Дисертації з теми "Far-from-equilibrium dynamics"

We consider the state of a one-dimensional critical quantum system after a \thermal cut-and-glue quench", which is a local quench in which two independently thermalized halves are connected to form a homogeneous in nite system and left to evolve unitarily until they reach a non-equilibrium steady state (NESS). This quench was studied in [1], and exact CFT results for the current and its uctuations in the NESS were found. We add to these results by studying the growth of entanglement after the quench. Furthermore, we generalise to the case in which the system is not critical, but described by an integrable relativistic quantum eld theory (IQFT) with diagonal scattering, and nd exact expressions for the energy current and scaled cumulant generating function (CGF) in the NESS. Another generalisation we consider is the thermal cut-and-glue quench for N independently thermalised critical one-dimensional systems. These are made to form a quantum junction consisting of N one-dimensional critical systems that are connected at one point in a star graph con guration, with a particular, simple connection condition at the vertex. We nd in this situation the exact energy current and scaled CGF in the NESS. This thesis is based on the publications [2{4], which are incorporated in their published form in Chapters 3 and 4.

This work is centered on the study of self-organisation and pattern formation in a prototypical nanostructured system, namely colloidal nanoparticle assemblies. The particular system chosen for investigation, Au nanocrystals spin cast onto silicon substrates from a solvent, despite being chemically rather simple exhibits a rich variety of complex patterns. In the majority of experiments discussed in this thesis, far-from-equilibrium conditions are attained by a spin-casting process which drives rapid solvent evaporation. A systematic study was carried out to determine the various factors affecting the morphology of nanoparticle assemblies produced in this manner. These factors include the concentration of the nanoparticle solution, the particular solvent used, and the chemical/ physical nature of the substrate. Changing these variables can affect both the strength of interactions between individual nanoparticles and between nanoparticles and the substrate. The various morphologies of the nanoparticle structures produced were studied using atomic force microscopy (AFM). Particular attention is paid to the role of the substrate's surface chemistry in pattern selection. A range of different substrates are used to gauge the influence of differing surface chemistries. In addition, scanning probe lithography was employed to microscopically pattern surfaces. This facilitated the observation of effects caused by the presence of two radically different surface chemistries in the micron size range. This patterning process provides the experimenter some measure of control over the morphology of the nanoparticle assembly, allowing the enforcement of predefined length scales onto the network. Simulations of drying nanocrystal films produced using code written by Martin et al [1] have been shown to accurately reproduce the experimental results. These simulations are used to develop theoretical explanations of the experimental data in terms of the varying solvent evaporation rate on the substrate and the manner by which the solvent dewets on chemically and topologically differing areas of a surface. A remarkable probe-induced coarsening of nanoparticle assemblies by repetitive scanning with an AFM probe has been studied. Repeated scanning of colloidal nanoparticle systems causes the irreversible growth of nanoparticle assemblies. The size distribution of structures produced by this growth is shown to be self-similar. With the size of the domains growing with a power law dependence on scan time. From a combination of these results the growth of structures is explained using a model of coarsening based on cluster diffusion and coalescence. This model is subtly different from coalescence in a thermally driven system due to the novel nature of the mechanical coarsening process. Electrical transport through different array morphologies produced via the spin-coating process was studied using D. C. electrical measurements and electrostatic force microscopy (EFM). Measurements over temperatures ranging from 4.5K to room temperature were made. Variations in the manner that power law scaling of the conduction behaviour alters for different arrays is linked to the topological characteristics of the arrays.

Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of "patterns" learned from previous images as basis elements. The network attempts to do so "sparsely," so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size.
Doctor of Philosophy
Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of “patterns” learned from previous images as basis elements. The network attempts to do so “sparsely,” so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 245-252).
