TY - JOUR

T1 - Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions

AU - Kumar, Pankaj

AU - Miller, Bruce N.

AU - Pirjol, Dan

N1 - Publisher Copyright: © 2017 American Physical Society.

PY - 2017/2/14

Y1 - 2017/2/14

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevE.95.022116

DO - 10.1103/PhysRevE.95.022116

M3 - Article

C2 - 28297915

SN - 2470-0045

VL - 95

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 2

M1 - 022116

ER -