The two-particle correlation function for systems with long-range interactions

TL;DR

This paper investigates the behavior of two-particle correlation functions in systems with long-range interactions, establishing well-posedness, screening effects, and stability results for Coulombian and soft potentials.

Contribution

It provides new well-posedness results, demonstrates Debye screening in Coulomb systems, and analyzes stability of correlations for soft potentials.

Findings

Debye screening length identified in Coulomb systems

Well-posedness of equilibrium correlations established

Linear stability of correlations in soft potential systems

Abstract

In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the Coulombian case, we prove the onset of the Debye screening length in the equilibrium correlations, for suitable velocity distributions. Additionally, we give precise estimates on the effective range of interaction between particles. In the case of soft potential interaction the equilibrium correlations and their fluxes in the space of velocities are shown to be linearly stable.