Quantum Monte Carlo in Classical Phase Space with the Wigner-Kirkwood Commutation Function. Results for the Saturation Liquid Density of $^4$He

TL;DR

This paper introduces a Monte Carlo method for quantum statistical mechanics in complex phase space, applying it to helium-4 and achieving results consistent with experimental data.

Contribution

It presents a novel Monte Carlo algorithm for quantum phase space with complex weights, extending the Wigner-Kirkwood expansion to third order.

Findings

Accurately predicts saturation liquid density of helium-4 near the lambda transition.

Demonstrates the effectiveness of the method in quantum statistical simulations.

Results agree with experimental measurements.

Abstract

A Metropolis Monte Carlo algorithm is given for the case of a complex phase space weight, which applies generally in quantum statistical mechanics. Computer simulations using Lennard-Jones $^4$He near the $\lambda$-transition, including an expansion to third order of the Wigner-Kirkwood commutation function, give a saturation liquid density in agreement with measured values.