Ultrafast single-shot spectroscopy was developed and improved as a method to observe photoinduced dynamics far from equilibrium. The method was then employed to illuminate material dynamics in platinum-halide quasi-one-dimensional chain compounds (PtI) and in the semimetal bismuth. Both material systems exhibit strongly coupled energetic modes; as a result, their study under laser pulse excitation offers the opportunity to explore the same processes that underlie their unique properties. Our measurements have pushed the photoinduced study of these materials to new extremes toward a better understanding of material response and control far from equilibrium. In this thesis, the single-shot method is introduced and analyzed, and measurements on PtI and bismuth are presented and discussed. Collectively, the measurements offer a view into how materials with strong electron-phonon coupling respond to photoexcitation across dimension, timescale, and excitation density. Dimensionality is explored qualitatively between the PtI chain sample and bismuth samples of varying thickness. The time evolution upon laser excitation is monitored from the instantaneous response out to several hundred picoseconds. The photoexcitation itself is varied from weak (corresponding to most published literature on both materials) to very strong (exceeding the thresholds for visualizing dynamics with conventional methods). We describe our results in the context of material dynamics on the microscale and propose future directions. New dynamics were observed in PtI chains that suggest long-lived structural and electronic states under high irradiation. The possibility of collective structural rearrangement with a long lifetime is proposed. In bismuth, high photoexcitation measurements traversed the material's potential energy surface along the coordinate of structural distortion. We report control of the excitation-dependent photoinduced phase by dimensional constraint, as well as ballistic transport effects that govern this interplay. This research enables future advancements on two fronts. The instrumental developments enable visualization of irreversible events for a wider range of materials. The physical insights gained for the materials studied here characterize key processes pertinent to technological applications and off insights that may govern behavior far from equilibrium for broader classes of materials.
by Johanna Wendlandt Wolfson.
Ph.D.

La plupart des systèmes non linéaires loin de l'équilibre sont sensibles aux fluctuations internes. Dans ce travail, les effets stochastiques dans des modèles génériques de réaction-diffusion sont étudiés à deux échelles différentes. Dans l'approche mésoscopique, l'évolution du système est gouvernée par une équation maîtresse résolue par des simulations de Monte Carlo cinétique. A l'échelle microscopique, des simulations de dynamique des particules sont réalisées. Ces approches stochastiques sont comparées à des équations macroscopiques, déterministes de réaction-diffusion. Dans l'introduction, les différentes échelles, les concepts concernant les systèmes non linéaires et les méthodes numériques utilisées sont présentés. La première partie du chapitre consacré aux résultats est dédiée à l'étude de la perturbation de la distribution des vitesses des particules induite par la réaction pour un système bistable et la propagation d'un front d'onde. Une équation maîtresse incluant cette perturbation est écrite et comparée à des simulations de la dynamique microscopique. La seconde partie concerne la formation de structures dans les systèmes réaction-diffusion dans le contexte de la biologie du développement. Une méthode pour simuler des structures de Turing à l'échelle microscopique est développée à partir de l'algorithme DSMC (direct simulation Monte Carlo). Ensuite, des expériences consistant à perturber la formation de la colonne vertébrale sont expliquées dans le cadre du mécanisme de Turing. Enfin, un modèle de réaction-diffusion associé à un mécanisme différent, connu sous le nom de "Clock and wavefront", est proposé pour rendre compte de la segmentation
Many nonlinear systems under non-equilibrium conditions are highly sensitive to internal fluctuations. In this dissertation, stochastic effects in some generic reaction-diffusion models are studied using two approaches of different precision. In the mesoscopic approach, evolution of the system is governed by the master equation, which can be solved numerically or used to set up kinetic Monte Carlo simulations. On the microscopic level, particle computer simulations are used. These two stochastic approaches are compared with deterministic, macroscopic reaction-diffusion equations.In the Introduction, key information about the different approaches is presented, together with basics of nonlinear systems and a presentation of numerical algorithms used.The first part of the Results chapter is devoted to studies on reaction-induced perturbation of particle velocity distributions in models of bistability and wave front propagation. A master equation including this perturbation is presented and compared with microscopic simulations.The second part of the Results deals with pattern formation in reaction-diffusion systems in the context of developmental biology. A method for simulating Turing patternsat the microscopic level using the direct simulation Monte Carlo algorithm is developed. Then, experiments consisting of perturbing segmentation of vertebrate embryo’s bodyaxis are explained using the Turing mechanism. Finally, a different possible mechanism of body axis segmentation, the “clock and wavefront” model, is formulated as a reaction-diffusion model

Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.
