Universality of giant diffusion in tilted periodic potentials

TL;DR

This paper introduces a universal stochastic model for giant diffusion in tilted periodic potentials, demonstrating a peak in diffusion coefficient across various potentials, especially at low temperatures, using renewal theory.

Contribution

It proposes a biased CTRW model with flight times to explain giant diffusion and shows its universal peak behavior in different periodic potentials.

Findings

Diffusion coefficient peaks universally in tilted periodic potentials.

Giant diffusion is significantly enhanced at low temperatures.

Maximum diffusion and optimal force depend on potential shape and temperature.

Abstract

Giant diffusion, where the diffusion coefficient of a Brownian particle in a periodic potential with an external force is significantly enhanced by the external force, is a non-trivial non-equilibrium phenomenon. We propose a simple stochastic model of giant diffusion, which is based on a biased continuous-time random walk (CTRW) with flight time. By introducing a flight time representing traversal dynamics, we derive the diffusion coefficient using renewal theory and demonstrate its universal peak behavior under various periodic potentials, especially in low-temperature regimes. Giant diffusion is universally observed in the sense that there is a peak of the diffusion coefficient for any tilted periodic potentials and the degree of the diffusivity is greatly enhanced especially for low-temperature regimes. The biased CTRW models with flight times are applied to diffusion under three tilted periodic potentials. Furthermore, the temperature dependence of the maximum diffusion coefficient and the external force that attains the maximum are presented for diffusion under a tilted sawtooth potential.