Gravity in one dimension: A dynamical and statistical study

Abstract

Computer experiments performed on a one-dimensional self-gravitating system are discussed from a dynamical and a statistical point of view. Statistically, the time-averaged position and velocity densities are shown to approach their respective microcanonical ensemble averages for four, five, and six particles. The relaxation time is much longer than previously expected. For three particles the system does not relax to the microcanonical distribution. We have explored the surface of sections for the $N=3\mathrm{}$ case and have correlated the statistical properties with explicit dynamical features. We show that this dynamical method is consistent with the statistical interpretation. The mechanism which generates the chaotic behavior for the $N=3\mathrm{}$ case is multiple encounters.