Based on the publications [P1–P6], the cumulative dissertation at hand addresses quite diverse
aspects of non-equilibrium behavior in isolated quantum systems. The works presented in
publications [P1, P2] concern the issue of finding generally valid upper bounds on equilibration
times, which ensure the eventual occurrence of equilibration in isolated quantum systems. Recently,
a particularly compelling bound for physically relevant observables has been proposed. Said
bound is examined analytically as well as numerically. It is found that the bound fails to give
meaningful results in a number of standard physical scenarios. Continuing, publication [P4]
examines a particular integral fluctuation theorem (IFT) for the total entropy production of a
small system coupled to a substantially larger but finite bath. While said IFT is known to hold
for canonical states, it is shown to be valid for microcanonical and even pure energy eigenstates
as well by invoking the physically natural conditions of “stiffness” and “smoothness” of transition
probabilities. The validity of the IFT and the existence of stiffness and smoothness are numerically
investigated for various lattice models. Furthermore, this dissertation puts emphasis on the issue
of the route to equilibrium, i.e., to explain the omnipresence of certain relaxation dynamics in
nature, while other, more exotic relaxation patterns are practically never observed, even though
they are a priori not disfavored by the microscopic laws of motion. Regarding this question, the
existence of stability in a larger class of dynamics consisting of exponentially damped oscillations
is corroborated in publication [P6]. In the same vein, existing theories on the ubiquity of certain
dynamics are numerically scrutinized in publication [P3]. Finally, in publication [P5], the recently
proposed “universal operator growth hypothesis”, which characterizes the complexity growth of
operators during unitary time evolution, is numerically probed for various spin-based systems in
the thermodynamic limit. The hypothesis is found to be valid within the limits of the numerical
approach.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:osnadocs.ub.uni-osnabrueck.de:ds-202209067381 |
| Date | 06 September 2022 |
| Creators | Heveling, Robin |
| Contributors | Prof. Dr. Jochen Gemmer, Prof. Dr. Robin Steinigeweg |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/zip, application/pdf |
| Rights | Attribution 3.0 Germany, http://creativecommons.org/licenses/by/3.0/de/ |
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