Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions
arXiv:cond-mat/0612124 · doi:10.1140/epjb/e2007-00187-2
Abstract
We derive the exact expression of the diffusion coefficient of a self-gravitating Brownian gas in two dimensions. Our formula generalizes the usual Einstein relation for a free Brownian motion to the context of two-dimensional gravity. We show the existence of a critical temperature T_{c} at which the diffusion coefficient vanishes. For T<T_{c} the diffusion coefficient is negative and the gas undergoes gravitational collapse. This leads to the formation of a Dirac peak concentrating the whole mass in a finite time. We also stress that the critical temperature T_{c} is different from the collapse temperature T_{*} at which the partition function diverges. These quantities differ by a factor 1-1/N where N is the number of particles in the system. We provide clear evidence of this difference by explicitly solving the case N=2. We also mention the analogy with the chemotactic aggregation of bacteria in biology, the formation of ``atoms'' in a two-dimensional (2D) plasma and the formation of dipoles or supervortices in 2D point vortex dynamics.
References in corpus (15)
- Thermodynamics of self-gravitating systems
- Gravitational instability of finite isothermal spheres
- Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
- Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
- Hamiltonian and Brownian systems with long-range interactions
- Post-collapse dynamics of self-gravitating Brownian particles in D dimensions
- Virial theorem and dynamical evolution of self-gravitating Brownian particles and bacterial populations in an unbounded domain
- Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas
- Self-gravitating Brownian systems and bacterial populations with two or more types of particles
- Accurate discretization of advection-diffusion equations
- Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations
- Jeans type instability for a chemotactic model of cellular aggregation
- Newtonian gravity in d dimensions
- Self diffusion in a system of interacting Langevin particles
- Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot
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- Novel Topological Phases and Self-Correcting Memories in Interacting Anyon Systems
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- Anisotropic long-range interaction investigated with cold atoms
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