We study the time evolution of four distance measures in the presence of initial systemenvironment correlations. It is well-known that the trace distance between two quantum states of an open system may increase due to initial correlations which leads to a breakdown of the contractivity of the reduced dynamics. Here we compare and analyze, for two different models, the time evolution of the trace distance, the Bures metric, the Hellinger distance and the Jensen-Shannon divergence regarding an increase above their initial values, witnessing initial correlations. This work generalizes, deepens and corrects the study performed by Dajka et al. [Phys. Rev. A 84 032120 (2011)] and thereby reveals generic features of the considered distance measures with respect to the capability of detecting initial system-environment correlations.
We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to describe in a quantitative way the dependence of the equilibrium state on the initial condition. Our results show that the thermalization of quantum systems is favored if the dynamics induces small system-environment correlations, as well as small changes in the environment, as measured by the trace distance.
Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence on the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.
Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integro-differential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and uni-directional information flow from the system to the reservoir associated to time-dependent Markovian processes.
Recently a model of metric fluctuations has been proposed which yields an effective Schrodinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization of the inertial mass tensor results from a local space average over the fluctuations of the metric over a fixed background metric. Here, we demonstrate that the metric fluctuations of this model lead to a further physical effect, namely to an effective decoherence of the quantum particle. We derive a quantum master equation for the particles density matrix, discuss in detail its dissipation and decoherence properties, and estimate the corresponding decoherence time scales. By contrast to other models discussed in the literature, in the present approach the metric fluctuations give rise to a decay of the coherences in the energy representation, i. e., to a localization in energy space.
We apply the time-convolutionless (TCL) projection operator technique to the model of a central spin which is coupled to a spin bath via nonuniform Heisenberg interaction. The second-order results of the TCL method for the coherences and populations of the central spin are determined analytically and compared with numerical simulations of the full von Neumann equation of the total system. The TCL approach is found to yield an excellent approximation in the strong field regime for the description of both the short-time dynamics and the long time behavior.
