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.
| Author: | Jörn Dunkel, Peter HänggiORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-2517 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/314 |
| Type: | Preprint |
| Language: | English |
| 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; www.elsevier.com/locate/physa |
| 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 |
