Anisotropic diffusion in square lattice potentials: giant enhancement and control

TL;DR

This paper investigates how an external ac drive can induce highly anisotropic and controllable giant diffusion enhancements in a Brownian particle within a square lattice potential, with potential applications in directed transport.

Contribution

It demonstrates that external ac driving can significantly control and enhance anisotropic diffusion in a square lattice potential, revealing new ways to manipulate particle transport.

Findings

Diffusion becomes highly anisotropic with a dominant principal axis.

The principal diffusion axis can be tuned by external parameters.

Giant diffusion enhancement occurs at low temperatures.

Abstract

The unbiased thermal diffusion of an overdamped Brownian particle in a square lattice potential is considered in the presence of an externally applied ac driving. The resulting diffusion matrix exhibits two orthogonal eigenvectors with eigenvalues $D_1>D_2>0$, indicating anisotropic diffusion along a "fast" and a "slow principal axis". For sufficiently small temperatures, $D_1$ may become arbitrarily large and at the same time $D_2$ arbitrarily small. The principal diffusion axis can be made to point into (almost) any direction by varying either the driving amplitude or the coupling of the particle to the potential, without changing any other property of the system or the driving.