser Arbeit untersuchen wir, ob die Bose-Einstein-Kondensation in nicht wechselwirkenden Gasen fern des Gleichgewichtes überlebt. Diese Frage stellt sich beispielsweise in Floquet-Systemen, welche Energie mit einer thermischen Umgebung austauschen. In diesen zeitperiodisch getriebenen Systemen verteilen sich die Teilchen auf Floquet-Zustände, die bis auf einen Phasenfaktor zeitperiodischen Lösungen der Schrödinger-Gleichung. Die fehlende Definition eines Grundzustandes wirft die Frage nach der Existenz eines Bose-Kondensates auf. Wir finden eine Generalisierung der Bose-Kondensation in Form einer Selektion mehrerer Zustände. Die Besetzung in jedem selektierten Zustand ist proportional zur Gesamtteilchenzahl, während die Besetzung aller übrigen Zustände begrenzt bleibt. Wir beobachten diesen Effekt nicht nur in Floquet-Systemen, z.B. getriebenen quartischen Fallen, sondern auch in Systemen die an zwei Wärmebäder gekoppelt sind, wobei die Besetzung des einen invertiert ist. In vielen Fällen ist die Teilchenzahl in den selektierten Zuständen makroskopisch, sodass nach dem Penrose-Onsager Kriterium ein fragmentiertes Kondensat vorliegt. Die Wärmeleitfähigkeit des Systems kann durch den Wechsel zwischen einem und mehreren selektierten Zuständen kontrolliert werden. Die Anzahl der selektierten Zustände ist stets ungerade, außer im Falle von Feintuning. Wir beschreiben ein Kriterium, welches bestimmt, ob es nur einen selektierten Zustand (z.B. Bose-Kondensation) oder viele selektierte Zustände gibt. In offenen Systemen, die auch Teilchen mit der Umgebung austauschen, ist der stationäre Nichtgleichgewichtszustand durch ein Wechselspiel zwischen der (Teilchenzahl-erhaltenden) Intermodenkinetik und den (Teilchenzahl-ändernden) Pump- und Verlustprozessen bestimmt. Für eine Vielzahl an Modellsystemen zeigen wir folgendes typisches Verhalten mit steigender Pumpleistung: Zunächst ist kein Zustand selektiert. Die erste Schwelle tritt auf, wenn der Gewinn den Verlust in einer Mode ausgleicht und entspricht der klassischen Laserschwelle. Bei stärkerem Pumpen treten weitere Übergänge auf, an denen je ein einzelner Zustand entweder selektiert oder deselektiert wird. Schließlich ist die Selektion überraschenderweise unabhängig von der Charakteristik des Pumpens und der Verlustprozesse. Die Selektion ist vielmehr ausschließlich durch die Intermodenkinetik bestimmt und entspricht damit den oben beschriebenen geschlossenen Systemen. Ist die Kinetik durch ein thermisches Bad hervorgerufen, tritt wie im Gleichgewicht eine Grundzustands-Kondensation auf. Unsere Theorie ist in Übereinstimmung mit experimentellen Beobachtungen von Exziton-Polariton-Gasen in Mikrokavitäten. In einer Kooperation mit experimentellen Gruppen konnten wir den Modenwechsel in einem bimodalen Quantenpunkt-Mikrolaser erklären

Cette thèse examine les propriétés de l’interface entre deux phases dans un système de phases séparées. Nous regardons comment les effets de taille finies modifient les propriétés statistiques de ces interfaces,en particulier comment la dépendance de l’énergie libre par rapport à la taille du système donne lieu à des interactions de Casimir critique à longue portée proche du point critique. Souvent, les interfaces sont décrites par des modèles simplifiés ou coarse-grained dont les seuls degrés de libertés ont les hauteurs de l’interface. Nous rappelons comment les propriétés statiques et dynamiques de ces interfaces sont retrouvées à partir de modèles microscopiques de spins et de la théorie statistique des champs. Nous étudions ensuite les effets de taille finie pour les interfaces continues comme le modèle Edwards-Wilkinson ou discrètes comme le modèle Solid-On-Solid,et discutons leur pertinence dans le cadre de l’effet Casimir critique. Dans la seconde partie de la thèse, nous examinons des modèles d’interfaces sous écoulement possédant des états stationnaires hors-équilibre. Nous développons ces équations dans le cadre du modèle C d’une interface,ayant un état stationnaire hors-équilibre lorsque soumis à un écoulement uniforme. L’état stationnaire hors-équilibre résultant exhibe des propriétés retrouvées dans les expériences sur des colloïdes sous cisaillement ,notamment la suppression des fluctuations de la hauteur de l’interface et une augmentation de la longueur de corrélation des fluctuations. Finalement,nous proposons un nouveau modèle pour des interfaces uni-dimensionnelles qui est une modification du modèle Solid-on-Solid contenant un terme supplémentaire d’entropie, dont la correspondance à des systèmes physiques reste à être trouvée
