Jörn Dunkel
Relativistic Brownian Motion and Diffusion Processes
Supervisor: Prof. Dr. Peter Hänggi [Theoretical physics I]
Date of oral examination: 07/22/2008
153 pages, english , OPUS
This thesis investigates how the concept of Brownian motion can be generalized within the framework of special relativity. Our analysis begins with an overview of the history and applications, followed by a short introduction of basic concepts from the Langevin theory of nonrelativistic Brownian motions. Subsequently, relativistic Langevin equations in phase space are considered in detail. In doing so, we address relevant questions concerning the choice of time parameters, discretization rules and relativistic fluctuation-dissipation theorems. Furthermore, we will discuss approximations that must be made in order to obtain Langevin-type equations from microscopic models. The final part is dedicated to Non-Markovian relativistic diffusion models in Minkowski space-time. The thesis concludes with a summary of open questions, which may serve as a starting point for future investigations and extensions of the present theory.