Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasidegenerate eigenvalues from the purely exponential decrease with 1/Planck's over 2pi obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the invariant tori, allows one to quantitatively reproduce the behavior of the eigenvalue splittings.

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found.

We show that the time evolution of entanglement under incoherent environment coupling can be faithfully recovered by monitoring the system according to a suitable measurement scheme.PACS numbers: 03.67.Mn,03.65.Yz,42.50.Lc Quantum information processing requires the ability to produce entangled states and coherently perform operations on them. Under realistic laboratory conditions, however, entanglement is degraded through uncontrolled coupling to the environment. It is of crucial practical importance to quantify this degradation process [1][2][3], though also extremely difficult in general, due to the intricate mathematical notions upon which our understanding of entanglement relies [4][5][6]. Up to now, no general observable is known which would complement such essentially formal concepts with a specific experimental measurement setup.In the present Letter, we come up with a dynamical characterization of entanglement, through the continuous observation of a quantum system which evolves under incoherent coupling to an environment. We show that, at least for small, yet experimentally relevant systems, there is an optimal measurement strategy to monitor the entanglement of the time evolved, mixed system state. Mixed state entanglement is then given as the average entanglement of the pure states generated by single realisations of the optimal measurement-induced, stochastic time evolution.Consider a bipartite quantum system composed of subsystems A and B, interacting with its environment. Due to this coupling, an initially pure state |Ψ 0 of the composite system will evolve into a mixed state ρ(t), in a way governed by the master equatioṅwhere the Hamiltonian H generates the unitary system dynamics. The superoperators L k describe the effects of the environment on the system, and, for a Markovian bath, have the standard form [7]where the operators J k depend on the specific physical situation under study.To extract the time evolution of entanglement under this incoherent dynamics, one solution is to evaluate a given entanglement measure M (ρ) for the solution ρ(t), at all times t. One starts from one of the known pure state measures M (Ψ) [5,6,8], together with a pure state decomposition of ρ,where the p i are the positive, normalized weights of each pure state |Ψ i . The most naive generalization for a mixed state would then be to consider the averagewhich, however, is not suitable, since the decomposition (3) is not unique: M would thus give rise to different values of entanglement for different valid decompositions of ρ [9], inconsistently with the general requirements for a bona fide entanglement measure [5,6]. The proper definition of M (ρ) therefore is the infimum of all possible averages M [10], but holds two main drawbacks: (i) it turns into a hard numerical problem for higher dimensional or multipartite systems, and, (ii) even for bipartite qubits, where analytical solutions for some measures M (ρ) are known [8], there is no obvious interpretation of this optimal decomposition, in physical terms. Our a...

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