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Relaxation of the Probability Characteristics of Brownian Motion under the Action of a Non-Delta-Correlated Random Force

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Abstract

We consider the relaxation of the moments of the coordinates of one-dimensional Brownian motion of particles in a symmetric potential profile under the action of a Gaussian, exponentially correlated random force. An analytical-numerical method of analysis based on obtaining and numerically solving a chain of differential equations for joint cumulants of some functions of particle coordinates and a random force is used. A priori constraints on the intensity and correlation time of noise are not imposed. Numerical procedure is checked by comparison with analytical results, which can be found in the limiting cases of delta-correlated and quasistatic random force. The dependence of the relaxation of the average value and variance on the intensity and spectrum of a random force and the character of the initial distribution of particles is elucidated. In particular, the presence of a variance minimum during distribution relaxation is established. The evolution of the model probability distribution of particle coordinates is constructed on the basis of the moment relaxation.

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Authors and Affiliations

  1. N. I. Lobachevsky State University, Nizhny Novgorod, Russia

    A. N. Malakhov

  2. Nizhny Novgorod Architectural and Civil-Engineering University, Nizhny Novgorod, Russia

    O. V. Muzychuk

Authors
  1. A. N. Malakhov
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  2. O. V. Muzychuk
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Malakhov, A.N., Muzychuk, O.V. Relaxation of the Probability Characteristics of Brownian Motion under the Action of a Non-Delta-Correlated Random Force. Radiophysics and Quantum Electronics 44, 907–914 (2001). https://doi.org/10.1023/A:1014224216322

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  • DOI: https://doi.org/10.1023/A:1014224216322

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