Speaker
Description
The Bohr-van Leeuwen 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 contribution, we raise the question of whether this theorem applies to systems of particles undergoing a non-Markovian Brownian motion among other particles in a static magnetic field. We consider charged Brownian particles immersed in a bath of neutral particles. The Brownian particles interact with the surrounding particles, which are mutually independent. The basic theory that we are coming from is the famous Caldeira-Legget model for bath oscillators. Generalizing this model to the presence of an external magnetic field, we derive the equations of motion for the oscillators and the Brownian particle. The latter equation has the form of a generalized Langevin equation that accounts for memory effects in the dynamics of the system. We show a way to obtain exact analytical solutions for the particles’ displacements and time correlation functions such as the mean square displacement. Using these solutions for the Ornstein-Uhlenbeck thermal noise, we show that at long times, when the system reaches equilibrium, the magnetic moment of the Brownian particles vanishes in accordance with the Bohr-van Leeuwen theorem.
Acknowledgements
This work was supported by the grant VEGA 1/0353/22.
