The quantum density of states of the helium-3. Wigner approach in path integral Monte Carlo

Abstract

A new path integral representation of the quantum density of states (DOS) and distribution functions of strongly correlated fermions are derived in the Wigner formulation of quantum mechanics. A new path integral Monte Carlo approach to calculate DOS and thermodynamic functions is suggested. Using helium-3 as an interesting example, we calculate the DOS, internal energy distrubution (IED), momentum distribution functions (MDFs), spin--resolved radial distribution functions at different densities and temperatures. The physical meaning and parameters of exchange-- correlation holes, the quantum oscillations of IEDs and DOS as well as the high--momentum asymptotic (``quantum tails'') of MDFs have been considered and explained.