Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-04-04Bitstream added on 2014-06-13T18:43:09Z : No. of bitstreams: 1 seewald_ncc_dr_ift.pdf: 980110 bytes, checksum: a8da01736f6d240fb7a6880d23b95d14 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O objetivo da Tese é investigar a aplicabilidade e propor extensões do método do hamiltoniano termodinamicamente equivalente (MHTE) para sistemas de muitos corpos descritos por uma teoria de campos. Historicamente, o MHTE tem sua origem na teoria quântica de muitos corpos para descrever o fenômeno da supercondutividade. O método consiste na observação de que o hamiltoniano de um sistema pode ser diagonalizado exatamente através de uma transformação unitária quando um número finito de momentos transferidos que contribuem para a interação é levado em conta no limite termodinâmico. Essa transformação unitária depende explicitamente de funções de gap que podem ser determinadas através do método variacional de Gibbs. Na presente Tese, extensões do método são feitas visando aplicações em sistemas de muitos corpos em diferentes situações, tais como: transições de fase estáaticas, evolução temporal de parâmetros de ordem descrita por equações dinâmicas estocásticas do tipo Ginzburg-Landau-Langevin (GLL), teorias quânticas de campos escalares relativísticos e teorias de muitos corpos para sistemas fermiônicos não relativísticos. Mostra-se, em particular, que o MHTE é um esquema de aproximação sistemático e controlável que permite incorporar acoplamentos de componentes de Fourier de parâmetros de ordem além do modo zero, da mesma forma que em teorias quânticas relativísticas ou não relativísticas ele incorpora correlações não perturbativas entre as partículas além daquelas levadas em conta pelas tradicionais aproximações de campo médio. Métodos são desenvolvidos para obtermos soluções numéricas explícitas com o objetivo de avaliar a aplicabilidade do MHTE em alguns casos específicos. Particular atenção é dedicada ao controle de divergências de Rayleigh-Jeans nas simulações numéricas de equações de GLL / The general objective of the Thesis is to apply the Method of the Thermodynamically Equivalent Hamiltonian (MTEH) to many-body systems described by a field theory. Historically, the MTEH has its origins in the quantum theory of manybody systems to describe the phenomenon of superconductivity. The method is based on the observation that the Hamiltonian of the system can be diagonalized exactly with a unitary transformation when a finite number of transfer momenta of the interaction are taken into account in the thermodynamic limit. This unitary transformation depends explicitly on gap functions that can be determined with the use of the Gibbs variational principle. In the present Thesis, extensions of the method are made envisaging applications in many-body systems in different situations, like: static phase transitions, time evolution of order parameters described by dynamic stochastic Ginzburg-Landau-Langevin equations, relativistic quantum scalar field theories, and many-body theories for nonrelativistic fermionic systems. It is shown that the MTEH is a systematic and controllable approximation scheme that in the theory of phase transitions allows to incorporate Fourier modes of the order parameter beyond the zero mode, in the same way that in the relativistic and nonrelativistic theories it incorporates particle nonperturbative correlations beyond those taken into account by the traditional mean field approximation. Methods are developed to obtain explicit numerical solutions with the aim to assess the applicability of the MTEH in specific situations. Particular attention is devoted to the control of Rayleigh-Jeans ultraviolet divergences in the numerical simulations of Ginzburg-Landau-Langevin equations

Orientador: Gastão Inácio Krein / Banca: Marcus Benghi Pinto / Banca: Ney Lemke / Banca: Sandra dos Santos Padula / Banca: Yogiro Hama / Resumo: O objetivo da Tese é investigar a aplicabilidade e propor extensões do método do hamiltoniano termodinamicamente equivalente (MHTE) para sistemas de muitos corpos descritos por uma teoria de campos. Historicamente, o MHTE tem sua origem na teoria quântica de muitos corpos para descrever o fenômeno da supercondutividade. O método consiste na observação de que o hamiltoniano de um sistema pode ser diagonalizado exatamente através de uma transformação unitária quando um número finito de momentos transferidos que contribuem para a interação é levado em conta no limite termodinâmico. Essa transformação unitária depende explicitamente de funções de gap que podem ser determinadas através do método variacional de Gibbs. Na presente Tese, extensões do método são feitas visando