Stochastic dynamics of gravity in one dimension

Abstract

The observed relaxation time for the one-dimensional self-gravitating system (OGS) has recently been shown to be much longer than was anticipated. In this paper, a stochastic model (diffusion) of the acceleration and velocity of a labeled particle in the OGS is used to provide a method for studying the exploration of the phase space of the system by a single system member. The stochastic assumption leads to a theory of fluctuations of the discrete system away from mean field (Vlasov) dynamics. These fluctuations are studied in a series of dynamical simulations and compared to those predicted by the theory. The results compare well for system members of low energy but fail for higher energies. The magnitude of the fluctuations grows much more rapidly in the theoretical predictions than in the dynamical simulations, suggesting the existence of slow modes of relaxation.