The “Mixed” Green’s Function Approach to Quantum Kinetics with Initial Correlations

A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green’s function formalism. The method is applicable to a wide range of correlated initial states described by nonequilibrium statistical thermodynamics. Initial correlations and the real-time evolution are treated by a unified technique employing manycomponent “mixed” Green’s functions. The Dyson equation for the mixed Green’s function leads to a set of equations for real-time Green’s functions and new (cross) components linking initial correlations with dynamical processes. These equations are used to formulate a generalized Kadanoff-Baym ansatz for correlated initial states. A non-Markovian short-time kinetic equation is derived within the T -matrix approximation for the self-energies. The properties of the memory kernels in this equation are considered in detail in Born approximation for the T -matrices. The kinetic equation is demonstrated to conserve the total energy of the system. An explicit expression for the time-dependent correlation energy is obtained.