This thesis examines the properties of the interface between two phases in phase separated systems. We are interested in how finite size effects modify the statistical properties of these interfaces, in particular how the dependence of the free energy on the system size gives rise to long range critical Casimir forces close to thecritical point. Often the interfaces in phase separated systems are described by simplified or coarsegrained models whose only degrees of freedom are the interface height. We review how the statics and dynamics of these interface models can be derived from microscopic spin models and statistical field theories. We then examine finite size effects for continuous interface models such as the Edwards Wilkinson model and discrete models such as the Solid-On-Solid model and discuss their relevance to the critical Casimir effect. In the second part of the thesis we examine models of driven interfaces which have nonequilibrium steady states. We develop a model C type model of an interface which shows a nonequlibrium steady state even with constant driving. The resulting nonequlibrium steady state shows properties seen in experiments on sheared colloidal systems, notably the suppression of height fluctuations but an increase in the fluctuations’correlation length. Finally we propose a new model for one dimensional interfaces which is a modification of the solid on-solid model and containing an extra entropic term ,whose correspondance with physical systems is yet to be found

The understanding of nonequilibrium phenomena, of fundamental importance in statistical physics, has great implications for many physical, chemical, and biological systems. Such phenomena are observed almost everywhere in the natural world. These phenomena are characterized by complicated spatiotemporal evolution. To explore nonequilibrium phenomena we often study simple model systems that embody their essential characteristics. In this thesis, we report the results of our investigations of the statistically steady state properties of three one-dimensional models: multispecies asymmetric simple exclusion processes, the Kuramoto- Sivashinsky equation, and the Burgers equation. The thesis is divided into two parts: Part I and Part II. In Chapters 2–5 of Part I, we present our results for multispecies exclusion models, principally the phase diagrams and statistical properties of their nonequilibrium steady state (NESS). We list below abstracts of these chapters. • In Chapter 2, we consider a multispecies ASEP (mASEP) on a one-dimensional lattice with semipermeable boundaries in contact with particle reservoirs. The mASEP involves ¹2𝑟 ¸1º species of particles: 𝑟 species of positive charges and their negative counterparts as well as vacancies. At the boundaries, a species can replace or be replaced by its negative counterpart. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localization when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks. • In Chapter 3, we study an asymmetric exclusion process with two species and vacancies on an open one-dimensional lattice called the left-permeable ASEP (LPASEP). The left boundary is permeable for the vacancies but the right boundary is not. We find a matrix product solution for the stationary state and the exact stationary phase diagram for the densities and currents. By calculating the density of each species at the boundaries, we find further structure in the stationary phases. In particular, we find that the slower species can reach and accumulate at the far boundary, even in phases where the bulk density of these particles approaches zero. • In Chapter 4, we study a multispecies generalization of the model in Chapter 3. We determine all phases in the phase diagram using an exact projection to the LPASEP solved earlier. In most phases, we observe the phenomenon of dynamical expulsion of one or more species. We explain the density profiles in each phase using interacting shocks. This explanation is corroborated by simulations. • In Chapter 5, we investigate a multispecies generalization of the single-species asymmetric simple exclusion process defined on an open one-dimensional, finite lattice connected to particle reservoirs. At the boundaries, a