title: Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions.
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.
authors.affiliation: Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129, USA.
authors.forename: Pankaj
authors.initials: P
authors.lastname: Kumar
authors.affiliation: Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129, USA.
authors.forename: Bruce N
authors.initials: BN
authors.lastname: Miller
authors.affiliation: Department of Particle Physics, National Institute of Physics and Nuclear Technology, Bucharest, Romania.
authors.forename: Dan
authors.initials: D
authors.lastname: Pirjol