Quantum fluctuations approach to the nonequilibrium GW approximation

The quantum dynamics of fermionic or bosonic many-body systems following external excitation can be successfully studied using two-time nonequilibrium Green's functions (NEGF) single-time reduced density matrix methods. Approximations are introduced via a proper choice the many-particle self-energy decoupling BBGKY hierarchy. These approximations based on Feynman's diagram approaches cluster expansions into single-particle and correlation operators. Here, we develop different approach where, instead equations motion for NEGF (or operators), fluctuations analyzed. We present derivation first two alternative hierarchy discuss possible approximations. In particular, derive polarization approximation (PA) which is shown to equivalent version [following by applying generalized Kadanoff-Baym ansatz (GKBA)] $GW$ with exchange effects theory, weak coupling. main advantage that standard ensemble average replaced semiclassical over initial realizations, as was demonstrated before Lacroix co-workers [see e.g. D. et al., Phys. Rev. B, 2014, 90, 125112]. introduce stochastic (SGW) (SPA) without exchange, respectively, in coupling limit. Our numerical tests confirm our has same favorable linear scaling computation time recently developed G1-G2 scheme [Schluenzen Lett., 2020, 124, 076601].