The statistical mechanics of a one-dimensional self-gravitating system

Abstract

A series of numerical computer experiments on a one-dimensional self-gravitating system has been conducted. Hohl and Broaddus (1967) have estimated the thermalization time for this system to be N('2)(tau)c, based on oscillations in the kinetic energy covariance. We have used the direct comparison of the time-averaged density with the ensemble-averaged density to show that the relaxation time is orders of magnitude longer than their estimate. We compare the degree of convergence to the ensemble-average for systems of 4, 5, and 6 particles. The N = 6 case converges better than the N = 4 case, which we show is consistent with the Froeschle and Scheidecker (1975) interpretation of this model. A systematic exploration of the surface of sections for 3 particles is made. A dynamical interpretation of the stable and chaotic orbits is given.