Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations

TL;DR

This paper derives the equation of state for a seven-dimensional hard-sphere fluid using Percus-Yevick theory and validates it with molecular dynamics simulations, providing insights into high-dimensional fluid behavior.

Contribution

It explicitly solves the Percus-Yevick equation for seven dimensions and compares theoretical results with molecular dynamics simulations.

Findings

Derived the equation of state from Percus-Yevick theory.

Analyzed virial coefficients and convergence of virial series.

Compared theoretical and simulation results for the compressibility factor.

Abstract

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.