A self-consistent mode-coupling theory for dynamical correlations in quantum liquids: Rigorous formulation

A quantum molecular hydrodynamic formalism is developed for the study of dynamical correlations in dense quantum liquids. The approach is based on augmenting an exact closed, self-consistent quantum generalized Langevin equation for the Kubo transform of the dynamical correlation of interest, with a suitable approximation for the memory kernel obtained within the framework of a quantum mode-coupling theory. The solution to the quantum generalized Langevin equation requires as input static equilibrium information which is generated from a path-integral Monte Carlo method. Examples are given for the intermediate and self-intermediate scattering functions, and for the velocity autocorrelation function. The attractive advantages of the present approach are discussed.