Vortex and translational currents due to broken time-space symmetries

TL;DR

This paper analyzes how broken time-space symmetries in a particle's dynamics within periodic potentials lead to nonzero averaged translational and vortex currents, supported by computational and symmetry analysis, with implications for cold atom experiments.

Contribution

It provides a general symmetry analysis and computational validation of conditions for generating directed and vortex currents in classical particles.

Findings

Broken symmetries induce nonzero averaged currents.

Computational results confirm symmetry-based predictions.

Potential experimental observation in cold atom systems.

Abstract

We consider the classical dynamics of a particle in a $d=2,3$-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify conditions, when the particle will generate a nonzero averaged translational and vortex currents. We perform computational studies of the equations of motion and of corresponding Fokker-Planck equations, which confirm the symmetry predictions. We address the experimentally important issue of current control. Cold atoms in optical potentials and magnetic traps are among possible candidates to observe these findings experimentally.