Expansion into the vacuum of stochastic gases with long-range interactions

TL;DR

This paper investigates the expansion dynamics of many-particle systems with long-range repulsive interactions and Brownian noise, deriving hydrodynamic equations and self-similar solutions, especially for Coulomb gases in various dimensions.

Contribution

It introduces a comprehensive analysis of stochastic gases with long-range interactions, deriving non-local hydrodynamic equations and explicit self-similar solutions for different interaction exponents.

Findings

Expansion governed by non-local hydrodynamics for s<d

Self-similar solutions in 1D for s in (-2,1)

Uniform density in Coulomb gases in the infinite-particle limit

Abstract

We study the evolution of a system of many point particles initially concentrated in a small region in $d$ dimensions. Particles undergo overdamped motion caused by pairwise interactions through the long-ranged repulsive $r^{-s}$ potential; each particle is also subject to Brownian noise. When $s<d$, the expansion is governed by non-local hydrodynamic equations. In the one-dimensional case, we deduce self-similar solutions for all $s\in (-2,1)$. The expansion of Coulomb gases remains well-defined in the infinite-particle limit: The density is spatially uniform and inversely proportional to time independent of the spatial dimension.