This cumulative dissertation is based on the publications [P1–P6], covering various aspects in theoretical studies of isolated quantum many-body systems. The transport and relaxation dynamics in quantum lattice models are studied with a particular focus on (i) the effect of a mass imbalance between different particles on their relaxation dynamics as well as (ii) the influence of generic perturbations on different reference dynamics. As for (i), the dynamics of two mutually interacting fermionic particle species on a lattice are investigated for different mass ratios between the two species [P4]. Numerical studies of density dynamics show that diffusive transport which is expected for small mass imbalances persists also for moderate imbalances and becomes anomalous for stronger imbalances. On the other hand, while transport is suppressed in the limit of infinite imbalance, i.e., if one particle species is immobile, this effective localization is shown to give way to anomalous diffusion as soon as the heavy particle species gains a finite mobility. Regarding (ii), the effect of perturbations on dynamics is investigated from the perspective of projection-operator techniques [P6]. As a main result, it is demonstrated that simple exponential damping, which is expected in the overwhelming majority of cases, may only occur for the density matrix in the interaction picture. Within this approach, this simple damping carries over to the time dependence of standard correlation functions only in certain cases. In particular, the possibility of nontrivial damping in physically relevant perturbation scenarios is discussed. A considerable portion of this work is concerned with the implementation of powerful numerical and (semi-)analytical tools to overcome the enhanced computational complexity in numerical studies of quantum many-body systems. This includes the concept of dynamical quantum typicality [P2, P3], numerical linked-cluster expansions [P5], and projection-operator techniques, as well as the combined use of available symmetries [P1].

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.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21549号 / 理博第4456号 / 新制||理||1640(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)教授 高橋 義朗, 教授 田中 耕一郎, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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