Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 62: Poster - Dynamics

DY 62.1: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

Ergodicity criterion for small Hamiltonian systems — •Patrick Pietzonka and Udo Seifert — II. Institut für Theoretische Physik, Universität Stuttgart

We study the long-time behavior of Hamiltonian systems in the context of a formalism developed by H. Mori, R. Zwanzig and M. H. Lee (MZL) [1]. This formalism leads to the representation of autocorrelation functions of dynamical observables as infinite continued fractions. From the convergence properties and the analysis of these mathematical constructs we derive a simple formulation of an ergodicity criterion. We illustrate this criterion by applying it to non-linear oscillators and short chains of non-linearly coupled particles. These examples require the numerical computation of a large number of continued fraction coefficients.

Our approach reveals some general limits of the MZL formalism for certain classes of correlation functions. To overcome these limits we suggest a generalization that may lead to better approximations of correlation functions and entail a refined ergodicity criterion.

[1] M. H. Lee, Phys. Rev. Lett. 49, 1072 (1982)