Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions

Abstract

We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, we derive the analytic form of the density scaling profile which decays as f(x)=x^{-α}, with alpha=2. In the microcanonical ensemble, we show that f decays as f(x)=x^{-α_{max}}, where α_{max} is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features.

References in corpus (6)

• Thermodynamics of self-gravitating systems
• Gravitational instability of finite isothermal spheres
• Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
• Kinetic theory of point vortices: diffusion coefficient and systematic drift
• Phase diagram of self-attracting systems
• Gravitational instability of polytropic spheres and generalized thermodynamics

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