https://doi.org/10.1140/epjp/s13360-024-05733-8
Regular Article
Stochastic harmonies: navigating Brownian paths through magnetic fields with Langevin approach
Department of Physics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, 641112, Coimbatore, Tamil Nadu, India
b
s_saravanaveni@cb.amrita.edu
Received:
13
September
2024
Accepted:
9
October
2024
Published online:
27
October
2024
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