aplicações em sistemas de muitos corpos em diferentes situações, tais como: transições de fase estáaticas, evolução temporal de parâmetros de ordem descrita por equações dinâmicas estocásticas do tipo Ginzburg-Landau-Langevin (GLL), teorias quânticas de campos escalares relativísticos e teorias de muitos corpos para sistemas fermiônicos não relativísticos. Mostra-se, em particular, que o MHTE é um esquema de aproximação sistemático e controlável que permite incorporar acoplamentos de componentes de Fourier de parâmetros de ordem além do modo zero, da mesma forma que em teorias quânticas relativísticas ou não relativísticas ele incorpora correlações não perturbativas entre as partículas além daquelas levadas em conta pelas tradicionais aproximações de campo médio. Métodos são desenvolvidos para obtermos soluções numéricas explícitas com o objetivo de avaliar a aplicabilidade do MHTE em alguns casos específicos. Particular atenção é dedicada ao controle de divergências de Rayleigh-Jeans nas simulações numéricas de equações de GLL / Abstract: The general objective of the Thesis is to apply the Method of the Thermodynamically Equivalent Hamiltonian (MTEH) to many-body systems described by a field theory. Historically, the MTEH has its origins in the quantum theory of manybody systems to describe the phenomenon of superconductivity. The method is based on the observation that the Hamiltonian of the system can be diagonalized exactly with a unitary transformation when a finite number of transfer momenta of the interaction are taken into account in the thermodynamic limit. This unitary transformation depends explicitly on gap functions that can be determined with the use of the Gibbs variational principle. In the present Thesis, extensions of the method are made envisaging applications in many-body systems in different situations, like: static phase transitions, time evolution of order parameters described by dynamic stochastic Ginzburg-Landau-Langevin equations, relativistic quantum scalar field theories, and many-body theories for nonrelativistic fermionic systems. It is shown that the MTEH is a systematic and controllable approximation scheme that in the theory of phase transitions allows to incorporate Fourier modes of the order parameter beyond the zero mode, in the same way that in the relativistic and nonrelativistic theories it incorporates particle nonperturbative correlations beyond those taken into account by the traditional mean field approximation. Methods are developed to obtain explicit numerical solutions with the aim to assess the applicability of the MTEH in specific situations. Particular attention is devoted to the control of Rayleigh-Jeans ultraviolet divergences in the numerical simulations of Ginzburg-Landau-Langevin equations / Doutor

O presente trabalho apresenta o estudo das propriedades da condensação de Bose-Einstein e da superfluidez em um sistema bosônico disposto em um arranjo unidimensional de potenciais periódicos em formato de anel. O Hamiltoniano efetivo usual em termos dos operadores de campo é implementado na representação construída em termos das funções de Bloch da primeira banda e o problema é resolvido por meio da sua diagonalização através de métodos numéricos. No limite de hopping pequeno, este modelo é essencialmente equivalente à representação usual do modelo de Bose-Hubbard, mas incorpora efeitos adicionais através das energias de Bloch de partícula independente e dos elementos da matriz de dois corpos na situação em que o hopping é grande [19]. Através da inclusão de rotação no sistema, as energias de partícula independente são forçadas a depender da velocidade angular. Isto implica, correspondentemente, uma dependência da velocidade angular nas funções de onda de partícula independente e nos resultados de muitos corpos obtidos através da diagonalização do Hamiltoniano. Com o objetivo de estudar a superfluidez, o critério de dois fluidos é empregado e através de resultados numéricos obtêm-se a variação da fração de superfluido com o quadrado da velocidade angular. Ainda, considera-se aqui uma expressão perturbativa para o parâmetro inercial do sistema expresso em termos das excitações do sistema sem rotação, o que permite relacionar as energias do sistema com rotação com aquelas do sistema sem rotação. Isto é particularmente interessante para obter a fração de superfluido em termos da informação espectral do sistema sem rotação. Resultados semelhantes podem ser encontrados através da definição de superfluido baseada na resposta do sistema a uma variação de fase, imposta através de condições de contorno torcidas [30, 33], mas com a diferença de que os desenvolvimentos aqui não fazem uso da hipótese do modo condensado. De