Statistical distribution of bonding distances in a unidimensional solid

TL;DR

This paper derives an explicit analytical expression for the probability density of bonding distances in a one-dimensional solid modeled by a Fermi-Pasta-Ulam-like chain, validated by simulations.

Contribution

It introduces a new analytical formula for bonding distance distribution in a unidimensional solid with realistic potentials.

Findings

Analytical expression matches simulation results with high accuracy.

Distribution depends on temperature similarly to velocity distribution.

Provides insights into microscopic structure of 1D solids at finite temperatures.

Abstract

We study a Fermi-Pasta-Ulam-like chain with realistic potentials, which models a unidimensional solid in contact with heat baths at some temperature. We formulate an explicit analytical expression for the probability density of bonding distances between neighbor particles, which depends on temperature similarly to the distribution of velocities. Its validity is verified with a striking accuracy through simulations.