Ph. D.

Cold-atom quantum simulators offer unique possibilities to prepare, manipulate, and probe quantum many-body systems. However, despite the high level of control in modern experiments, not all observables of interest are easily accessible. This thesis aims at establishing protocols to measure currently elusive static and dynamic properties of quantum systems. The experimental feasibility of these schemes is illustrated by means of numerical simulations for relevant applications in many-body physics and quantum simulation. In particular, we introduce a general method for measuring dynamical correlations based on non-Hermitian linear response. This enables unbiased tests of the famous fluctuation-dissipation relation as a probe of thermalization in isolated quantum systems. Furthermore, we develop ancilla-based techniques for the measurement of currents and current correlations, permitting the characterization of strongly correlated quantum matter. Another application is geared towards revealing signatures of supersolidity in spin-orbit-coupled Bose gases by exciting the relevant Goldstone modes. Finally, we explore a scenario for quantum-simulating post-inflationary reheating dynamics by parametrically driving a Bose gas into the regime of universal far-from-equilibrium dynamics. The presented protocols also apply to other analog quantum simulation platforms and thus open up promising applications in the field of quantum science and technology.
I simulatori quantistici ad atomi freddi offrono possibilità uniche per preparare, manipolare e sondare sistemi quantistici a molti corpi. Tuttavia, nonostante l'alto livello di controllo raggiunto negli esperimenti moderni, non tutte le osservabili di interesse sono facilmente accessibili. Lo scopo di questa tesi è quello di stabilire protocolli per misurare delle proprietà statiche e dinamiche dei sistemi quantistici attualmente inaccessibili. La fattibilità sperimentale di questi schemi è illustrata mediante simulazioni numeriche per applicazioni rilevanti nella fisica a molti corpi e nella simulazione quantistica. In particolare, introduciamo un metodo generale per misurare le correlazioni dinamiche basato su una risposta lineare non hermitiana. Ciò consente test imparziali della famosa relazione fluttuazione-dissipazione come sonda di termalizzazione in sistemi quantistici isolati. Inoltre, sviluppiamo tecniche basate su ancilla per la misura di correnti e correlazioni di corrente, consentendo la caratterizzazione della materia quantistica fortemente correlata. Un'altra applicazione è orientata a rivelare l'impronta della supersolidità nei gas Bose con accoppiamento spin-orbita eccitando il corrispondente modo di Goldstone. Infine, esploriamo uno scenario per la simulazione quantistica della dinamica di riscaldamento post-inflazione modulando parametricamente un gas Bose e portandolo nel regime della dinamica universale lontana dall'equilibrio. I protocolli presentati si applicano anche ad altre piattaforme di simulazione quantistica analogica e aprono quindi applicazioni promettenti nel campo della scienza e della tecnologia quantistica.