maneira geral, os resultados numéricos obtidos indicam, que pelo menos para este sistema, as frações de superfluido e condensado são quantidades sem relação direta, sugerindo então que mesmo para sistemas gasosos diluídos a idéia de que a superfluidez é uma consequência da condensação de Bose-Einstein deve ser considerada com mais cuidado. / In this work we study the properties of Bose-Einstein condensation and superfluidity in a finite bosonic system in a 1-dimensional ring with a periodic potential under rotation. The usual field effective Hamiltonian is implemented in a representation constructed in terms of the first band Bloch functions and the problem is solved by numeric diagonalization. In the limit of small hopping, this model is essentially equivalent to the quasi-momentum representation of the usual Bose-Hubbard model but incorporates additional effects via Bloch single particle energies and two-body matrix elements in the case of large hopping [19]. By including rotation in the system we force the single particle energies to be a function of the angular velocity. This implies a corresponding angular velocity dependence of the single particle wavefunctions and many-body diagonalization results. In order to study superfluidity, we consider the two fluid criterion. Numerical results for the superfluid fraction involving the change of in rinsic ground state energy with the square of the angular velocity are obtained. We also consider a perturbative expression for the system inertial parameter expressed in terms of the excitation spectrum of the non rotating system, which enables us to relate the energies in the rotating system to the ones in the system without rotation. This is particularly interesting for obtaining superfluid fraction in terms of spectral information of the non rotating system. Similar results can be found by using the definition of superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions [30, 33], but with the difference that our developments do not assume the hypothesis of a condensate mode. Our numerical results indicate that in this system condensate and superfluid fractions are quite unrelated in terms of parameter values, indicating that even for dilute gases the concept that superfluidity is a consequence of Bose-Einstein condensation should be considered more carefully.

The ability to isolate single atomic layers of van der Waals materials has led to renewed interest in the electronic and optical properties of these materials as they can be fundamentally different at the monolayer limit. Moreover, these 2D crystals can be assembled together layer by layer, with controllable sequence and orientation, to form artificial materials that exhibit new features that are not found in monolayers nor bulk. Twisted bilayer graphene is one such prototype system formed by two monolayer graphene layers placed on top of each other with a twist angle between their lattices, whose electronic band structure depends on the twist angle. This thesis presents the efforts to explore the electronic and optical properties of twisted bilayer graphene by Raman spectroscopy and scanning tunneling microscopy measurements. We first synthesize twisted bilayer graphene with various twist angles via chemical vapor deposition. Using a combination of scanning tunneling microscopy and Raman spectroscopy, the twist angles are determined. The strength of the Raman G peak is sensitive to the electronic band structure of twisted bilayer graphene and therefore we use this peak to monitor changes upon doping. Our results demonstrate the ability to modify the electronic and optical properties of twisted bilayer graphene with doping. We also fabricate twisted bilayer graphene by controllable stacking of two graphene monolayers with a dry transfer technique. For twist angles smaller than one degree, many body interactions play an important role. It requires eight electrons per moire unit cell to fill up each band instead of four electrons in the case of a larger twist angle. For twist angles smaller than 0.4 degree, a network of domain walls separating AB and BA stacking regions forms, which are predicted to host topologically protected helical states. Using scanning tunneling microscopy and spectroscopy, these states are confirmed to appear on the domain walls when inversion symmetry is broken with an external electric field. We observe a double-line profile of these states on the domain walls, only occurring when the AB and BA regions are gaped. These states give rise to channels that could transport charge in a dissipationless manner making twisted bilayer graphene a promising platform to realize controllable topological networks for future applications.