species can be replaced with any other species. We devise an exact projection scheme to find the phase diagram in terms of densities and currents of all species. In most of the phases, one or more species are absent in the system due to dynamical expulsion. We observe shocks as well in some regions of the phase diagram. We explain the density profiles using a generalized shock structure that is substantiated by numerical simulations. In Chapters 7 and 8 of Part II, we study the statistical properties of turbulent, but statistically steady, states of the Kuramoto-Sivashinsky and the Burgers equations in one dimension. Our main results are summarized below. • In Chapter 7, we investigate the long time and large system size properties of the onedimensional Kuramoto-Sivashinsky equation. Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state of KS deterministic PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile h(x,t) for different initial conditions. We establish, therefore, that the statistical properties of the one-dimensional (1D) KS PDE in this state are in the 1D KPZ universality class. • In Chapter 8, we study the statistical properties of decaying turbulence in the onedimensional Burgers equation, in the vanishing-viscosity limit; we start with random initial conditions, whose energy spectra have simple functional dependences on the wavenumber k: E_0(k) = A \mathcal{E}(k) exp[ - 2 k^2 / k^2_c ] , where A is a positive real number, and k_c is a cutoff wavenumber. The simplest case is the single-power law \mathcal{E}(k) = k^{n}. We focus here on the case of the Gaussian laws which are characterized by E_0(k) = exp[ - 2 (k-k_c)^2 / k^2_c +2 k^2 / k^2_c]; in addition, we consider initial spectra which are combinations of either two or four single-power law spectral regions. For all these initial conditions, we systematize (a) the temporal decay of the total energy, (b) the rich temporal evolution of the energy spectrum, and (c) the spatiotemporal evolution of the velocity field. We present our results in the context of earlier studies of this problem.

The dissipation function is a key quantity in nonequilibrium statistical mechanics. It was originally derived for use in the Evans-Searles Fluctuation Theorem, which quantitatively describes thermal fluctuations in nonequilibrium systems. It is now the subject of a number of other exact results, including the Dissipation Theorem, describing the evolution of a system in time, and the Relaxation Theorem, proving the ubiquitous phenomena of relaxation to equilibrium. The aim of this work is to study the significance of the dissipation function, and examine a number of exact results for which it is the argument. First, we investigate a simple system relaxing towards equilibrium, and use this as a medium to investigate the role of the dissipation function in relaxation. The initial system has a non-uniform density distribution. We demonstrate some of the existing significant exact results in nonequilibrium statistical mechanics. By modifying the initial conditions of our system we are able to observe both monotonic and non-monotonic relaxation towards equilibrium. A direct result of the Evans-Searles Fluctuation Theorem is the Nonequilibrium Partition Identity (NPI), an ensemble average involving the dissipation function. While the derivation is straightforward, calculation of this quantity is anything but. The statistics of the average are difficult to work with because its value is extremely dependent on rare events. It is often observed to converge with high accuracy to a value less than expected. We investigate the mechanism for this asymmetric bias and provide alternatives to calculating the full ensemble average that display better statistics. While the NPI is derived exactly for transient systems it is expected that it will hold in steady state systems as well. We show that this is not true, regardless of the statistics of the calculation. A new exact result involving the dissipation function, the Instantaneous Fluctuation Theorem, is derived and demonstrated computationally. This new theorem has the same form as previous fluctuation theorems, but provides information about the instantaneous value of phase functions, rather than path integrals. We extend this work by deriving an approximate form of the theorem for steady state systems, and examine the validity of the assumptions used.

