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Physics Letters A

On the path integral representation of the Wigner function and the Barker–Murray ansatz

Dries Sels, F. Brosens, Wim Magnus

Published Jan 1, 2012• 7 citations
Publisher
DOI
10.1016/j.physleta.2012.01.020

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We continue our study of Wigner path integrals. We first define a Wigner path integral for the kernel of the Wigner–Bloch equation, solve it for the free particle and harmonic oscillator cases, discuss the physical interpretation which is new and then we apply it (along with the path integral representation of the Liouville equation) to obtain a path integral representation in phase space of the quantum transition state theory of Miller. We also obtain an expression involving products of Wigner kernels for the correlation function form of the exact bimolecular rate constant.
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.