Quantensimulatoren auf Basis ultrakalter Atome eröffnen einzigartige Möglichkeiten zur Präparation, Manipulation und Untersuchung von Quanten-Vielteilchen-Systemen. Trotz des hohen Maßes an Kontrolle in modernen Experimenten sind jedoch nicht alle interessanten Observablen auf einfache Weise zugänglich. Ziel dieser Arbeit ist es, Protokolle zur Messung aktuell nur schwer erfassbarer statischer und dynamischer Eigenschaften von Quantensystemen zu etablieren. Die experimentelle Realisierbarkeit dieser Verfahren wird durch numerische Simulationen anhand relevanter Anwendungen in der Vielteilchenphysik und Quantensimulation veranschaulicht. Insbesondere wird eine allgemeine Methode zur Messung dynamischer Korrelationen basierend auf der linearen Antwort auf nicht-hermitesche Störungen vorgestellt. Diese ermöglicht unabhängige Tests des berühmten Fluktuations-Dissipations-Theorems als Indikator der Thermalisierung isolierter Quantensysteme. Darüber hinaus werden Verfahren zur Messung von Strömen und Strom-Korrelationen mittels Kopplung an einen Hilfszustand entwickelt, welche die Charakterisierung stark korrelierter Quantenmaterie erlauben. Eine weitere Anwendung zielt auf die Enthüllung spezifischer Merkmale von Supersolidität in Spin-Bahn-gekoppelten Bose-Einstein-Kondensaten ab, indem die relevanten Goldstone-Moden angeregt werden. Schließlich wird ein Szenario zur Quantensimulation post-inflationärer Thermalisierungsdynamik durch die parametrische Anregung eines Bose-Gases in das Regime universeller Dynamik fern des Gleichgewichts erschlossen. Die dargestellten Protokolle lassen sich auch auf andere Plattformen für analoge Quantensimulation übertragen und eröffnen damit vielversprechende Anwendungen auf dem Gebiet der Quantentechnologie.

There are still many open questions regarding spatiotemporal chaos although many well developed theories exist for chaos in time. Rayleigh-B'enard convection is a paradigmatic example of spatiotemporal chaos that is also experimentally accessible. Discoveries uncovered using numerics can often be compared with experiments which can provide new physical insights. Lyapunov diagnostics can provide important information about the dynamics of small perturbations for chaotic systems. Covariant Lyapunov vectors reveal the true direction of perturbation growth and decay. The degree of hyperbolicity can also be quantified by the covariant Lyapunov vectors. To know whether a dynamical system is hyperbolic is important for the development of a theoretical understanding. In this thesis, the degree of hyperbolicity is calculated for chaotic Rayleigh-B'enard convection. For the values of the Rayleigh number explored, it is shown that the dynamics are non-hyperbolic. The spatial distribution of the covariant Lyapunov vectors is different for the different Lyapunov vectors. Localization is used to quantify this variation. The spatial localization of the covariant Lyapunov vectors has a decreasing trend as the order of the Lyapunov vector increases. The spatial localization of the covariant Lyapunov vectors are found to be related to the instantaneous Lyapunov exponents. The correlation is stronger as the order of the Lyapunov vector decreases. The covariant Lyapunov vectors are also computed using a spectral element approach. This allows an exploration of the covariant Lyapunov vectors in larger domains and for experimental conditions. The finite conductivity and finite thickness of the lateral boundaries of an experimental convection domain is also studied. Results are presented for the variation of the Nusselt number and fractal dimension for different boundary conditions. The fractal dimension changes dramatically with the variation of the finite conductivity.
Ph. D.

