Evolution of a sharp peak in the distribution of diatomic molecules over vibrational states

An analysis is made of the initial stage of evolution of a sharp peak in the molecular distribution over vibrational states. The nonlinear Fokker–Planck equation is used as the initial equation. The kinetic coefficients contained in this equation are calculated directly by solving the quantum-mechanical problem of vibrational quantum exchange in collisions between highly excited molecules. It is found that the evolution of the distribution function is described by a function which differs from the traditional solution of the diffusion equation, although the growth of the function width with time completely corresponds to familiar relationships.