Dresden 2009 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 1: Statistical physics I (general)
DY 1.8: Vortrag
Montag, 23. März 2009, 12:30–12:45, HÜL 386
Variational Methods with and without Replicas for a Zero-Dimensional Disorder Model — •Markus Düttmann1, Jürgen Dietel1, and Axel Pelster1,2 — 1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany — 2Fachbereich Physik, Universität Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg, Germany
We analyze the stationary probability distribution of the Smoluchowski equation for an overdamped harmonic oscillator in a random potential with three analytic approximation methods. A standard method for tackling such a zero-dimensional disorder problem is the replica method [1]. However, the replica-symmetric solution breaks down for sufficiently small temperatures. Improved results are obtained by the replica symmetry breaking approach which was originally developed by Giorgio Parisi to treat spin-glass systems. Furthermore, we work out another variational approach, which does not rely on replicas and involves the temperature as a variational parameter. All three analytical approximation methods are compared with numerical results from Monte-Carlo simulations.
[1] A. Engel, Nucl. Phys. B 410, 617 (1993)