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

The probability per unit time for a thermally activated Brownian particle to escape over a potential well is, in general, well-described by Kramers's 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's 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 a vortex flow. While the 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 vortex and the applied magnetic field. Notably, the last case corresponds to enhanced escape dynamics.

Nondiffusive fluxes in a Brownian system with Lorentz force.

The Fokker-Planck equation provides a complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial coefficient, which reflects the anisotropy of the particle's motion. This tensor, however, cannot be interpreted as a diffusion tensor; there are antisymmetric terms which give rise to fluxes perpendicular to the density gradients. Here, we show that for an inhomogeneous magnetic field these nondiffusive fluxes have finite divergence and therefore affect the density evolution of the system. Only in the special cases of a uniform magnetic field or carefully chosen initial condition with the same full rotational symmetry as the magnetic field can these fluxes be ignored in the density evolution.