Publication

Abstract : In this study, we explore a system where charged particles are subjected to a harmonic potential while immersed in a constant magnetic field, manifesting characteristics of Brownian motion. The influence of the magnetic field creates coupled equations along the axes orthogonal to the field direction. To address this complex problem, we employ the Langevin approach. By using this method, we derive expressions for the mean square displacement and mean square velocity in the absence of the harmonic potential. We then extend our analysis with the harmonic potential and calculated the variances of displacement and velocity, as well as the covariance. These analytical results are rigorously compared with numerical simulations to validate their accuracy. Furthermore, our analysis incorporates the Bohr-van Leeuwen theorem, providing a comprehensive understanding of the system’s behavior under these conditions.