The non-Poissonian collision model for the condensed phase activated rate processes

The non-Poissonian collision model (CM) of energy dissipation (friction) in condensed phase activated rate processes is proposed and analyzed in detail. This model describes the instantaneous change of the velocity distribution of a probe particle caused by the collisions with particles of a medium. In the considered CM the statistics of collisions is assumed to be non-Poissonian. The efficiency of collisions is determined by the transition kernel K(v,v′) in the velocity space which can model both the weak and the strong collision limits including the cases of complete velocity randomization and backscattering (v≈−v′). In the proposed CM simple formulas for the diffusion coefficient D and the rate kr of passage over a barrier are derived in the moderate-to-strong friction limit. They accurately reproduce the known analytical and numerical results. The non-Poissonian CM predicts the interesting phenomenon, the kinetic cage effect, which is observed for the special type of the collision distribution functions corresponding to the nearly periodic collisions and shows itself in the small absolute value of D and kr in the case of backscattering. This effect as well as some other predictions of the proposed CM are discussed in detail.