Hidden symmetries, instabilities, and current suppression in Brownian ratchets

TL;DR

This paper uncovers hidden symmetries in Brownian ratchets that standard analysis misses, and shows how instabilities can break symmetries to produce directed transport, advancing understanding of Brownian motor control.

Contribution

It reveals hidden symmetries in Brownian ratchets and demonstrates how instabilities can induce symmetry breaking and current generation, providing new insights into transport mechanisms.

Findings

Identification of hidden symmetries beyond standard analysis

Spontaneous symmetry breaking due to system instabilities

Controlled current direction near symmetry points

Abstract

The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of {\it hidden} symmetries, which escape the identification by the standard symmetry analysis, and require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.