Magnetic-Field-Induced Angular Momentum in a Neutral Bath Containing a Charged Brownian Particle

We study the response of a system consisting of a neutral heat bath (liquid or gaseous) 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 original or generalized Langevin stochastic equations with memory effects. For memoryless overdamped dynamics, we find that individual bath particles acquire a nonzero mean angular momentum, while the collective angular momentum of the bath grows linearly with time; at the same time, their mean kinetic energy obeys equipartition. Closed-form analytical solutions are obtained for the individual bath particles and for the entire bath if the dynamics of the BP is overdamped. The problem offers several possibilities for further generalizations.