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Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation

Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still δ correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation

Dunkel, Jörn; Hänggi, Peter
Physical Review E , Volume 74 (5) – Nov 1, 2006
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Publisher
American Physical Society (APS)
Copyright
Copyright © 2006 The American Physical Society
ISSN
1550-2376
DOI
10.1103/PhysRevE.74.051106
pmid
17279876
Publisher site
See Article on Publisher Site

Abstract

The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still δ correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.

Journal

Physical Review E – American Physical Society (APS)

Published: Nov 1, 2006

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