English

Mean-Field Approximation for Spacing Distribution Functions in Classical Systems

Statistical Mechanics 2015-01-12 v1

Abstract

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s)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)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.

Keywords

Cite

@article{arxiv.1111.5212,
  title  = {Mean-Field Approximation for Spacing Distribution Functions in Classical Systems},
  author = {Diego Luis González and Alberto Pimpinelli and T. L. Einstein},
  journal= {arXiv preprint arXiv:1111.5212},
  year   = {2015}
}
R2 v1 2026-06-21T19:39:53.492Z