Multiple time scale stochastic formulation for collision problems with more than one degree of freedom

Individual molecular collisions have been described by nonequilibrium statistical mechanics in previous work. The present paper deals mainly with refinements and extensions of the theory for systems with more than one internal degree of freedom. For example, it is shown how quantum mechanics for one internal mode can be combined with stochastic equations for the other kinds of motion. A multiple time scale stochastic formulation, which allows each degree of freedom its own "natural" time scale is also described. It is shown, by an application to vibration-rotation inelasticity in the He ⁴-para-H₂ system, that this method gives results in good agreement with full quantum calculations and experimental measurements. A computationally simple technique for restoring microscopic reversibility to time-dependent quantum calculations that employ the classical path approximation is also described.