Closed kinetic equation for the density matrix of a subsystem interacting with phonons

Influence of Initial Correlations on Evolution of a Subsystem in a Heat Bath and Polaron Mobility

“…We have derived the exact equation (16), which defines the evolution in time of the two-time correlation function (4) of a subsystem interacting with a boson field (a heat bath) and accounts for initial correlations. The obtained equation provides the regular procedure for including into consideration the influence of initial correlations (ignored as a rule) on the evolution process.…”

“…The equilibrium current-current correlation function was calculated by the Green superoperator technique in [15]. In the papers [16] and [17], the closed Markovian equation for the density matrix of a subsystem interacting with a boson field (serving as a thermostat) was derived using the same Green superoperator method. As in the path integrals approach of FHIP, the bosonic degrees of freedom were eliminated exactly from the obtained equation.…”

“…The reason was that if we consider the long times t − t 0 ∼ τ rel >> β ( = 1, τ rel is a subsystem relaxation time, t cor ∼ β), then the influence of initial correlations on an evolution process is small or vanishes (see also [6]). The same approximation was also used in papers [16,17,18], where the initial condition for the statistical operator of the whole system at the initial moment of time was selected (conventionally) as the factorized one (the product of the statistical operators of the subsystem and the thermal bath).…”