Tailoring the escape rate of a Brownian particle by combining a vortex flow with a magnetic field

TL;DR

This paper demonstrates how combining a vortex flow with a magnetic field can tailor the escape rate of a charged Brownian particle by effectively modifying the potential landscape, enabling control over escape dynamics.

Contribution

It introduces a method to modify the effective potential experienced by a Brownian particle using vortex flow and magnetic field, extending Kramers theory for escape rates.

Findings

External vortex flow combined with magnetic field alters the effective potential.

The effective potential can be tuned to flat, stable, or unstable configurations.

Enhanced escape dynamics occur when the potential becomes unstable.

Abstract

The probability per unit time for a thermally activated Brownian particle to escape over a potential well is in general well-described by Kramers theory. Kramers showed that the escape time decreases exponentially with increasing barrier height. The dynamics slow down when the particle is charged and subjected to a Lorentz force due to an external magnetic field. This is evident via a rescaling of the diffusion coefficient entering as a prefactor in the Kramers escape rate without any impact on the barrier-height-dependent exponent. Here we show that the barrier height can be effectively changed when the charged particle is subjected to an external vortex flow. While the external vortex alone does not affect the mean escape time of the particle, when combined with a magnetic field it effectively pushes the fluctuating particle either radially outside or inside depending on its sign relative to that of the magnetic field. In particular, the effective potential over which the particle escapes can be changed to a flat, a stable, and an unstable potential by tuning the signs and magnitudes of the external vortex and the applied magnetic field. Notably, the last case corresponds to enhanced escape dynamics.