The ``Mixed'' Green's Function Approach to Quantum Kinetics with Initial Correlations

TL;DR

This paper introduces a unified Green's function method to derive quantum kinetic equations that incorporate initial correlations, enabling accurate modeling of correlated quantum systems' real-time evolution.

Contribution

It develops a novel mixed Green's function approach that unifies initial correlations with dynamical evolution in quantum kinetic equations.

Findings

Derivation of a generalized Kadanoff-Baym ansatz for correlated initial states.

Formulation of a non-Markovian short-time kinetic equation within the T-matrix approximation.

Demonstration of energy conservation and explicit expression for correlation energy.

Abstract

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 many-component ``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.