Microscopic origin of the jump diffusion model

摘要

The present paper is aimed at studying the microscopic origin of the jump diffusion. Starting fromthe N-body Liouville equation and making only the assumption that molecular reorientation isoverdamped, we derive and solve the new (hereafter generalized diffusion) equation. This is themost general equation which governs orientational relaxation of an equilibrium molecular ensemblein the hindered rotation limit and in the long time limit. The generalized diffusion equation is anextension of the small-angle diffusion equation beyond the impact approximation. We establish theconditions under which the generalized diffusion equation can be identified with the jump diffusionequation, and also discuss the similarities and differences between the two approaches.