Fractional generalization of the quantum Markovian master equation

Vittorio Gorini, Alberto Frigerio, Maurizio Verri +2 more

Eliade N. Stefanescu, Paul E. Sterian

In a unitary approach generally used in quantum optics, we consider Lindblad's Markovian master equation and the non- Markovian master equation of Ford, Lewis and O'Connell. We show that the second-order master equation in the hierarchy obtained from a Krylov-Bogoliubov expansion corresponds to the Born approximation. By time averaging, and neglecting the rapidly varying terms, Lindblad's master equation is obtained. With these two equations, we calculate the decay spectrum. We find that for rather low dissipated energies, only the non-Markovian master equation provides correct results. Based on the independent oscillator model of the dissipative coupling, explicit expressions of the dissipative coefficients are obtained.

Alexander Semenovich Holevo

Quantum Markovian master equations with generally unbounded generators, having physically relevant symmetries, such as Weyl, Galilean or boost covariance, are characterized. It is proven in particular that a fully Galilean covariant zero spin Markovian evolution reduces to the free motion perturbed by a covariant stochastic process with independent stationary increments in the classical phase space. A general form of the boost covariant Markovian master equation is discussed and a formal dilation to the Langevin equation driven by quantum Boson noises is described.

K. Lendi

Alireza Shabani, Daniel A. Lidar

Ángel Rivas, A Douglas K Plato, Susana F Huelga +1 more

We derive Markovian master equations for single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding master equations with numerical simulations of the global system's evolution, we delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced Markovian dynamics. The results of these illustrative examples serve to clarify the general properties of other open quantum system scenarios subject to treatment within a Markovian approximation.