Maxwellian relaxation of elastic particles in one dimension

摘要

The statistical mechanics of one-dimensional binary mixtures is discussed from both a theoretical and simulation point of view at a level suitable for senior and introductory graduate level courses in statistical mechanics. By using a simple mathematical technique, the nonlinear Boltzmann equation is solved exactly in Fourier space. An efficient simulation algorithm is presented which yields results that are in excellent agreement with theory. We show that the velocity distribution of each type of particle relaxes to a Maxwellian for all mass ratios other than unity and infinity, and the relaxation time is a minimum for the mass ratio of 3+2√2.