Quantum systems that are in weak contact with a thermal heat bath will ultimately relax to an equilibrium state which is characterized by the temperature of the environment only. This state is independent of the specific properties of the bath and of how it is coupled to the system. This changes completely, when the system is additionally driven. Such a driven-dissipative situation can emerge, for example, due to an additional time-periodic modulation of the system, or when it is brought into contact with a second bath of different temperature. Then, the system will run into a well-defined nonequilibrium steady state. This state, however, will depend on the very details of the environment and its coupling to the system. We study whether this freedom can be used to engineer interesting properties of quantum systems, which are not found in their equilibrium states, i.e. in the absence of a drive. We focus on bosonic quantum many-body systems. We investigate when far-from-equilibrium ideal gases feature Bose condensation in a group of single-particle states, as opposed to situations where Bose condensation is completely absent in the nonequilibrium steady state. We show that Bose condensation can be induced in a finite one-dimensional ideal gas by the competition of two heat baths whose temperatures both lie well above the equilibrium condensation temperature. This setup also allows to engineer condensation in excited single-particle states. We discuss first ideas to study similar setups in weakly interacting Bose gases. Describing the microscopic dynamics of interacting many-body systems coupled to thermal baths is extremely challenging, due to the fact that generally the full many-body spectrum is inaccessible. Using ideas from semiclassics, we develop an approximation to the dynamics that yields good results at high and intermediate bath temperatures. We also investigate the transient dynamics of driven-dissipative quantum systems. Our studies are motivated by a result that is well known for isolated quantum systems: for a system whose dynamics is generated by a time-periodic Hamiltonian, the stroboscopic dynamics (observed at integer multiples of the driving period) can always be understood as if it would stem from a time-independent Hamiltonian, the Floquet Hamiltonian. For open quantum systems in contact with an environment, we ask if a similar mapping to an effective generator, the Floquet Lindbladian, is always possible. For a simple qubit model we show that there are two extended parameter regions, one in which the Floquet Lindbladian exists, and one in which it does not. We discuss problems of analytical expansions that can give rise to this Floquet Lindbladian and discuss how we can interpret the region where it does not exist. These results are important for dissipative Floquet engineering and open up new perspectives for the control of open quantum systems via time-periodic driving.:1. Introduction 2. Master equation for open quantum systems 3. Existence of the Floquet Lindbladian 4. Number of Bose-selected modes in driven-dissipative ideal Bose gases 5. High-temperature nonequilibrium Bose condensation induced by a hot needle 6. Weakly interacting Bose gases far from thermal equilibrium 7. Summary and outlook
Quantensysteme, die in schwacher Wechselwirkung mit einem thermischen Wärmebad stehen, relaxieren stets in einen Gleichgewichtszustand, welcher allein durch die Temperatur der Umgebung beschrieben ist. Dieser Zustand ist unabhängig von den spezifischen Eigenschaften des Bades, und davon wie dieses an das System gekoppelt ist. Dies ändert sich, wenn das System zusätzlich angetrieben wird. Ein solches getrieben-dissipatives Szenario kann beispielsweise durch einen zusätzlichen zeitperiodischen Antrieb entstehen, oder wenn das System mit einem zweiten Bad unterschiedlicher Temperatur in Kontakt gebracht wird. In diesem Fall läuft das System in einen wohldefinierten stationären Nichtgleichgewichtszustand. Dieser Zustand hängt jedoch von den Details der Umgebung, und davon wie diese an das System gekoppelt ist, ab. Es wird untersucht ob diese Freiheit genutzt werden kann um interessante Eigenschaften von Quantensystemen zu konstruieren, die in deren Gleichgewichtszuständen, d.h. in Abwesenheit des Antriebs, nicht zu finden sind. Der Fokus der Arbeit liegt auf bosonischen Quantenvielteilchensystemen. Es wird ergründet unter welchen Bedingungen ideale Gase fernab des thermischen Gleichgewichts Bose Kondensation in einer Gruppe von Einteilchenzuständen aufweisen, im Gegensatz zu Szenarien in denen überhaupt keine Bose Kondensation im stationären Nichtgleichgewichtszustand auftritt. Weiterhin wird gezeigt, dass Bose Kondensation in einem eindimensionalen idealen Gas durch das Wechselspiel zweier Wärmebäder induziert werden kann. Die Temperatur beider Bäder liegt dabei weit über der Kondensationstemperatur des Gleichgewichts. Diese Anordnung erlaubt außerdem kontrollierte Kondensation in angeregten Einteilchenzuständen. Erste Ideen für das theoretische Studium ähnlicher Anordnungen für schwach wechselwirkende Bosegase