A simple phenomenologic model for particle transport in space-periodic potentials in underdamped systems

TL;DR

This paper introduces a phenomenological model that simplifies the understanding of particle transport in space-periodic potentials for underdamped systems, by mapping it to an overdamped motion in velocity space, supported by analytical and simulation results.

Contribution

It presents a new phenomenological model that describes underdamped particle motion as overdamped in velocity space, providing simple analytical expressions validated by simulations.

Findings

Analytical expressions for mobility and diffusion coefficient match simulation data.

Model effectively describes particle dynamics across a wide temperature range.

Simplifies analysis of underdamped particle transport in periodic potentials.

Abstract

We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in space-periodic potentials can be considered as the overdamped motion in the velocity space in the effective double-well potential. Simple analytic expressions for the particle mobility and diffusion coefficient have been derived with the use of the presented model. The results of analytical computations match well with numerical simulation data.