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

2025/12/08 by Phil Attard, Attard, Phil
Physics and Astronomy · Chemistry · #Quantum, superfluid, helium dynamics #Statistical Mechanics and Entropy #Advanced Physical and Chemical Molecular Interactions

paper · pdf · doi:10.48550/arxiv.2512.09948

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 ⁴He 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.

Citations

• Bose-Einstein Condensation and the Lambda Transition for Interacting Lennard-Jones Helium-4
• The molecular nature of superfluidity: Viscosity of helium from quantum stochastic molecular dynamics simulations over real trajectories
• Quantum Statistical Mechanics in Classical Phase Space. V. Quantum Local, Average Global
• Quantum Statistical Mechanics Results for Argon, Neon, and Helium Using Classical Monte Carlo
• Quantum Statistical Mechanics as an Exact Classical Expansion with Results for Lennard-Jones Helium
• Path integrals in the theory of condensed helium

Related

• Quantum Statistical Mechanics in Classical Phase Space. III. Mean Field Approximation Benchmarked for Interacting Lennard-Jones Particles
• Quantum Monte Carlo in Classical Phase Space. Mean Field and Exact Results for a One Dimensional Harmonic Crystal
• Monte Carlo wave-function method in quantum optics
• Quantum Statistical Mechanics as an Exact Classical Expansion with Results for Lennard-Jones Helium
• Quantum Monte Carlo Methods in Statistical Mechanics