The BBGKY hierarchy for ultracold bosonic systems

Two-Time Correlation Functions in Dissipative and Interacting Bose-Hubbard Chains

“…One possible way to access the non-equilibrium dynamics of such systems is with the help of Green functions. The two-time correlators, such as the time-dependent first order coherences from Equations ( 6) and ( 7), or the density-density correlation functions Equation (28), allow one to characterize the outof-equilibrium dynamics of many-body interacting quantum systems. We have presented a method on how to systematically compute a hierarchy of approximations for two-time correlation functions, in principle of arbitrary operators, which applies to a wide class of interacting systems whose dissipation is described by a master equation of the form of Equation ( 2).…”

“…Based on our method, we can treat particle interactions on a mean-field level (see Section IV) and also one-order beyond (see Section V). Higher-order expansions are possible, at the cost of very lengthy formulae, which at some point will become difficult to deal with even numerically (see e.g., [28,29] for just time-equal correlators).…”