Quantum Statistical Mechanics in Classical Phase Space. V. Quantum Local, Average Global

2020/05/13 by Phil Attard, Attard, Phil · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Physics (quant-ph) #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2005.06165

openalex publication_date 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the non-commutativity of the position and momentum operators. Used in Monte Carlo simulations for a one-dimensional Lennard-Jones fluid, the results prove more reliable than a high temperature expansion and a harmonic local field approach, and at intermediate temperatures agree with benchmark numerical results. Results are presented for distinguishable particles, fermions, and bosons.

Cited by

• Quantum Monte Carlo in Classical Phase Space with the Wigner-Kirkwood Commutation Function. Results for the Saturation Liquid Density of ⁴He
• The Two-Fluid Theory for Superfluid Hydrodynamics and Rotational Motion

Related

• Quantum Statistical Mechanics in Classical Phase Space. III. Mean Field Approximation Benchmarked for Interacting Lennard-Jones Particles
• Quantum Statistical Mechanics in Classical Phase Space. Expressions for the Multi-Particle Density, the Average Energy, and the Virial Pressure
• Quantum Statistical Mechanics in Classical Phase Space. Test Results for\n Quantum Harmonic Oscillators
• Quantum Statistical Mechanics as an Exact Classical Expansion with Results for Lennard-Jones Helium
• Quantum particles from classical probabilities in phase space