Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions

Pankaj Kumar, Bruce N. Miller, Dan Pirjol

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10 Scopus citations

Abstract

We study the thermodynamic properties of a one-dimensional gas with one-dimensional gravitational interactions. Periodic boundary conditions are implemented as a modification of the potential consisting of a sum over mirror images (Ewald sum), regularized with an exponential cutoff. As a consequence, each particle carries with it its own background density. Using mean-field theory, we show that the system has a phase transition at a critical temperature. Above the critical temperature the gas density is uniform, while below the critical point the system becomes inhomogeneous. Numerical simulations of the model, which include the caloric curve, the equation of state, the radial distribution function, and the largest Lyapunov exponent, confirm the existence of the phase transition, and they are in good agreement with the theoretical predictions.

Original languageEnglish
Article number022116
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume95
Issue number2
DOIs
StatePublished - 14 Feb 2017

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