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One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

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  • Dunkel, Jörn
  • Hänggi, Peter

Abstract

We study a simple microscopic model for the one-dimensional stochastic motion of a (non-)relativistic Brownian particle, embedded into a heat bath consisting of (non-)relativistic particles. The stationary momentum distributions are identified self-consistently (for both Brownian and heat bath particles) by means of two coupled integral criteria. The latter follow directly from the kinematic conservation laws for the microscopic collision processes, provided one additionally assumes probabilistic independence of the initial momenta. It is shown that, in the non-relativistic case, the integral criteria do correctly identify the Maxwellian momentum distributions as stationary (invariant) solutions. Subsequently, we apply the same criteria to the relativistic case. Surprisingly, we find here that the stationary momentum distributions differ slightly from the standard Jüttner distribution by an additional prefactor proportional to the inverse relativistic kinetic energy.

Suggested Citation

  • Dunkel, Jörn & Hänggi, Peter, 2007. "One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 559-572.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:2:p:559-572
    DOI: 10.1016/j.physa.2006.07.013
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    Cited by:

    1. Debbasch, F., 2008. "Equilibrium distribution function of a relativistic dilute perfect gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2443-2454.

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