Stochastic theory of vibrational energy transfer in collinear atom-diatom collisions: The role of non-markovian effects

The role of non-markovian effects in the stochastic treatment of vibrational- translational energy transfer in collinear atom—diatom collisions is examined. A comparison of transition probabilities using both markovian and nonmarkovian types of master equations, as well as exact time dependent quantum mechanics, is made for various values of the system parameters m and a. We find that for certain ranges of the system parameters, the deviations between markovian and non-markovian theories are substantial. Only in the perturbation theory limit and in the limit of low m/α² values and high enough initial translational energies such that an impulsive approximation for translational motion is accurate are the markovian and non-markovian results similar. An analysis of the collision dynamics indicates that the markovian and non-markovian probabilities agree with each other and with the exact probabilities when action-angle correlations are weak while none of these theories agree (except by accident) when such effects are strong.