Density response and correlation functions in the Wigner path integral representation. Monte Carlo simulations

Abstract

The Wigner formulation of quantum mechanics and the Wiener—Khinchin theorem are employed to derive novel path integral representations of the imaginary part of the density-density response function (IMRF) and the dynamic structure factor (DSF) for a strongly coupled system of soft sphere fermions. To characterize the exchange interaction of fermions, a positive semi-definite Gram determinant is utilized to circumvent the “fermionic sign problem”. The Wigner path integral Monte Carlo (WPIMC) method is employed to compute the IMRFs, DSFs, and spin-resolved radial distribution functions (RDFs) across a broad spectrum of densities and temperatures. The physical significance of the RDF, IMRF, and DSF behavior is elucidated through the demonstration of interference effects arising from exchange and interparticle interactions.