Microscopic origin of the jump diffusion model

TL;DR

This paper derives a generalized diffusion equation from microscopic principles to explain molecular orientational relaxation, bridging the gap between small-angle diffusion and jump diffusion models.

Contribution

It introduces a new generalized diffusion equation based on microscopic derivation, extending the small-angle diffusion model and clarifying its relation to jump diffusion.

Findings

Derived a generalized diffusion equation from N-body Liouville dynamics.

Identified conditions linking the generalized diffusion to jump diffusion.

Discussed similarities and differences between the two models.

Abstract

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