Mean-Field Approximation for Spacing Distribution Functions in Classical Systems

TL;DR

This paper introduces a mean-field approach to approximate spacing distribution functions in 1D classical systems, comparing its effectiveness with existing methods and demonstrating its accuracy across various examples.

Contribution

A novel mean-field method for calculating spacing distributions in 1D classical systems, offering a simpler yet effective alternative to existing approaches.

Findings

Mean-field method provides good results in several systems.

Comparison shows the method's effectiveness relative to IIA and EWS.

Physical interpretations of each method are discussed.

Abstract

We propose a mean-field method to calculate approximately the spacing distribution functions $p^{(n)}(s)$ in 1D classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation (IIA) and the extended Wigner surmise (EWS). In our mean-field approach, $p^{(n)}(s)$ is calculated from a set Langevin equations which are decoupled by using a mean-field approximation. We found that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples in which the three methods mentioned previously give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.