ENGLISH ABSTRACT: In this dissertation, we give an overview of disordered systems, where we concentrate on the theoretical calculation techniques used in this field. We first discuss the general properties of disordered ...

ENGLISH ABSTRACT: This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework is established in the initial chapter and used as a background for the entire ...

ENGLISH ABSTRACT: In this thesis, generalized Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion ...

ENGLISH ABSTRACT: Due to the minimal length scale induced by non-commuting co-ordinates, it is not clear a priori what is meant by a position measurement on a non-commutative space. It was shown recently in a paper by ...

The aim of this thesis is the semi-classical implementation of Wegner’s flow equations and comparison with the well-established Wentzel-Kramers-Brillouin method. We do this by converting operators, in particular the ...

The goal of this thesis is the development and implementation of a non-perturbative solution method for Wegner’s flow equations. We show that a parameterization of the flowing Hamiltonian in terms of a scalar function ...

The propagation of electromagnetic radiation in homogeneous or periodically modulated media can be described by the coupled mode equations. The aim of this study was to derive analytical expressions modeling the solutions ...

It was Wigner that in the 1950’s first introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of Random Matrix ...

ENGLISH ABSTRACT: The aim of this thesis is threefold. Firstly, I give an overview of non-commutative quan- tum mechanics and build up a description of non-commutative piecewise constant poten- tial wells in this context. ...

ENGLISH ABSTRACT: A constructive procedure to build gravitational duals from quantum mechanical models is developed with the aim of studying aspects of the gauge/gravity duality. The construction is simplified as far as ...