Brownian motion in magnetic field: A model for a semi-quantum stochastic process

Abstract

The Brownian motion of an ensemble of charged particles in a quantizing magnetic field is considered in a simple ‘quasi-classical’ model. The model describes random jumps between the Landau levels—corresponding to the quantized motion perpendicular to the magnetic field, and markovian fluctuations in momentum space—corresponding to the classical motion parallel to the field. A random walk dynamics is adopted for the former while an Ornstein-Uhlenbeck process is considered for the latter. The resulting Fokker-Planck equations constitute a semi-quantum stochastic process. The equations are solved and several physical aspects of the underlying system are discussed.