Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-08-12
Nucl.Phys. B654 (2003) 427-444
Physics
Condensed Matter
Statistical Mechanics
21 pages, 5 figures, minor revisions, to appear in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(03)00050-6
We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum $\lambda_c$ (or, in the canonical language, a critical angular velocity $\omega_c$) exists, such that for $\lambda<\lambda_c$ the system's behaviour is qualitatively similar to that of a non-rotating gas, with a high energy disordered phase and a low energy collapsed phase ending with Antonov's limit, below which there is no equilibrium state. For $\lambda>\lambda_c$, instead, the low-energy phase is characterized by the formation of two dense clusters (a ``binary star''). Remarkably, no Antonov limit is found for $\lambda>\lambda_c$. The thermodynamics of the system (phase diagram, caloric curves, local stability) is analyzed and compared with the recently-obtained picture emerging from a different type of statistics which forbids particle overlapping.
Gross D. H. E.
Martino Alessandro de
Votyakov Evgeny V.
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