Applications of Time-Dependent Density-Matrix Approach

Abstract

The equations of motion for reduced density matrices form a coupled chain known as the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. To close the coupled chain at the two-body level, approximations for a three-body density matrix with one-body and two-body density matrices are needed. The time-dependent density-matrix theory (TDDM) assumes that the three-body density matrix is given by the antisymmetrized products of the one-body and two-body density matrices. In this review the truncation schemes of the BBGKY hierarchy beyond TDDM are discussed and a formulation for the study of excited states which is derived from the time-dependent approach is explained. The truncation schemes and the formulation for excited states are applied to the Lipkin model and the Hubbard model to corroborate their validity. Two realistic applications of the TDDM approaches are also presented. One is the dipole and quadrupole excitations of 40Ca and 48Ca and the other the fusion reactions of 16O + 16O.