Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Jörn Dunkel, Peter Hänggi
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 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 -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 discussed.
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