Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems

TL;DR

This paper investigates how anomalous diffusion signals a phase transition in a two-dimensional self-gravitating system, revealing distinct dynamical behaviors and the influence of particle number on transport properties.

Contribution

It introduces a Hamiltonian model demonstrating a phase transition with unique diffusion characteristics and analyzes how finite particle number affects long-term anomalous transport.

Findings

Superdiffusive motion in collapsing phase

Ballistic motion in homogeneous phase

Anomalous diffusion persists up to a time proportional to particle number

Abstract

A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view, the two phases are characterized by two distinct single-particle motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous diffusion is observed up to a time $\tau$ that increases linearly with $N$. Therefore, the finite particle number acts like a white noise source for the system, inhibiting anomalous transport at longer times.