Escape Dynamics in an Anisotropically Driven Brownian Magneto-System

TL;DR

This study investigates how anisotropic noise and magnetic fields influence the escape dynamics of a charged Brownian particle in a potential, revealing tunable escape times and symmetry restoration at high magnetic fields.

Contribution

It introduces a detailed analysis of anisotropic driving effects on escape times in a magnetic field, highlighting the role of Lorentz force in coupling spatial degrees of freedom.

Findings

Escape time can be tuned by anisotropic noise strengths.

Large magnetic fields restore spatial symmetry.

Theoretical results match Brownian dynamics simulations.

Abstract

Thermally activated escape of a Brownian particle over a potential barrier is well understood within Kramers theory. When subjected to an external magnetic field, the Lorentz force slows down the escape dynamics via a rescaling of the diffusion coefficient without affecting the exponential dependence on the barrier height. Here, we study the escape dynamics of a charged Brownian particle from a two-dimensional truncated harmonic potential under the influence of Lorentz force due to an external magnetic field. The particle is driven anisotropically by subjecting it to noises with different strengths along different spatial directions. We show that the escape time can largely be tuned by the anisotropic driving. While the escape process becomes anisotropic due to the two different noises, the spatial symmetry is restored in the limit of large magnetic fields. This is attributed to the Lorentz force induced coupling between the spatial degrees of freedom which makes the difference between two noises irrelevant at high magnetic fields. The theoretical predictions are verified by Brownian dynamics simulations. In principle, our predictions can be tested by experiments with a Brownian gyrator in the presence of a magnetic field.