Non-ergodicity of two particles interacting via a smooth potential
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.
scientific article; zbMATH DE number 1404172