Breaking of general rotational symmetries by multi-dimensional classical ratchets

TL;DR

This paper investigates how multi-dimensional classical ratchets can break rotational symmetries, leading to persistent rotational flows driven by uncorrelated noise in complex potentials, with analytical and flow pattern analyses.

Contribution

It introduces a theoretical framework for analyzing rotational symmetry breaking in multi-dimensional ratchets driven by colored noise, deriving explicit particle current expressions.

Findings

Particle rotations are independent of initial conditions.

Derived explicit formulas for particle currents based on noise and potential asymmetries.

Identified diverse flow patterns, including laminar and rotational flows.

Abstract

We demonstrate that a particle driven by a set of spatially uncorrelated, independent colored noise forces in a bounded, multidimensional potential exhibits rotations that are independent of the initial conditions. We calculate the particle currents in terms of the noise statistics and the potential asymmetries by deriving an n-dimensional Fokker-Planck equation in the small correlation time limit. We analyze a variety of flow patterns for various potential structures, generating various combinations of laminar and rotational flows.