TITLE:
Phase Space Path Integral Representation for Wigner Function
AUTHORS:
A. S. Larkin, V. S. Filinov
KEYWORDS:
Wigner Function, Path Integral, Quantum Monte Carlo, Momentum Distribution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.2,
February
17,
2017
ABSTRACT: Quantum interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperatures and under extreme conditions. In this work we have generalized the path integral representation for Wigner function to strongly coupled three-dimensional quantum system of particles with Boltzmann and Fermi statistics. In suggested approach the explicit expression for Wigner function was obtained in harmonic approximation and Monte Carlo method allowing numerical calculation of Wigner function, distribution functions and average quantum values has been developed. As alternative more accurate single-momentum approach and related Monte Carlo method have been developed to calculation of the distribution functions of degenerate system of interacting fermions. It allows partially overcoming the well-known sign problem for degenerate Fermi systems.