Novel approach to accounting for correlations in evolution of an open quantum system and the Lindblad equation

A projection operator is introduced which exactly transforms the inhomogeneous Nakajima–Zwanzig generalized master equation for the relevant part of a system +bath statistical operator, containing the inhomogeneous irrelevant term comprising the initial correlations, into the homogeneous equation accounting for initial correlations in the kernel governing its evolution. No ”factorizing initial state” approximation has been used. The obtained equation is equivalent to completely closed (homogeneous) equation for the statistical operator of a system of interest interacting with a bath. In the Born approximation (weak system–bath interaction) this equation can be presented as the time-local Redfield-like equation with additional terms caused by initial correlations. As an application, a quantum oscillator, interacting with a Boson field and driven from the Gibbs initial equilibrium system+bath state by a weak external force, is considered. All terms determining the oscillator evolution over time are explicitly calculated at all timescales. They show how initial correlations influence the evolution process. It is also demonstrated that at the large timescale this influence vanishes, and the evolution equation for the quantum oscillator statistical operator acquires the Lindblad form.