Pointwise decay of truncated correlations in chaotic states at low density

TL;DR

This paper investigates how correlations between particles in a low-density classical gas decay with distance, establishing exponential bounds for truncated correlations in systems with finite-range interactions.

Contribution

It provides rigorous bounds on the decay of truncated correlations in classical gases under Boltzmann-Grad scaling, highlighting exponential decay for finite-range potentials.

Findings

Exponential decay of correlations established

Bounds valid for arbitrary order correlations

Applicable in low-density, finite-range interaction regimes

Abstract

We study simple nonequilibrium distributions describing a classical gas of particles interacting via a pair potential ${\phi}(x/{\epsilon})$, in the Boltzmann-Grad scaling ${\epsilon} \rightarrow 0$. We establish bounds for truncated correlations (cumulants) of arbitrary order as a function of the internal separation of particles in a cluster, showing exponential decay for finite range interactions.