Spectral density, memory function, and mean relaxation time for resonant subsystem-reservoir interactions

Post-Markovian quantum master equations from classical environment fluctuations

In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. Both Shabani-Lidar equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and its associated approximated integrodifferential kernel master equation are obtained by tracing out two different bipartite Markovian Lindblad dynamics where the environment fluctuations are taken into account by an ancilla system. Furthermore, conditions under which the non-Markovian system dynamics can be unraveled in terms of an ensemble of measurement trajectories are found. In addition, a non-Markovian quantum jump approach is formulated. Contrary to recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010)], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.

Random Lindblad equations from complex environments

In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies on the possibility of splitting the complex environment into a direct sum of subreservoirs, each one being able to induce by itself a Markovian system evolution. Strong non-Markovian effects, which microscopically originate from the entanglement with the different subreservoirs, characterize the average system decay dynamics. As an example, we study the anomalous irreversible behavior of a quantum tunneling system described in an effective two-level approximation. Stretched exponential and power law decay behaviors arise from the interplay between the dissipative and unitary hopping dynamics.

Numerical method for integrodifferential generalized Langevin and master equations

We show that the integrodifferential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary-differential equations. On the basis of this transformation we develop a numerical method for solving such integrodifferential equations. Physically motivated example calculations are performed to demonstrate the accuracy and convergence of the method.

Non-Hermiticity in a kicked model: decoherence and the semiclassical limit

We study the effects of non-Hermitian perturbations on a quantum kicked model exhibiting a localization transition. Using an exact renormalization scheme, we show that the critical line separating the extended and localized phases approaches its semiclassical limit as the imaginary part of the kicking parameter is steadily increased. Further, the metastability of the quantum states appears to be directly correlated with the deviation between the semiclassical and quantum results. This direct evidence of quantum-classical correspondence suggests that decoherence may be usefully modeled by non-Hermitian perturbations.