Quantifying environment non-classicality in dissipative open quantum dynamics

Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. By restricting to dissipative dynamics, here we propose a measure that quantifies how far the environment action on a system departs from the influence of classical noise fluctuations. It relies on the lack of commutativity between the initial reservoir state and the system-environment total Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.Comment: 11 pages, 2 figure

Fluctuating observation time ensembles in the thermodynamics of trajectories

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free-energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This "thermodynamics of trajectories" approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there is a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show that an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates, is equivalent to the fixed-time ensemble, and the LD functions that describe one ensemble can be obtained from those that describe the other. We discuss how the equivalence between generalised ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.Comment: 12 pages, 5 figure

Solvable class of non-Markovian quantum multipartite dynamics

We study a class of multipartite open quantum dynamics for systems with an arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms, expressed in terms of strings of Pauli operators. We formulate the general constraints that guarantee the complete positivity of this dynamics. We characterize in detail the underlying mechanisms that lead to memory effects, together with properties of the dynamics encoded in the associated system rates. We specifically derive multipartite “eternal” non-Markovian master equations that we term hyperbolic and trigonometric due to the time dependence of their rates. For these models we identify a transition between positive and periodically divergent rates. We also study non-Markovian effects through an operational (measurement-based) memory witness approach

Langevin approach to synchronization of hyperchaotic time-delay dynamics

In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical properties of a class of hyperchaotic attractors can be reproduced with a linear Langevin equation, defined by replacing the non-linear delay force by a delta-correlated noise. Therefore, the synchronization phenomenon can be analytically characterized by a set of coupled Langevin equations. We apply this formalism to study anticipated synchronization dynamics subject to external noise fluctuations as well as for characterizing the effects of parameter mismatch in a hyperchaotic communication scheme. The same procedure is applied to second order differential delay equations associated to synchronization in electro-optical devices. In all cases, the departure with respect to perfect synchronization is measured through a similarity function. Numerical simulations in discrete maps associated to the hyperchaotic dynamics support the formalism.Comment: 12 pages, 6 figure

Non-Markovian non-stationary completely positive open quantum system dynamics

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is defined by a set of disruptive events, consisting in the action of a completely positive superoperator over the system density matrix. The random time intervals between events are described by an arbitrary waiting-time distribution. We show that, in contrast to the Markovian case, if one performs a system-preparation (measurement) at an arbitrary time, the subsequent evolution of the density matrix evolution is modified. The non-stationary character refers to the absence of an asymptotic master equation even when the preparation is performed at arbitrary long times. In spite of this property, we demonstrate that operator expectation values and operators correlations have the same dynamical structure, establishing the validity of a non-stationary quantum regression hypothesis. The non-stationary property of the dynamic is also analyzed through the response of the system to an external weak perturbation.Comment: 13 pages, 3 figure

Lindblad rate equations

In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develops strong non-local effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantees the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of non-trivial structured dephasing and depolarizing reservoirs over a single qubit.Comment: 12 pages, 2 figure

From power law intermittence to macroscopic coherent regime

Article addressing the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of "light on" and "light off" fluorescence fluctuations in blinking quantum dots