Jan Busa | Searcharxiv

arXiv2025

Effect of Magnetic Field on Neutral Bath Containing Charged Brownian Particles

Based on the Zwanzig-Caldeira-Legget theory generalized to systems under the influence of a static magnetic field, we obtain equations of motion for the Brownian particle (BP) and oscillators constituting the bath in which the BP is embedded. The equations are of the type of a generalized Langevin equation, which accounts for the frictional memory of the system. The BP is assumed to be charged while the bath particles are neutral. They thus do not directly respond to the external field, but their interaction with the BP leads to changes in the bath state. Using the solution of the equations found, we calculate the average bath angular momentum and show that it persists for long times when the system is assumed to reach equilibrium. This indicates a possible violation of the Bohr-van Leeuwen theorem for baths consisting of charged particles. However, this must be confirmed by a substantial generalization of the presented model when the bath particles feel the external field, which affects the memory in the dynamics of the system.

cond-mat.soft↗

arXiv2025

Memory effects of a static magnetic field on Brownian motion and the question of the absence of classical magnetism

The Bohr-van Leeuwen (BvL) theorem, stating the absence of classical magnetization in equilibrium, a fundamental result in the field of magnetic phenomena, was originally proved for an electron gas. In the present work, we deal with the problem of whether this theorem applies to particles undergoing a non-Markovian Brownian motion in a static magnetic field. We consider a charged Brownian particle (BP) immersed in a bath of neutral particles. Generalizing the Zwanzig-Caldeira-Legget theory to the presence of a static external magnetic field, we come to the equation of motion for the BP in the form of a generalized Langevin equation that accounts for memory effects in the dynamics of the system. By using its solutions for the displacement and velocity of the BP, we calculate the angular momentum for the Ornstein-Uhlenbeck thermal noise. At long times, when the system should reach equilibrium, this momentum and, consequently, the classical magnetic moment of the BP are nonzero, in contrast to the BvL theorem. With the help of analytical and precise numerical calculations for different sets of system parameters, a simple formula for the angular momentum has been deduced.

cond-mat.soft↗