Brownian motion in a magnetic field - art. no. 021105

We derive explicit forms of Markovian transition probability densities for the velocity-space, phase-space, and the Smoluchowski configuration-space B rownian motion of a charged particle in a constant magnetic field. By invok ing a hydrodynamical formalism for those stochastic processes, we quantify a continual (net on the local average) heat transfer from the thermostat to diffusing particles.