Non-ergodicity of two particles interacting via a smooth potential
type: Item
instance of: scholarly article
title: Non-ergodicity of two particles interacting via a smooth potential
zbMATH Open document ID: 0986.37012
DOI: 10.1023/A:1004688200435
author: Victor J. Donnay
published in: Journal of Statistical Physics
publication date: 2000-02-20T00:00:00Z
review text: The general philosophy of the paper is condensed in the statement: when one takes an ergodic system governed by inelastic collision and replaces the inelastic collision by an interaction caused by a smooth potential, ergodicity can be destroyed. Two particles are examined on a two-dimensional torus, while interacting via a smooth Lennard-Jones type potential of finite range. Situations are found such that this system contains a stable, elliptic periodic orbit and hence is not ergodic, this observation is contrasted to the case of hard spheres interacting via inelastic collisions, when ergodicity always holds true for the two-particle system. For this interaction, ergodicity conjectures exist in the arbitrary many particle case when elliptic periodic orbits cannot arise. Possible mechanisms of non-ergodicity in \(N\)-particle systems \((N>2)\) are analysed.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 37A60
Mathematics Subject Classification ID: 82C21
Mathematics Subject Classification ID: 37D50
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 1404172
zbMATH Keywords: Boltzmann ergodic hypothesis
zbMATH Keywords: non-ergodic system
zbMATH Keywords: elliptic orbit
zbMATH Keywords: KAM theory
zbMATH Keywords: Lennard-Jones potential
zbMATH Keywords: Sinai billiard
zbMATH Keywords: ergodic property
MaRDI profile type: Publication
full work available at URL: a:1004688200435
OpenAlex ID: W1553628425
description: scientific article; zbMATH DE number 1404172