Strong Collision Model for Energy Transfer in Systems of Oscillators

Abstract

Transition probabilities are formulated for single quantized oscillators which interact with a similar heat bath such that vibrational energy is conserved and randomly distributed between collision partners. Explicit solutions have been obtained for the corresponding relaxation and mean‐passage‐time problem, and results for the latter are compared with both ``equilibrium'' behavior and the predictions of the Landau—Teller scheme. Deviations from the equilibrium hypothesis tend toward a well‐defined limit as the level spacing decreases to zero but are effectively negligible except where dissociation occurs within about 10 collisions. It is shown that the notion of random energy distribution leads to a ``principal relaxation time'' of two collision intervals, which seems likely to be a lower bound for realizable energy‐transfer models.