Nature changes continuously and is only seemingly at equilibrium. Environmental parameters like temperature, humidity or insolation may strongly fluctuate on scales ranging from seconds to millions of years. Being part of an ecosystem, species have to cope with these environmental changes. For ecologists, it is of special interest how individual responses to environmental changes affect the dynamics of an entire population – and, if this behavior is predictable. In this context, the demographic structure of a population plays a decisive role since it originates from processes of growth and mortality. These processes are fundamentally influenced by the environment. But, how exactly does the environment influence the behavior of populations? And what does the transient behavior look like? As a result from environmental influences on demography, so called cohorts form. They are age or size classes that are disproportionally represented in the demographic distribution of a population. For instance, if most old and young individuals die due to a cold spell, the population finally consists of mainly middle-aged individuals. Hence, the population got synchronized. Such a population tends to show regular fluctuations in numbers (denoted as oscillations) since the alternating phases of individual growth and population growth (due to reproduction) are now performed synchronously by the majority of the population.That is, one time the population growths, and the other time it declines due to mortality. Synchronous behavior is one of the most pervasive phenomena in nature. Gravitational synchrony in the solar system; fireflies flashing in unison; coordinate firing of pacemaker cells in the heart; electrons in a superconductor marching in lockstep. Whatever scale one looks at, in animate as well as inanimate systems, one is likely to encounter synchrony. In experiments with phytoplankton populations, I could show that this principle of synchrony (as used by physicists) could well-explain the oscillations observed in the experiments, too. The size of the fluctuations depended on the strength by which environmental parameters changed as well as on the demographic state of a population prior to this change. That is, two population living in different habitats can be equally influenced by an environmental change, however, the resulting population dynamics may be significantly different when both populations differed in their demographic state before. Moreover, specific mechanisms relevant for the dynamic behavior of populations, appear only when the environmental conditions change. In my experiments, the population density declined by 50% after ressource supply was doubled. This counter-intuitive behavior can be explained by increasing ressource consumption. The phytoplankton cells grew larger and enhanced their individual constitution. But at the same time, reproduction was delayed and the population density declined due to the losses by mortality. Environmental influences can also synchronize two or more populations over large distances, which is denoted as Moran effect. Assume two populations living on two distant islands. Although there is no exchange of individuals between them, both populations show a high similarity when comparing their time series. This is because the globally acting climate synchronizes the regionally acting weather on both island. Since the weather fluctuations influence the population dynamics, the Moran effect states that the synchrony between the environment equals the one between the populations. My experiments support this theory and also explain deviations arising when accounting for differences in the populations and the habitats they are living in. Moreover, model simulations and experiments astonishingly show that the synchrony between the populations can be higher than between the environment, when accounting for differences in the environmental fluctuations (“noise color”).
Die Natur unterliegt ständigen Veränderungen und befindet sich nur vermeintlich in einem Gleichgewicht. Umweltparameter wie Temperatur, Luftfeuchtigkeit oder Sonneneinstrahlung schwanken auf einer Zeitskala von Sekunden bis Jahrmillionen und beinhalten teils beträchtliche Unterschiede. Mit diesen Umweltveränderungen müssen sich Arten als Teil eines Ökosystems auseinandersetzen. Für Ökologen ist interessant, wie sich individuelle Reaktionen auf die Umweltveränderungen im dynamischen Verhalten einer ganzen Population bemerkbar machen und ob deren Verhalten vorhersagbar ist. Der Demografie einer Population kommt hierbei eine entscheidende Rolle zu, da sie das Resultat von Wachstums- und Sterbeprozessen darstellt. Eben jene Prozesse werden von der Umwelt maßgeblich beeinflusst. Doch wie genau beeinflussen Umweltveränderungen das Verhalten ganzer Populationen? Wie sieht das vorübergehende, transiente Verhalten aus? Als Resultat von