You need JavaScript to view this

Numerical approaches to complex quantum, semiclassical and classical systems

Abstract

In this work we analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give  More>>
Authors:
Publication Date:
Nov 03, 2008
Product Type:
Thesis/Dissertation
Report Number:
INIS-DE-0647
Resource Relation:
Other Information: TH: Diss. (Dr.rer.nat.)
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; PARTICLES; POTENTIALS; EIGENSTATES; WIGNER DISTRIBUTION; SHEETS; KERNELS; POLYNOMIALS; HILBERT SPACE; POLARONS; ABSORPTION; SEMICLASSICAL APPROXIMATION; INTERFERENCE; PROPAGATOR; DYNAMICS; PLASMA; DUSTS; NUMERICAL SOLUTION; QUANTUM MECHANICS; CLASSICAL MECHANICS; MANY-BODY PROBLEM; ENERGY-LEVEL DENSITY; EQUIVALENT CIRCUITS; ELECTRIC CONDUCTIVITY; CARBON; TWO-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE; SERIES EXPANSION; QUANTUM OPERATORS; TEMPERATURE DEPENDENCE; ONE-DIMENSIONAL CALCULATIONS; TUNNEL EFFECT; WAVE FUNCTIONS; DENSITY MATRIX; DISTRIBUTION FUNCTIONS; PLASMA SIMULATION; THREE-DIMENSIONAL CALCULATIONS
OSTI ID:
21169716
Research Organizations:
Greifswald Univ. (Germany). Mathematisch-Naturwissenschaftliche Fakultaet
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
TRN: DE09F5314
Availability:
Commercial reproduction prohibited; INIS; OSTI as DE21169716
Submitting Site:
DEN
Size:
123 pages
Announcement Date:
Jun 04, 2009

Citation Formats

Schubert, Gerald. Numerical approaches to complex quantum, semiclassical and classical systems. Germany: N. p., 2008. Web.
Schubert, Gerald. Numerical approaches to complex quantum, semiclassical and classical systems. Germany.
Schubert, Gerald. 2008. "Numerical approaches to complex quantum, semiclassical and classical systems." Germany.
@misc{etde_21169716,
title = {Numerical approaches to complex quantum, semiclassical and classical systems}
author = {Schubert, Gerald}
abstractNote = {In this work we analyse the capabilities of several numerical techniques for the description of different physical systems. Thereby, the considered systems range from quantum over semiclassical to classical and from few- to many-particle systems. In chapter 1 we investigate the behaviour of a single quantum particle in the presence of an external disordered background (static potentials). Starting from the quantum percolation problem, we address the fundamental question of a disorder induced (Anderson-) transition from extended to localised single-particle eigenstates. Distinguishing isolating from conducting states by applying a local distribution approach for the local density of states (LDOS), we detect the quantum percolation threshold in two- and three-dimensions. Extending the quantum percolation model to a quantum random resistor model, we comment on the possible relevance of our results to the influence of disorder on the conductivity in graphene sheets. For the calculation of the LDOS as well as for the Chebyshev expansion of the time evolution operator, the kernel polynomial method (KPM) is the key numerical technique. In chapter 2 we examine how a single quantum particle is influenced by retarded bosonic fields that are inherent to the system. Within the Holstein model, these bosonic degrees of freedom (phonons) give rise to an infinite dimensional Hilbert space, posing a true many-particle problem. Constituting a minimal model for polaron formation, the Holstein model allows us to study the optical absorption and activated transport in polaronic systems. Using a two-dimensional variant of the KPM, we calculate for the first time quasi-exactly the optical absorption and dc-conductivity as a function of temperature. In chapter 3 we come back to the time evolution of a quantum particle in an external, static potential and investigate the capability of semiclassical approximations to it. We address basic quantum effects as tunneling, interference and anharmonicity. To this end we consider the linearised semiclassical propagator method, the Wigner-Moyal approach and the recently proposed quantum tomography. Finally, in chapter 4 we calculate the dynamics of a classical many-particle system under the influence of external fields. Considering a low-temperature rf-plasma, we investigate the interplay of the plasma dynamics and the motion of dust particles, immersed into the plasma for diagnostic reasons. (orig.)}
place = {Germany}
year = {2008}
month = {Nov}
}