Combining projection superoperators and cumulant expansions in open quantum dynamics with initial correlations and fluctuating Hamiltonians and environments

摘要

The evolution of a small system a interacting with a bath b has been described by two different kinds of master equations for its reduced density matrix rho(a) (t): (i) Nakajima-Zwanzig 'memory' equations resulting from the use of projection superoperators; (ii) Time-local equations based on cumulant expansions. It is pointed out that their solution rho(a)(t) may be expressed in the 'hybrid' form (> signifies time-ordering) rho(a)(t) = B(t, tau) + integral(tau)(t) ds B(t, s)C(s, tau), B(t, t') = e(>)(integraltt, ds L(s, t')) where L(s, t') is a cumulant expansion independent of initial correlations, while C(s, tau), defined in terms of projectors, is the initial correlation term appearing in the 'memory' equation. Thus, the convolution represents the effect of initial correlations on rho(a)(t). We analyse the physical meanings of weak coupling approximations to the 'memory' and 'time-local' equations, elucidating why the latter are more accurate in general. We allow time-dependent Hamiltonians and non-stationary bath states. (C) 2003 Elsevier B.V. All rights reserved. [References: 14]