Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-10-30
Phys. Rev. E 71, 016124 (2005)
Physics
Condensed Matter
Statistical Mechanics
see cond-mat/0607082 for an improved theory
Scientific paper
10.1103/PhysRevE.71.016124
We construct a theory for the 1+1-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity, and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a heat bath (white noise), are generalized in the framework of special relativity. Subsequently, the corresponding relativistic Langevin equations are discussed in the context of the generalized Ito (pre-point discretization rule) vs. the Stratonovich (mid-point discretization rule) dilemma: It is found that the relativistic Langevin equation in the Haenggi-Klimontovich interpretation (with the post-point discretization rule) is the only one that yields agreement with the relativistic Maxwell distribution. Numerical results for the relativistic Langevin equation of a free Brownian particle are presented.
Dunkel Jörn
Hänggi Peter
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