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].
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:osnadocs.ub.uni-osnabrueck.de:ds-202205246978 |
| Date | 24 May 2022 |
| Creators | Heitmann, Tjark |
| Contributors | Prof. Dr. Robin Steinigeweg, Prof. Dr. Jochen Gemmer |
| Source Sets | Universität Osnabrück |
| Language | German |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/zip, application/pdf |
| Rights | Attribution-NonCommercial 3.0 Germany, http://creativecommons.org/licenses/by-nc/3.0/de/ |
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