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Non-ergodicity of Two Particles Interacting via a Smooth Potential

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Abstract

We examine two point particles interacting via a smooth Lennard-Jones-type potential of finite range on a two-dimensional torus. We find situations under which this system contains a stable, elliptic periodic orbit and hence is not ergodic. This result is in contrast to the case of hard spheres interacting via inelastic collision, which are always ergodic for two particles, are conjectured to be ergodic for arbitrarily many particles, and can never contain elliptic periodic orbits.

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  1. Department of Mathematics, Bryn Mawr College, Bryn Mawr, Pennsylvania, 19010

    Victor J. Donnay

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  1. Victor J. Donnay
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Donnay, V.J. Non-ergodicity of Two Particles Interacting via a Smooth Potential. Journal of Statistical Physics 96, 1021–1048 (1999). https://doi.org/10.1023/A:1004688200435

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  • DOI: https://doi.org/10.1023/A:1004688200435

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