Anomalous fluxes in overdamped Brownian dynamics with Lorentz force

Abstract

We study the stochastic motion of a particle subject to spatially varying Lorentz force in the smallmass limit. The limiting procedure yields an additional drift term in the overdamped equation that cannot be obtained by simply setting mass to zero in the velocity Langevin equation. We show that whereas the overdamped equation of motion accurately captures the position statistics of the particle, it leads to unphysical fluxes in the system that persist in the long time limit; an anomalous result inconsistent with thermal equilibrium. These fluxes are calculated analytically from the overdamped equation of motion and found to be in quantitative agreement with Brownian dynamics simulations. Our study suggests that the overdamped approximation, though perfectly suited for position statistics, can yield unphysical values for velocity-dependent variables such as flux and entropy production. arXiv:1812.01298v2 [cond-mat.soft]

Correlations in multithermostat Brownian systems with Lorentz force

“…Note that when the magnetic field is absent, equation ( 13) reduces to the diagonal matrix consistent with the previous studies [19,24]. In the case of the same temperatures along the spatial degrees of freedom and a nonzero magnetic field, the matrix D reduces to the well-known matrix [2,5,6], which is given as…”

“…We consider a single diffusing particle of mass m and charge q subjected to Lorentz force due to an external magnetic field B = Bn, directed along the unit vector n. Each spatial degree of freedom of the particle is coupled to a different thermostat at temperature T i where i = x, y, z. The stochastic dynamics of the particle are described by the following Langevin equation [1,2,5,6]:…”

“…However, the Lorentz force affects the dynamics of the system. For instance, it is well known that in diffusive systems Lorentz force reduces the diffusion coefficient of the particle in the plane perpendicular to the magnetic field, whereas the diffusion along the field is unaffected [1][2][3]. Even in overdamped systems, the hallmark signature of Lorentz force -deflection of trajectories in the direction perpendicular to the velocity -is manifested.…”

Nondiffusive fluxes in a Brownian system with Lorentz force

“…While the effect of the Lorentz force on the properties of materials has been thoroughly studied in the context of solid-state physics, much less is known about its influence on soft-matter systems which are dominated by overdamped dynamics. This becomes particularly interesting in light of the recent finding that the Lorentz force induces a particle flux perpendicular to density gradients, thus preventing a diffusive description of the dynamics [1,2]. In this paper, we study the unusual fluxes induced by the Lorentz force and their effect on the nonequilibrium dynamics of the system.…”

“…Whereas the Langevin equations are convenient for simulations, a statistical description is often preferred for theoretical analysis. To this end one derives the Fokker-Planck equation for the position degrees of freedom, which for a Brownian particle subject to inhomogeneous Lorentz force, is given as [2,5] ∂P (r, t) ∂t = ∇ · D(r)∇P (r, t) ,…”