Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws

TL;DR

This paper analyzes the diffusion behavior of N interacting classical particles in one dimension, deriving general probability distributions, transport coefficients, and asymptotic laws, revealing how diffusion constants and correlations scale with N.

Contribution

It provides new analytical expressions for the probability distributions and transport coefficients for N particles, including asymptotic laws for large N within a Gaussian approximation.

Findings

Diffusion constant scales as N^{-1} for the central particle.

Diffusion constant scales as (\ln N)^{-1} for edge particles.

Edge particle correlations increase as (\ln N)^{2}.

Abstract

I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of large N, and within a gaussian approximation, the diffusion constant is found to behave as N^{-1} for the central particle and as (\ln N)^{-1} for the edge ones. Absolute correlations between the edge particles increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and discussed in relation of the statistics of extreme events.