Dynamics of strongly correlated quantum systems from an extended Singwi-Tosi-Land-Sjölander closure for the BBGKY hierarchy

The BBGKY hierarchy in the Wigner representation is used with an extended Singwi-Tosi-Land-Sjölander (STLS) ansatz for the two-particle distribution function [H. Kählert, G. J. Kalman, and M. Bonitz, Phys. Rev. E 90, 011101 (2014)] to study the density response function and the dispersion relation of collective modes in a strongly coupled quantum system. It is shown that the local field correction (LFC) and the dispersion relation reduce to the results of the Quasi-Localized Charge Approximation (QLCA) in the classical limit. In the quantum case, the LFC acquires a frequency-dependence, similar to the quantum version of the STLS theory. The dispersion relation is governed by a generalization of the QLCA dynamical matrix. The results are expected to be relevant for the analysis of collective modes in quantum liquids with strong correlations.