Open AccessHarmonic oscillator Brownian motion: Langevin approach revisited
Author(s) -
O. Contreras-Vergara,
N. Lucero-Azuara,
N. Sánchez-Salas,
J. I. Jiménez-Aquino
Publication year - 2021
Publication title -
revista mexicana de física e
Language(s) - English
Resource type - Journals
eISSN - 2683-2216
pISSN - 1870-3542
DOI - 10.31349/revmexfise.18.97
Subject(s) - langevin equation , brownian dynamics , brownian motion , harmonic oscillator , white noise , langevin dynamics , statistical physics , physics , noise (video) , stochastic differential equation , harmonic , gaussian , simple harmonic motion , relaxation (psychology) , classical mechanics , mathematics , quantum mechanics , computer science , psychology , social psychology , statistics , artificial intelligence , image (mathematics)
The original strategy applied by Langevin to the Brownian movement problem is used to solve the case of a free particle under a harmonic potential. Such a straightforward strategy consists of separating the noise term in the Langevin equation to solve a deterministic equation associated with the Mean Square Displacement. In this work, we use the Langevin’s original strategy to calculate the statistical properties of the harmonic oscillator Brownian Motion, in the damped and periodic cases. It is shown that, in the long time limit, Langevin’s original method is consistent with the exact theoretical solutions reported by Chandrasekhar and Lemons, these latter obtained using the statistical properties of a Gaussian white noise. Also, unexpected results are presented when the method is applied to a free particle case. Our results are compared with the exact theoretical solutions, as well as with the numerical simulations.
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