Year: 2017
Type: dissertation
Abstract: The framework of nonequilibrium Green functions is developed to accurately describe interacting quantum systems evolving in the presence of strongly exciting ultra-fast fields. At its core stands the selfconsistent determination of the selfenergy, a functional of the single-particle Green function, which incorporates all relevant many-body physics. The single-particle Green function is the solution of a coupled set of kinetic equations. Its intrinsic dependence on two independent time-arguments, ranging over the complete past of the system, not only enables the determination of all single-particle observables but also provides access to important two-particle observables and spectral information. With this coupling to the history, though, comes the practical necessity to apply physically motivated approximation techniques to the structure of the selfenergy and the Green functions, to achieve numerical tractability. This thesis is devoted to provide a thorough overview of the possible approximation techniques including perturbative and non-perturbative approaches. Starting from the exact coupled set of equations of motion for the Green functions, the expressions for all selfenergy approximations are derived in the most general basis representation and the special cases of a diagonal basis and the Hubbard basis with scalar interaction. In the second part of this thesis, the quality of the selfenergy approximations to describe time-dependent as well as ground-state properties of interacting systems is tested. A special focus lies on fermionic Hubbard nano-clusters, where the effect of the interaction strength and the filling factor on the performance of the approximations is studied.
Author: Hermanns, Sebastian
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7110471007