Umwelteinflüssen bilden sich in Populationen sogenannte Kohorten, hinsichtlich der Zahl an Individuen überproportional stark vertretene Alters- oder Größenklassen. Sterben z.B. aufgrund eines außergewöhnlich harten Winters, die alten und jungen Individuen einer Population, so besteht diese anschließend hauptsächlich aus Individuen mittleren Alters. Sie wurde sozusagen synchronisiert. Eine solche Populationen neigt zu regelmäßigen Schwankungen (Oszillationen) in ihrer Dichte, da die sich abwechselnden Phasen der individuellen Entwicklung und der Reproduktion nun von einem Großteil der Individuen synchron durchschritten werden. D.h., mal wächst die Population und mal nimmt sie entsprechend der Sterblichkeit ab. In Experimenten mit Phytoplankton-Populationen konnte ich zeigen, dass dieses oszillierende Verhalten mit dem in der Physik gebräuchlichen Konzept der Synchronisation beschrieben werden kann. Synchrones Verhalten ist eines der verbreitetsten Phänomene in der Natur und kann z.B. in synchron schwingenden Brücken, als auch bei der Erzeugung von Lasern oder in Form von rhythmischem Applaus auf einem Konzert beobachtet werden. Wie stark die Schwankungen sind, hängt dabei sowohl von der Stärke der Umweltveränderung als auch vom demografischen Zustand der Population vor der Veränderung ab. Zwei Populationen, die sich in verschiedenen Habitaten aufhalten, können zwar gleich stark von einer Umweltveränderung beeinflusst werden. Die Reaktionen im anschließenden Verhalten können jedoch äußerst unterschiedlich ausfallen, wenn sich die Populationen zuvor in stark unterschiedlichen demografischen Zuständen befanden. Darüber hinaus treten bestimmte, für das Verhalten einer Population relevante Mechanismen überhaupt erst in Erscheinung, wenn sich die Umweltbedingungen ändern. So fiel in Experimenten beispielsweise die Populationsdichte um rund 50 Prozent ab nachdem sich die Ressourcenverfügbarkeit verdoppelte. Der Grund für dieses gegenintuitive Verhalten konnte mit der erhöhten Aufnahme von Ressourcen erklärt werden. Damit verbessert eine Algenzelle zwar die eigene Konstitution, jedoch verzögert sich dadurch die auch die Reproduktion und die Populationsdichte nimmt gemäß ihrer Verluste bzw. Sterblichkeit ab. Zwei oder mehr räumlich getrennte Populationen können darüber hinaus durch Umwelteinflüsse synchronisiert werden. Dies wird als Moran-Effekt bezeichnet. Angenommen auf zwei weit voneinander entfernten Inseln lebt jeweils eine Population. Zwischen beiden findet kein Austausch statt – und doch zeigt sich beim Vergleich ihrer Zeitreihen eine große Ähnlichkeit. Das überregionale Klima synchronisiert hierbei die lokalen Umwelteinflüsse. Diese wiederum bestimmen das Verhalten der jeweiligen Population. Der Moran-Effekt besagt nun, dass die Ähnlichkeit zwischen den Populationen jener zwischen den Umwelteinflüssen entspricht, oder geringer ist. Meine Ergebnisse bestätigen dies und zeigen darüber hinaus, dass sich die Populationen sogar ähnlicher sein können als die Umwelteinflüsse, wenn man von unterschiedlich stark schwankenden Einflüssen ausgeht.

Based on the works [R1] - [R10], this thesis tackles various aspects of the dynamics of interacting quantum many-body systems. Particular emphasis is given to the understanding of transport and thermalization phenomena in isolated (quasi) one-dimensional quantum spin models. Employing a variety of methods, these phenomena are studied both, close to equilibrium where linear response theory (LRT) is valid, as well as in far-from-equilibrium situations where LRT is supposed to break down. The main results of this thesis can be summarized as follows. First, it is shown that conventional hydrodynamic transport, i.e., diffusion, occurs in a number of (integrable and nonintegrable) quantum models and can be detected by looking at different signatures in position and momentum space as well as in the time and the frequency domain. Furthermore, the out-of-equilibrium dynamics resulting from a realistic class of initial states is explored. These states are thermal states of the model in the presence of an additional static force, but become nonequilibrium states when this force is eventually removed. Remarkably, it is shown that in some cases, the full time-dependent relaxation process can become independent of whether the initial state is prepared close to or far away from equilibrium. In this context, a new connection between the eigenstate thermalization hypothesis and linear response theory is unveiled. Finally, this thesis also reports progress on the development and improvement of numerical and (semi-)analytical techniques to access the dynamics of quantum many-body systems. Specifically, a novel combination of dynamical quantum typicality and numerical linked cluster expansions is employed to study current-current correlation functions in chain and ladder geometries in the thermodynamic limit.