In a many-body fermionic system, the suppression of continuous transitions to absolute zero can result in a low temperature quantum fluid which deviates strongly from typical metallic behaviour; unconventional superconductivity can be induced by the strange metal region surrounding the zero-temperature phase transition. In this thesis we focus on three systems which demonstrate a highly tunable phase transition, with the aim of pushing them toward the border of a zero-temperature phase transition, and potentially superconductivity. CeAgSb2 is a uniaxial 4f ferromagnet, where physical pressure or a transverse field may be used to tune the magnetic transition towards T = 0 K. Our investigations, however, did not reveal the presence of superconductivity. It is likely that the field tuned transition does not correspond to a true critical point, whilst the high pressure region may be occupied by an antiferromagnetic phase, with the true critical point at higher pressures. However, other interesting features emerge in the electrical resistivity and AC-susceptibility, along with novel thermodynamic signatures linking the magnetisation to the specific heat. The doping series Lu(1-x)YxFe2Ge2 shows an antiferromagnetic transition which is suppressed to absolute zero at a critical concentration x_c=0.2. YFe2Ge2 displays anomalous low temperature behaviour consistent with the proximity to quantum critical fluctuations, along with a superconducting transition which appears in the electrical resistivity beneath a critical temperature of T_c ~ 1.7 K. Using low temperature DC magnetisation measurements, we show that this is a bulk effect, and that the superconductivity in YFe2Ge2 is of type-II. The thermodynamic and BCS properties of the superconducting phase are analysed in line with the parameters we extract experimentally. The superconducting 3-4-13 stannides (Ca,Sr)3Ir4Sn13 show a high temperature structural transition which may be suppressed by the application of hydrostatic pressure or effective chemical pressure. A superconducting dome is found, which appears to peak near where the structural transition extrapolates to zero temperature. Anomalous exponents are seen in the electrical resistivity over a wide temperature range. We investigate the influence of pressure on the superconducting critical temperature in Ca3Ir4Sn13 and the related compound Co3Ca4Sn13, along with an analysis of the upper critical field and flux-line phenomena in Ca3Ir4Sn13 and Sr3Ir4Sn13.

Many-body quantum dynamics is a challenging problem that has induced the development of many different computational techniques. One powerful technique is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method. This method allows proper consideration of electronic correlation with much less computational overhead compared to other similar methods. In this work, we present our implementation of the MCTDHF method on a non-uniform cylindrical grid. With the one-body limit of our code, we studied the controversial topic of tunneling delay, and showed that our results agree with one recent experiment while disagreeing with another. Using the fully correlated version of the code, we demonstrated the ability of MCTDHF to address correlation by calculating the ground state ionization energies of a few strongly correlated systems.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21571号 / 理博第4478号 / 新制||理||1642(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 菅沼 秀夫, 教授 永江 知文, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

A defining feature of quantum many-body systems is the presence of entanglement among their constituents. Besides providing valuable insights on several physical properties, entanglement is also responsible for the computational complexity of simulating quantum systems with variational methods. This thesis explores several aspects of entanglement in many-body systems, with the primary goal of devising efficient approaches for the study of topological properties and quantum dynamics of lattice models. The first focus of this work is the development of variational wavefunctions inspired by artificial neural networks. These can efficiently encode long-range and extensive entanglement in their structure, as opposed to the case of tensor network states. This feature makes them promising tools for the study of topologically ordered phases, quantum critical states as well as dynamical properties of quantum systems. In this thesis, we characterize the representational power of a specific class of artificial neural network states, constructed from Boltzmann machines. First, we show that wavefunctions obtained from restricted Boltzmann machines can efficiently parametrize chiral topological phases, such as fractional quantum Hall states. We then turn our attention to deep Boltzmann machines. In this framework, we propose a new class of variational wavefunctions, coined generalized transfer matrix states, which encompass restricted Boltzmann machine and tensor network states. We investigate the entanglement properties of this ansatz, as well as its capability of representing physical states. Understanding how the entanglement properties of a system evolve in time is the second focus of this thesis. In this context, we first investigate the manifestation of topological properties in the unitary dynamics of systems after a quench, using the degeneracy of the entanglement spectrum as a possible signature. We then analyze the phenomenon of entanglement growth, which limits to short timescales the applicability of tensor network methods in out-of-equilibrium problems. We investigate whether these limitations can be overcome by exploiting the dependence of entanglement entropies on the chosen computational basis. Specifically, we study how the spreading of quantum correlations can be contained by means of time-dependent basis rotations of the state, using exact diagonalization to simulate its dynamics after a quench. Going beyond the case of sudden quenches, we then show how, in certain weakly interacting problems, the asymptotic value of the entanglement entropy can be tuned by modifying the velocity at which the parameters in the Hamiltonian are changed. This enables the simulation of longer timescales using tensor network approaches. We present preliminary results obtained with matrix product states methods, with the goal of studying how equilibration affects the transport properties of interacting systems at long times.

