Effect of Magnetic Field on Neutral Bath Containing Charged Brownian Particles

TL;DR

This paper extends the Zwanzig-Caldeira-Legget theory to analyze how a static magnetic field influences a neutral bath containing charged Brownian particles, revealing potential violations of classical magnetic theorems.

Contribution

It introduces a generalized Langevin equation model for charged Brownian particles in a magnetic field, highlighting long-term bath angular momentum effects.

Findings

Persistent bath angular momentum at equilibrium

Potential violation of Bohr-van Leeuwen theorem

Charged particles influence neutral bath dynamics

Abstract

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.