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arXiv:1908.04749 [nlin.CD]AbstractReferencesReviewsResources

Exact hopping and collision times for two hard discs in a box

Wilhelm P. K. Zapfe, David P. Sanders, Rosa Rodríguez-Mota

Published 2019-08-13Version 1

We study the molecular dynamics of two discs undergoing Newtonian ("inertial") dynamics, with elastic collisions in a rectangular box. Using a mapping to a billiard model and a key result from ergodic theory, we obtain exact, analytical expressions for the mean times between the following events: hops, i.e.~horizontal or vertical interchanges of the particles; wall collisions; and disc collisions. To do so, we calculate volumes and cross-sectional areas in the four-dimensional configuration space. We compare the analytical results against Monte Carlo and molecular dynamics simulations, with excellent agreement.

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