Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-07-04
Phys.Rev.E74:051106,2006; Erratum-ibid.E74:069902,2006
Physics
Condensed Matter
Statistical Mechanics
v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33) added, thereby connection to earlier work clarified; v4:
Scientific paper
10.1103/PhysRevE.74.051106 10.11
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 $\gd$-correlated (white noise) but does \emph{no} longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Dunkel Jörn
Hänggi Peter
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