Stochastic model of collisional energy transfer based on the diffusion equation

Abstract

Collisional energy transfer from highly excited polyatomic molecules in a heat reservoir is considered as a diffusion process in energy space. It is taken into account that the density of the vibrational states of polyatomic molecules is very high and presented by a continuous energy function. Both the average energy transfer moments per collision and these moments averaged over an ensemble of molecules have been calculated to obtain an exact analytical solution to the diffusion equation. At long times, the solution to the diffusion equation converges to the equilibrium Boltzmann distribution. The conditional probability density decays at long times with a vibrational energy relaxation time. The ensemble averages tend to equilibrium with the same characteristic time.