Exact hopping and collision times for two hard discs in a box
Chaotic Dynamics
2019-08-19 v1 Statistical Mechanics
Abstract
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.
Cite
@article{arxiv.1908.04749,
title = {Exact hopping and collision times for two hard discs in a box},
author = {Wilhelm P. K. Zapfe and David P. Sanders and Rosa Rodríguez-Mota},
journal= {arXiv preprint arXiv:1908.04749},
year = {2019}
}
Comments
14 pages, 12 figures