Au sein de physique des systèmes quantiques désordonnés, le domaine des atomes ultra-froids est en pleine croissance. En l’occurrence, l'étude de la relation entre la localisation et les interactions a permis de découvrir la richesse de la physique de la localisation à N-corps. Ce phénomène remarquable fournit un mécanisme pour la brisure de l'ergodicité dans les systèmes quantiques isolés et désordonnés. Plusieurs questions ont été évoquées après cette découverte, comme la possibilité d'une transition fluide-isolant à température finie. Dans cette thèse, j'étudie la localisation à N-corps dans le contexte de bosons désordonnés à deux dimensions. Dans la première partie, je présente l'étude d'un gaz interactif de Bose bidimensionnel dans un potentiel aléatoire à température finie. Le système présente deux transitions à température finie: la transition de localisation à N-corps entre fluide et isolant, et la transition de Berezinskii-Kosterlitz-Thouless entre superfluide algébrique et fluide. J'examine ensuite l'influence de la troncature de la distribution d'énergie dû au piégeage, un phénomène générique dans le cadre du refroidissement d'atomes ultra-froids. Finalement, je conclus en discutant la stabilité de la phase isolante dans des systèmes définis sur un continuum. / The study of the interplay between localization and interactions in disordered quantum systems led to the discovery of the interesting physics of many-body localization (MBL). This remarkable phenomenon provides a generic mechanism for the breaking of ergodicity in quantum isolated systems, and has stimulated several questions such as the possibility of a finite-temperature fluid-insulator transition. At the same time, the domain of ultracold interacting atoms is a rapidly growing field in the physics of disordered quantum systems. In this thesis, we study many-body localization in the context of two-dimensional disordered ultracold bosons. After reviewing some importance concepts, we present a study of the phase diagram of a two-dimensional weakly interacting Bose gas in a random potential at finite temperatures. The system undergoes two finite-temperature transitions: the MBL transition from normal fluid to insulator and the Berezinskii-Kosterlitz-Thouless transition from algebraic superfluid to normal fluid. At T=0, we show the existence of a tricritical point where the three phases coexist. We also discuss the influence of the truncation of the energy distribution function at the trap barrier, a generic phenomenon for ultracold atoms. The truncation limits the growth of the localization length with energy and, in contrast to the thermodynamic limit, the insulator phase is present at any temperature. Finally, we conclude by discussing the stability of the insulating phase with respect to highly energetic particles in systems defined on a continuum.

In this thesis, we focus attention on the effects of disorder in closed interacting quantum systems that give rise to a many-body localization (MBL) transition between an ergodic phase and a many-body localized phase. This transition is not a conventional one, since it takes place at any finite energy density and can neither be described by thermodynamics nor conventional statistical mechanics. We explain why systems experiencing such an MBL transition can be regarded as generic in many ways, we do so by discussing many of their spectral properties and by giving a detailed account of their manifestation in the nonequilibrium dynamics and long-time behavior. Surprisingly, a wide variety of MBL systems consistently reflect strikingly similar characteristic effects in each side of the MBL transition. This is backed by myriads of numerical and experimental observations which in turn can be partially explained by theories developed in the past decade. However, some mechanisms behind the ergodic side of the MBL transition and the nature of the MBL transition itself remain elusive. These, as well as the lack of an accurate description of the nonergodic character of the steady states of such systems, have been some of the issues for active research and speculation by scholars that need to be timely addressed. In the following, we describe our modest contributions at bridging the gap of understanding of some of the issues exposed above. On the one hand, reduced density matrices are central objects for the description of the relaxation of local observables in closed quantum many-body systems, and on the other, quench protocols are experimentally relevant procedures. In the first part of this thesis we study the long-time behavior of the one-particle density matrix (OPDM) occupation spectrum after a quench. It was shown that, in the many-body localized phase (which can be understood in terms of localized quasiparticles), the OPDM occupation spectrum in