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

Phil Attard

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.

Quantum Monte Carlo in Classical Phase Space with the Wigner-Kirkwood Commutation Function. II. Diagonal Approximation in Position 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 He below 10\,K.
Paper Structure (17 sections, 39 equations, 1 figure, 2 tables)

This paper contains 17 sections, 39 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Formalism and Algorithm
  3. Phase Space Weight
  4. Fluctuation Expansion for the Commutation Function
  5. Momentum Integral in Diagonal Approximation
  6. Pair Commutation Function
  7. Triplet Commutation Function
  8. Metropolis Monte Carlo Step
  9. Average Energy and Heat Capacity
  10. Kinetic Energy
  11. Symmetrization Function
  12. Computational Results
  13. Model and Simulation Details
  14. Results
  15. Numerical Momentum Quadrature
  16. ...and 2 more sections

Figures (1)

  • Figure 1: Radial distribution function for Lennard-Jones $^4$He at $k_{\rm B}T/\varepsilon =0.5$ and $\rho\sigma^3=0.26$. The solid curve is the present third order diagonal approximation, the dashed curve is the full third order with numerical momentum quadrature, and the dotted curve is the classical result at $\rho\sigma^3=0.9331$.