Quantum Monte Carlo in Classical Phase Space with the Wigner-Kirkwood Commutation Function. II. Diagonal Approximation in Position Space

TL;DR

This paper develops a third order approximation of the Wigner-Kirkwood commutation function, integrating it over momentum to analyze quantum effects in classical phase space, with Monte Carlo simulations for liquid helium.

Contribution

It introduces a new third order approximation of the Wigner-Kirkwood function and applies it to quantum Monte Carlo simulations of liquid helium.

Findings

Successful approximation of the commutation function in position space.

Monte Carlo results for liquid helium below 10 K.

Enhanced understanding of quantum effects in classical phase space.

Abstract

A third order expansion for Wigner-Kirkwood commutation function, a complex function in classical phase space that accounts for the Heisenberg uncertainty relation, is approximated and integrated over momentum to give a real function in position configuration space. Metropolis Monte Carlo computer simulation results are given for liquid Lennard-Jones $^4$He below 10\,K.