Wigner approach to the semiclassical dynamics of a quantum many-body system: the dynamic scattering function of He-4

We review the formulation of time correlation functions for a quantum system at thermal equilibrium within the Wigner formalism of quantum mechanics. We derive their semiclassical limit and sketch a simple algorithm for their computation. We apply such a scheme to study the spectrum of density fluctuations of He-4 in the quantum region although far from the superfluid. Preliminary results compare encouraging well with recent infrared X-ray scattering data. (C) 1999 Elsevier Science B.V. All rights reserved