Description
The stochastic motion of charged particles in an external magnetic field has attracted the intense attention of researchers for more than half a century, but still, several problems remain unsolved. In this contribution, we study the response of a system consisting of a neutral heat bath that contains a charged Brownian particle (BP) to an external static magnetic field. The bath particles do not interact directly with the magnetic field, but it affects them due to their interaction with the BP. We obtain the equations of motion for the particles of the system within the framework of the generalized Zwanzig-Caldeira-Leggett model. Based on this theory, the motion of the BP is described by the Langevin stochastic equations. We have found that in the case of the memoryless theory, the angular momentum of the bath particles is nonzero and does not disappear even at long times after the magnetic field is switched on, while their kinetic energy obeys equipartition at all times. Closed-form analytical solutions are obtained for the individual bath particles and for the entire unbounded bath if the dynamics of the BP is overdamped. In the latter case, the mean angular momentum is simply proportional to time t, as is the mean square displacement of the BP in the plane perpendicular to the magnetic field. The problem offers several possibilities for further generalizations.