Non-ergodicity and localization of invariant measure for two colliding masses

Jiao Wang; Giulio Casati; Tomaz Prosen

doi:10.1103/physreve.89.042918

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arXiv · 1309.7617

Non-ergodicity and localization of invariant measure for two colliding masses

Jiao Wang·Giulio Casati·Tomaz Prosen

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Abstract

We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one-dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For non-generic mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of pi, the system is ergodic, in consistence with existing rigorous results.

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Jiao Wang, Giulio Casati, Tomaz Prosen. 2013-09-29. Non-ergodicity and localization of invariant measure for two colliding masses. https://doi.org/10.1103/physreve.89.042918

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