A Central Limit Theorem and Exponential Correlation Decay for the Coulomb Chain

TL;DR

This paper proves an exponential decay of correlations and a central limit theorem for a one-dimensional Coulomb chain with particles interacting via Coulomb forces, focusing on the statistical behavior of distances between particles.

Contribution

It establishes the exponential decay of correlations and a central limit theorem for the Coulomb chain with nearest and next-to-nearest neighbor interactions.

Findings

Correlation between particle clusters decays exponentially

Central limit theorem for particle distances

Quantitative decay rate of correlations

Abstract

We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as random variables. It is shown that the correlation between clusters of consecutive variables decay exponentially with the number of variables separating them. This result is then used to prove a central limit theorem.