# Quantum Statistical Mechanics Results for Argon, Neon, and Helium Using Classical Monte Carlo

## TL;DR

This paper computes quantum corrections to classical pressure for argon, neon, and helium using Monte Carlo simulations, revealing significant quantum effects especially in helium at liquid-like densities.

## Contribution

It introduces a method to calculate quantum corrections up to fourth order in Planck's constant for Lennard-Jones gases using classical Monte Carlo simulations.

## Key findings

- Quantum corrections are about 1% for argon, 1 for neon, and 1000 for helium.
- First order wave function symmetrization effects are negligible.
- Quantum effects are more pronounced in lighter gases like helium.

## Abstract

Quantum corrections to the classical pressure are obtained for Lennard-Jones models of argon, neon, and helium using classical Metropolis algorithm computer simulations. The corrections for non-commutativity are obtained to fourth order in Planck's constant. Compared to the classical virial pressure on all isotherms at liquid-like densities, the quantum correction is found to be ${\cal O}(10^{-2})$ for argon, ${\cal O}(10^{0})$ for neon, and ${\cal O}(10^{3})$ for helium. The first order correction due to wave function symmetrization is also obtained, but this is relatively negligible.