werden diskutiert. Eine Beschreibung der mikroskopischen Dynamik wechselwirkender Vielteilchensysteme ist extrem anspruchsvoll, da typischerweise das volle Vielteilchenspektrum unzugänglich ist. Unter Zurhilfenahme semiklassischer Ideen wird eine Näherung der Dynamik entwickelt, welche eine gute Beschreibung für hohe und intermediäre Temperaturen liefert. Weiterhin wird die transiente Dynamik getrieben-dissipativer Quantensysteme untersucht. Die Motivation bietet ein bekanntes Resultat für abgeschlossene Quantensysteme: Für ein System, dessen Dynamik durch einen zeitperiodischen Hamiltonoperator bestimmt ist, kann die stroboskopische Dynamik (unter Beobachtung zu Zeiten, die Vielfache der Antriebsperiode sind) immer so verstanden werden als würde sie von einem zeitunabhängigen Hamiltonoperator, dem Floquet Hamiltonian, induziert. Für offene Quantensysteme im Kontakt mit einer Umgebung wird untersucht ob eine ähnliche Abbildung auf einen effektiven Generator, den Floquet Lindbladian, existiert. Für ein einfaches Qubit Modell wird gezeigt, dass es zwei ausgedehnte Parameterregionen gibt, eine in welcher der Floquet Lindbladian existiert und eine weitere in der dieser nicht existiert. Es werden Probleme von analytischen Entwicklungen des Floquet Lindbladian diskutiert. Auch wird eine Interpretation der Region gegeben, in der dieser nicht existiert. Diese Resultate sind maßgeblich für dissipatives Floquetengineering und eröffnen neue Blickwinkel auf die zeitperiodische Kontrolle offener Quantensysteme.:1. Introduction 2. Master equation for open quantum systems 3. Existence of the Floquet Lindbladian 4. Number of Bose-selected modes in driven-dissipative ideal Bose gases 5. High-temperature nonequilibrium Bose condensation induced by a hot needle 6. Weakly interacting Bose gases far from thermal equilibrium 7. Summary and outlook

Bose-Einstein condensation is a collective quantum phenomenon where a macroscopic number of bosons occupies the lowest quantum state. For fixed temperature, bosons condense above a critical particle density. This phenomenon is a consequence of the Bose-Einstein distribution which dictates that excited states can host only a finite number of particles so that all remaining particles must form a condensate in the ground state. This reasoning applies to thermal equilibrium. We investigate the fate of Bose condensation in nonisolated systems of noninteracting Bose gases driven far away from equilibrium. An example of such a driven-dissipative scenario is a Floquet system coupled to a heat bath. In these time-periodically driven systems, the particles are distributed among the Floquet states, which are the solutions of the Schrödinger equation that are time periodic up to a phase factor. The absence of the definition of a ground state in Floquet systems raises the question, whether Bose condensation survives far from equilibrium. We show that Bose condensation generalizes to an unambiguous selection of multiple states each acquiring a large occupation proportional to the total particle number. In contrast, the occupation numbers of nonselected states are bounded from above. We observe this phenomenon not only in various Floquet systems, i.a. time-periodically-driven quartic oscillators and tight-binding chains, but also in systems coupled to two baths where the population of one bath is inverted. In many cases, the occupation numbers of the selected states are macroscopic such that a fragmented condensation is formed according to the Penrose-Onsager criterion. We propose to control the heat conductivity through a chain by switching between a single and several selected states. Furthermore, the number of selected states is always odd except for fine-tuning. We provide a criterion, whether a single state (e.g., Bose condensation) or several states are selected. In open systems, which exchange also particles with their environment, the nonequilibrium steady state is determined by the interplay between the particle-number-conserving intermode kinetics and particle-number-changing pumping and loss processes. For a large class of model systems, we find the following generic sequence when increasing the pumping: For small pumping, no state is selected. The first threshold, where the stimulated emission from the gain medium exceeds the loss in a state, is equivalent to the classical lasing threshold. Due to the competition between gain, loss and intermode kinetics, further transitions may occur. At each transition, a single state becomes either selected or deselected. Counterintuitively, at sufficiently strong pumping, the set of selected states is independent of the details of the gain and loss. Instead, it is solely determined by the intermode kinetics like in closed systems. This implies equilibrium condensation when the intermode kinetics is caused by a thermal environment. These findings agree well with observations of exciton-polariton gases in microcavities. In a collaboration with experimentalists, we observe and explain the pump-power-driven mode switching in a bimodal quantum-dot micropillar cavity.
