Slow dynamics and ergodicity in the one-dimensional self-gravitating system

TL;DR

This paper investigates the ergodic properties of one-dimensional self-gravitating systems, revealing that homogeneous states are non-ergodic while non-homogeneous states are ergodic over a relaxation timescale, with implications for long-range interacting systems.

Contribution

It demonstrates the differing ergodic behaviors of homogeneous and non-homogeneous states in 1D self-gravitating systems and characterizes their relaxation times.

Findings

Homogeneous states are non-ergodic with zero collision term.

Non-homogeneous states are ergodic within the relaxation time.

Relaxation time in the sheets model is significantly larger than in other long-range systems.

Abstract

We revisit the dynamics of the one-dimensional self-gravitating sheets models. We show that homogeneous and non-homogeneous states have different ergodic properties. The former is non-ergodic and the one-particle distribution function has a zero collision term if a proper limit is taken for the periodic boundary conditions. Non-homogeneous states are ergodic in a time window of the order of the relaxation time to equilibrium, as similarly observe in other systems with a long range interaction. For the sheets model this relaxation time is much larger than other systems with long range interactions if compared to the initial violent relaxation time.