Few-particle quantum dynamics---comparing Nonequilibrium Green's   functions with the generalized Kadanoff-Baym ansatz to density operator   theory
  The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green's functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations---the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green's functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open. 
S. Hermanns, K. Balzer, and M. Bonitz
cond-mat.str-el