Die Bose-Einstein-Kondensation ist ein Quantenphänomen, bei dem eine makroskopische Zahl von Bosonen den tiefsten Quantenzustand besetzt. Die Teilchen kondensieren, wenn bei konstanter Temperatur die Teilchendichte einen kritischen Wert übersteigt. Da die Besetzungen von angeregten Zuständen nach der Bose-Einstein-Statistik begrenzt sind, bilden alle verbleibenden Teilchen ein Kondensat im Grundzustand. Diese Argumentation ist im thermischen Gleichgewicht gültig. In dieser Arbeit untersuchen wir, ob die Bose-Einstein-Kondensation in nicht wechselwirkenden Gasen fern des Gleichgewichtes überlebt. Diese Frage stellt sich beispielsweise in Floquet-Systemen, welche Energie mit einer thermischen Umgebung austauschen. In diesen zeitperiodisch getriebenen Systemen verteilen sich die Teilchen auf Floquet-Zustände, die bis auf einen Phasenfaktor zeitperiodischen Lösungen der Schrödinger-Gleichung. Die fehlende Definition eines Grundzustandes wirft die Frage nach der Existenz eines Bose-Kondensates auf. Wir finden eine Generalisierung der Bose-Kondensation in Form einer Selektion mehrerer Zustände. Die Besetzung in jedem selektierten Zustand ist proportional zur Gesamtteilchenzahl, während die Besetzung aller übrigen Zustände begrenzt bleibt. Wir beobachten diesen Effekt nicht nur in Floquet-Systemen, z.B. getriebenen quartischen Fallen, sondern auch in Systemen die an zwei Wärmebäder gekoppelt sind, wobei die Besetzung des einen invertiert ist. In vielen Fällen ist die Teilchenzahl in den selektierten Zuständen makroskopisch, sodass nach dem Penrose-Onsager Kriterium ein fragmentiertes Kondensat vorliegt. Die Wärmeleitfähigkeit des Systems kann durch den Wechsel zwischen einem und mehreren selektierten Zuständen kontrolliert werden. Die Anzahl der selektierten Zustände ist stets ungerade, außer im Falle von Feintuning. Wir beschreiben ein Kriterium, welches bestimmt, ob es nur einen selektierten Zustand (z.B. Bose-Kondensation) oder viele selektierte Zustände gibt. In offenen Systemen, die auch Teilchen mit der Umgebung austauschen, ist der stationäre Nichtgleichgewichtszustand durch ein Wechselspiel zwischen der (Teilchenzahl-erhaltenden) Intermodenkinetik und den (Teilchenzahl-ändernden) Pump- und Verlustprozessen bestimmt. Für eine Vielzahl an Modellsystemen zeigen wir folgendes typisches Verhalten mit steigender Pumpleistung: Zunächst ist kein Zustand selektiert. Die erste Schwelle tritt auf, wenn der Gewinn den Verlust in einer Mode ausgleicht und entspricht der klassischen Laserschwelle. Bei stärkerem Pumpen treten weitere Übergänge auf, an denen je ein einzelner Zustand entweder selektiert oder deselektiert wird. Schließlich ist die Selektion überraschenderweise unabhängig von der Charakteristik des Pumpens und der Verlustprozesse. Die Selektion ist vielmehr ausschließlich durch die Intermodenkinetik bestimmt und entspricht damit den oben beschriebenen geschlossenen Systemen. Ist die Kinetik durch ein thermisches Bad hervorgerufen, tritt wie im Gleichgewicht eine Grundzustands-Kondensation auf. Unsere Theorie ist in Übereinstimmung mit experimentellen Beobachtungen von Exziton-Polariton-Gasen in Mikrokavitäten. In einer Kooperation mit experimentellen Gruppen konnten wir den Modenwechsel in einem bimodalen Quantenpunkt-Mikrolaser erklären.