Directing Brownian motion on a periodic surface

TL;DR

This paper investigates how an overdamped Brownian particle moves on a square lattice surface under combined ac and dc forces, revealing complex directional responses including motion opposite to the applied force due to symmetry breaking.

Contribution

It introduces a novel analysis of Brownian motion on a periodic surface under combined ac and dc forces, highlighting the role of symmetry breaking in particle mobility.

Findings

Mobility in any direction depending on driving amplitude.

Motion opposite to the applied dc-force can occur.

Particle dynamics exhibit spontaneous symmetry breaking.

Abstract

We consider an overdamped Brownian particle, exposed to a two-dimensional, square lattice potential and a rectangular ac-drive. Depending on the driving amplitude, the linear response to a weak dc-force along a lattice symmetry axis consist in a mobility in basically any direction. In particular, motion exactly opposite to the applied dc-force may arise. Upon changing the angle of the dc-force relatively to the square lattice, the particle motion remains predominantly opposite to the dc-force. The basic physical mechanism consists in a spontaneous symmetry breaking of the unbiased deterministic particle dynamics.