Emergence of nonwhite noise in Langevin dynamics with magnetic Lorentz force

Physical Review. E
Hyun-Myung ChunJae Dong Noh

Abstract

We investigate the low mass limit of Langevin dynamics for a charged Brownian particle driven by a magnetic Lorentz force. In the low mass limit, velocity variables relaxing quickly are coarse-grained out to yield effective dynamics for position variables. Without the Lorentz force, the low mass limit is equivalent to the high friction limit. Both cases share the same Langevin equation that is obtained by setting the mass to zero. The equivalence breaks down in the presence of the Lorentz force. The low mass limit cannot be achieved by setting the mass to zero. The limit is also distinct from the large friction limit. We derive the effective equations of motion in the low mass limit. The resulting stochastic differential equation involves a nonwhite noise whose correlation matrix has antisymmetric components. We demonstrate the importance of the nonwhite noise by investigating the heat dissipation by a driven Brownian particle, where the emergent nonwhite noise has a physically measurable effect.

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Citations

Jun 20, 2019·Physical Review. E·Sangyun Lee, Chulan Kwon
Feb 20, 2020·Physical Review. E·I AbdoliA Sharma
Dec 15, 2020·Soft Matter·Iman Abdoli, Abhinav Sharma
Apr 18, 2021·Physical Review. E·Youngkyoung BaeHawoong Jeong

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