eigenstates shows a zero-temperature Fermi liquid-like discontinuity at any finite energy density. In this thesis we show that in the steady state reached at long times after a global quench from a perfect density-wave state, the discontinuity in the OPDM occupation spectrum is absent, reminiscent of a Fermi liquid at a finite temperature, while the full occupation function remains strongly nonthermal. We discuss how one can understand this as a consequence of the local structure of the density-wave state and the resulting partial occupation of quasiparticles. We further show how these partial occupations can be controlled by tuning the structure of initial state and described by an effective temperature. Another part of this thesis was devoted to the study of dynamics on the ergodic side of the transition in periodically driven systems in the absence of global conservation laws. Most numerical studies in this context were done in models with conserved quantities (e.g., energy and/or particle number) which could account for the reduction of the overall complexity of the problem, while in this thesis, we use a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities, we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. This is reflected in anomalous behavior of the energy absorption of the system, as well as consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and cannot rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of nonmonotonic dependence of the exponents with time, with the dynamics initially slowing down but accelerating again at larger times, which could be consistent with the slow dynamics being a crossover phenomenon with a localized critical point. In addition, we observe no difference between the typical and average value of the autocorrelation function and therefore our results are inconsistent with the phenomenological explanation of the anomalous behavior based on Griffiths effects. In the last part of this thesis, we study dynamics in the ergodic phase relating to two main quantum information measures: One is the entanglement entropy, which is an intrinsic property of the wave function and generated by the time evolution operator, while the other is the operator entanglement entropy of the time evolution operator, which quantifies the complexity of the latter. It is known that generic quantum many-body systems typically show a linear growth of the entanglement entropy growth after a quench from a product state. In this thesis we show that there is a robust correspondence between the operator entanglement entropy of the time evolution operator and the entanglement entropy growth of typical product states, whereas special product states, e.g., $\sigma_z$ basis states, may exhibit faster entanglement production. We base our analysis on numerical simulations of a static and a periodically driven quantum spin chain in the presence of a disordered magnetic field, showing that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorder-dependent exponent. With this, we clarify the discrepancy between the exponents observed in previous results. Our results provide further evidence for slow information spreading on the ergodic side of the many-body localization transition in the absence of conservation laws. / In dieser Dissertation setzen wir uns mit dem Effekt von Unordnung auf geschlossene wechselwirkende Quantensysteme auseinander. Unordnung kann einen Übergang von einer ergodischen in eine lokalisierte Phase induzieren, eine sogenannte Vielteilchenlokalisierung oder Many body localization (MBL). Dieser Phasenübergang ist alles andere als konventionell: Er kann weder durch Thermodynamik noch durch klassische statistische Mechanik beschrieben werden. Wir erklären, warum Systeme, die solch einen MBL Übergang aufweisen, in vielerlei Hinsicht als generisch angesehen werden können. Dazu diskutieren wir die spektralen Eigenschaften, die Nichtgleichgewichtsdynamik und das Langzeitverhalten. Erstaunlicherweise weist eine große Vielfalt verschiedener MBL Systeme auf beiden Seiten des MBL Übergangs mit großer Konsistenz ähnliche Charakteristiken auf. Dies wird durch unzählige numerische und experimentelle Beobachtungen unterstützt, die wiederum zumindest teilweise durch theoretische Arbeiten aus dem letzten Jahrzehnt erklärt werden können. Trotzdem bleiben manche Mechanismen auf der ergodischen Seite des MBL Übergangs und die Art des MBL Übergangs weiterhin im Verborgenen. Zusammen mit der fehlenden akkuraten Beschreibung des nicht-ergodischen Charakters der stationären Zustände dieser Systeme sind diese Probleme im derzeitigen Fokus der Forschung, wobei es eine Vielzahl fundierter Vermutungen gibt, die diese Phänomene erklären. Im Folgenden beschreiben wir unseren Beitrag wie diese oben gelisteten Probleme überwunden werden können. Reduzierte