Localization properties of nonlinear disordered lattices

In this thesis, the properties of nonlinear disordered one dimensional lattices is investigated. Part I gives an introduction to the phenomenon of Anderson Localization, the Discrete Nonlinear Schroedinger Equation and its properties as well as the generalization of this model by introducing the nonlinear index α. In Part II, the spreading behavior of initially localized states in large, disordered chains due to nonlinearity is studied. Therefore, different methods to measure localization are discussed and the structural entropy as a measure for the peak structure of probability distributions is introduced. Finally, the spreading exponent for several nonlinear indices is determined numerically and compared with analytical approximations. Part III deals with the thermalization in short disordered chains. First, the term thermalization and its application to the system in use is explained. Then, results of numerical simulations on this topic are presented where the focus lies especially on the energy dependence of the thermalization properties. A connection with so-called breathers is drawn.

Level thesis:degree_level

master

Grantor dc:publisher

Universität Potsdam

Author dc:creator

• Mulansky, Mario

• Anderson
• Lokalisierung
• Unordnung
• Ausbreitung
• Chaos
• Localization
• Disorder
• Spreading

Statement dc:rights

• Keine öffentliche Lizenz: Unter Urheberrechtsschutz

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2988

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:2988