  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.