Dichteoperatoren sind zentrale Objekte, um die Relaxation von lokalen Observablen in geschlossenen Quantenvielkörpersystemen zu beschreiben und sogenannte Quenches, also die plötzliche Änderung einiger systemrelevanter Parameter, ähnlich wie beim Abschrecken mit Wasser oder Luft, sind experimentell relevante Vorgänge. Im ersten Teil dieser Arbeit untersuchen wir das Langzeitverhalten des Besetzungsspektrums des Einteilchendichteoperators (one-particle density matrix, OPDM) nach solch einem Quench. Wie zuvor gezeigt wurde, weist das OPDM Besetzungsspektrum in der MBL Phase (die im Sinne von lokalisierten Quasiteilchen verstanden werden kann) für alle endlichen Energiedichten eine Diskontinuität auf, ähnlich wie in Fermi-Flüssigkeiten. In dieser Arbeit zeigen wir, dass diese Diskontinuität in stationären Zuständen, die von perfekten Dichtewellen ausgehend nach langer Zeit nach einem globalen Quench erreicht werden, abwesend ist, ähnlich wie in einer Fermi-Flüssigkeit bei einer endlichen Temperatur, während die gesamte Besetzungsfunktion stark nicht-thermal bleibt. Wir diskutieren, wie man dies als Konsequenz der lokalen Struktur des Dichtewellenzustands und der daraus folgenden teilweisen Besetzung der Quasiteilchen verstehen kann. Wir zeigen außerdem, wie die teilweise Besetzung durch Änderung der Struktur des Ausgangszustands kontrolliert und durch eine effektive Temperatur beschrieben werden kann. Im nächsten Teil dieser Arbeit untersuchen wir die Dynamik der ergodischen Seite des MBL Übergangs in periodisch getriebenen Systemen ohne globale Erhaltungsgrößen. Die meisten bisherigen in diesem Zusammenhang vorgenommenen numerischen Untersuchungen wurden in Modellen mit Erhaltungsgrößen (wie Energie und/oder Teilchenzahl) durchgeführt, was an der Reduzierung der Komplexität des Problems liegen mag. In dieser Arbeit nutzen wir hingegen eine numerische Methode, die auf einer schnellen Walsh-Hadamard Transformation beruht, was uns ermöglicht, eine exakte Zeitentwicklung für lange Zeiten und große Systeme vorzunehmen. Wie in Modellen mit Erhaltungsgrößen beobachten wir eine Verlangsamung der Dynamik, wenn wir uns dem Übergangspunkt zu der MBL Phase nähern. Dies macht sich in einem ungewöhnlichen Verhalten der Energieabsorption des Systems bemerkbar, was mit einer unterballistischen Ausbreitung der Verschränkung und einem gedehnt-exponentiellen Abklingen der Autokorrelationsfunktion im Einklang steht, wobei die zugehörigen Exponenten die verlangsamte Dynamik für fixe Systemgrößen widerspiegeln. Durch den Zugang zu größeren Systemen können wir jedoch einen deutlichen Fluss der Exponenten Richtung schnellerer Dynamik feststellen und daher nicht ausschließen, dass die verlangsamte Dynamik durch die endlichen Systemgrößen hervorgerufen wird (ein sogenannter finite size effect). Des weiteren finden wir Beispiele für eine nicht-monotone Zeitabhängigkeit der Exponenten, wobei die Dynamik sich zunächst verlangsamt, bevor sie zu späteren Zeiten wieder beschleunigt. Dies könnte mit der Betrachtung der verlangsamten Dynamik als Crossover-Phänomen mit einem lokalisierten kritischen Punkt vereinbar sein. Außerdem können wir keinen Unterschied zwischen dem geometrischen und arithmetischen Mittel der Autokorrelationsfunktion feststellen, sodass unsere Ergebnisse der phänomenologischen Erklärung des ungewöhnlichen Verhaltens, die auf Griffiths-Effekten beruht, widersprechen. Im letzten Teil der Dissertation widmen wir der Dynamik in der ergodischen Phase und verknüpfen zwei zentrale Größen der Quanteninformation: die Verschränkungsentropie, eine der Wellenfunktion intrinsische Größe, die aus dem Zeitentwicklungsoperator generiert werden kann, und der Operatorverschränkungsentropie des Zeitentwicklungsoperators, die die Komplexität des Operators quantifiziert. In generischen Quantenvielkörpersystemen wächst die Verschränkungsentropie nach einem Quench aus einem Produktzustand typischerweise linear. In dieser Arbeit zeigen wir, dass es eine belastbaren Übereinstimmung zwischen der Operatorverschränkungsentropie des Zeitentwicklungsoperators und der Verschränkungsentropie typischer Produktzustände gibt, wobei bestimmte Produktzustände, z.B. $\sigma_z$-Basiszustände, eine schnellere Verschränkungsproduktion aufweisen können. Unsere Analyse basiert auf numerischen Simulationen von statischen und periodisch getriebenen Quanten-Spinketten in einem ungeordneten Magnetfeld. Sowohl die Verschränkungsentropie der Wellenfunktion als auch die Operatorverschränkungsentropie wächst einem Potenzgesetz folgend mit den selben unordnungsabhängigen Exponenten. Damit schaffen wir Klarheit bezüglich der Unstimmigkeiten der Exponenten in den vorherigen Ergebnissen. Unsere Resultate geben außerdem Hinweise auf eine verlangsamte Informationsausbreitung auf der ergodischen Seite des MBL Übergangs ohne Erhaltungsgrößen.