Systems of oscillators with statistical energy exchange in collisions

Abstract

Classical transition probabilities are derived for the exchange of energy between sets of weakly coupled harmonic oscillators, subject to the assumption that energy is ‘statistically redistributed’ in all collisions. In the case of single oscillators the result is particularly simple and an explicit solution of the relaxation equation for such a system is derived. A ‘mean first passage time’ for the dissociation of truncated harmonic oscillators is also obtained using Widom's theory and the limiting case of equilibrium reaction is discussed. The same approach is sketched briefly for the case of quantized systems in which statistical redistribution of energy is allowed. Within the general scope of the model, these transition probabilities represent the most efficient conceivable coupling between system and heat bath.