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 point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic 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 "delta"-correlated (white noise) but does no longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and elucidated.

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Author:Jörn Dunkel, Peter HänggiORCiDGND
Frontdoor URL
Publishing Institution:Universität Augsburg
Release Date:2006/08/30
Tag:Relativistic Brownian motion; Relativistic collision processes; Langevin equation
GND-Keyword:Brownsche Bewegung; Langevin-Gleichung; Weißes Rauschen
Source:One-dimensional non-relativistic and relativistic Brownian; erscheint in: Physica A: Statistical Mechanics and its Applications;
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik