Unusual stationary state in Brownian systems with Lorentz force

Abstract

In systems with overdamped dynamics, the Lorentz force reduces the diffusivity of a Brownian particle in the plane perpendicular to the magnetic field. The anisotropy in diffusion implies that the Fokker-Planck equation for the probabiliy distribution of the particle acquires a tensorial coefficient. The tensor, however, is not a typical diffusion tensor due to the antisymmetric elements which account for the fact that Lorentz force curves the trajectory of a moving charged particle. This gives rise to unusual dynamics with features such as additional Lorentz fluxes and a nontrivial density distribution, unlike a diffusive system. The equilibrium properties are, however, unaffected by the Lorentz force. Here we show that by stochastically resetting the Brownian particle, a nonequilibrium steady state can be created which preserves the hallmark features of dynamics under Lorentz force. We then consider a minimalistic example of spatially inhomogeneous magnetic field, which shows how Lorentz fluxes fundamentally alter the boundary conditions giving rise to an unusual stationary state.

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Cited by in corpus (11)

• Stochastic resetting with stochastic returns using external trap
• Resetting with stochastic return through linear confining potential
• Oscillatory force autocorrelations in equilibrium odd-diffusive systems
• Correlations in multithermostat Brownian systems with Lorentz force
• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
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