13 research outputs found
Relativistic Brownian Motion
Stimulated by experimental progress in high energy physics and astrophysics,
the unification of relativistic and stochastic concepts has re-attracted
considerable interest during the past decade. Focusing on the framework of
special relativity, we review, here, recent progress in the phenomenological
description of relativistic diffusion processes. After a brief historical
overview, we will summarize basic concepts from the Langevin theory of
nonrelativistic Brownian motions and discuss relevant aspects of relativistic
equilibrium thermostatistics. The introductory parts are followed by a detailed
discussion of relativistic Langevin equations in phase space. We address the
choice of time parameters, discretization rules, relativistic
fluctuation-dissipation theorems, and Lorentz transformations of stochastic
differential equations. The general theory is illustrated through analytical
and numerical results for the diffusion of free relativistic Brownian
particles. Subsequently, we discuss how Langevin-type equations can be obtained
as approximations to microscopic models. The final part of the article is
dedicated to relativistic diffusion processes in Minkowski spacetime. Due to
the finiteness of velocities in relativity, nontrivial relativistic Markov
processes in spacetime do not exist; i.e., relativistic generalizations of the
nonrelativistic diffusion equation and its Gaussian solutions must necessarily
be non-Markovian. We compare different proposals that were made in the
literature and discuss their respective benefits and drawbacks. The review
concludes with a summary of open questions, which may serve as a starting point
for future investigations and extensions of the theory.Comment: review article, 159 pages, references updated, misprints corrected,
App. A.4. correcte
[correspondence] Brief aan Ferdinand Vander Haeghen te Gent.
Record 000032671 versmolten met record 000053644