Detailed balance, Liapounov stability, and entropy in resonance fluorescence

Operator Correlations and Quantum Regression Theorem in Non-Markovian Lindblad Rate Equations

“…Here, we will find an equivalent condition which does not depends on the approximations used to arrive to the non-Markovian Lindblad equation. We will demonstrate that the previous result can be associated with a quantum detailed balance condition [10,11,12,13,14,15], which in turn is related with the microrreversibility of the underlying microscopic dynamics [10].…”

“…While the density matrixes ρ R (t) follow a Markovian evolution, the system state ρ S (t) evolves with a completely positive [1,2] non-Markovian evolution, property inherited from the random Lindblad structure Eq. (11). The average of this equation over the set {γ R , P R } can be performed in a Laplace domain, from where it follows…”

“…We have introduced dual and time reversed superoperators [10,11,12,13], which respectively are defined by…”

“…For an open Markovian system, it can be written as an statement of time symmetry for stationary two-time operator correlations [10,11,12,13] …”

“…While in classical stochastic processes this condition has a clear meaning in terms of transitions between the available states of the system [8,9], in quantum dissipative systems this condition relies in the time reversal property of the underlying stationary microscopic Hamiltonian evolution [10,11,12,13,14,15]. The breakdown of this condition has direct experimental implications [16].…”