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

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 $λ$-transition, including an expansion to third order of the Wigner-Kirkwood commutation function, give a saturation liquid density in agreement with measured values.