Generalized Master Equation with Two Times: Diffusion in External Field

TL;DR

This paper extends the generalized master equation with two times to model diffusion in inhomogeneous external fields, focusing on the quasi Fokker-Planck approximation where the transition probability lacks long tails.

Contribution

It introduces a formulation of the generalized master equation for diffusion in external fields within the quasi Fokker-Planck approximation, addressing cases without long tails in the PTD.

Findings

Applicable to diffusion in time-dependent external fields

Derives equations under the quasi Fokker-Planck approximation

Discusses future work on long-tailed PTD cases

Abstract

The generalized master equation with two times, introduced in earlier, applies to the problem of diffusion in an time-dependent (in general inhomogeneous) external field. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as the function of instantaneous displacements. The more complicated case of the long tails in PTD will be discussed separately.