Speaker
Description
In the last two decades, the stochastic motion of charged particles in external magnetic fields has attracted considerable attention, mainly due to the necessity of taking into account memory effects in particle dynamics. The problem considered in this contribution is closely related to the Bohr-van Leeuwen theorem, which governs the response of equilibrium systems to external magnetic fields. Based on the Caldeira-Legget theory generalized to systems under the influence of a static magnetic field, we obtain equations of motion for the Brownian particles and oscillators constituting the bath in which the particle is embedded. The former equation is known as the generalized Langevin equation, which accounts for the frictional memory of the system. The Brownian particle is assumed to be charged while the bath particles are neutral. They thus do not respond to the external field but their interaction with the Brownian particle 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 in 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 memory in the dynamics of the system.
Acknowledgements
This work was supported by the grant VEGA 1/0353/22.
