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

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