Multiple regimes of diffusion

TL;DR

This paper explores the complex diffusion behaviors of particles under variable forces and damping, introducing an asymptotic phase diagram to classify different limiting regimes of the model.

Contribution

It provides a comprehensive analysis of the full parameter space and introduces an asymptotic phase diagram for classifying diffusion regimes.

Findings

Identification of multiple asymptotic regimes

Development of an asymptotic phase diagram

Clarification of limiting behaviors in particle diffusion

Abstract

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases which are considered, some of which have been discussed in earlier work. Here we explore the full space of dimensionless parameters, and introduce an "asymptotic phase diagram" which delineates the limiting regimes.