Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
Abstract
We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. The equilibrium states correspond to polytropic distributions. The index n of the polytrope is related to the exponent of anomalous diffusion. We consider a high-friction limit and reduce the problem to the study of the nonlinear Smoluchowski-Poisson system. We show that the associated Lyapunov functional is the Tsallis free energy. We discuss in detail the equilibrium phase diagram of self-gravitating polytropes as a function of D and n and determine their stability by using turning points arguments and analytical methods. When no equilibrium state exists, we investigate self-similar solutions describing the collapse. These results can be relevant for astrophysical systems, two-dimensional vortices and for the chemotaxis of bacterial populations. Above all, this model constitutes a prototypical dynamical model of systems with long-range interactions which possesses a rich structure and which can be studied in great detail.
Keywords
Cite
@article{arxiv.cond-mat/0303088,
title = {Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions},
author = {Pierre-Henri Chavanis and Clement Sire},
journal= {arXiv preprint arXiv:cond-mat/0303088},
year = {2009}
}
Comments
Submitted to Phys. Rev. E