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Wave scattering in chaotic systems can be characterized by its spectrum of resonances, z&ldquor; = E&ldquor; -- i f, where E&ldquor; is related to the energy and T&ldquor; is the decay rate or width of the resonance. If the corresponding ray dynamics is chaotic, a gap is believed to develop in the large-energy limit: almost all T&ldquor; become larger than some y. However, rare cases with F < y may be present and actually dominate scattering events. We consider the statistical properties of these supersharp resonances. We find that their number does not follow the fractal Weyl law conjectured for the bulk of the spectrum. We also test, for a simple model, the universal predictions of random matrix theory for density of states inside the gap and the hereby derived probability distribution of gap size. [ABSTRACT FROM AUTHOR]

Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We obtain to all orders in perturbation theory the nonoscillatory parts of all correlation functions, showing that the off-diagonal contributions to these correlation functions cancel and the conjectured universality holds. The innovation that allows this calculation to be performed is the introduction of an auxiliary matrix model which is governed by the same diagrammatic rules as the semiclassical approach and which can be exactly solved. [ABSTRACT FROM AUTHOR]

We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and therefore provide constructive interference. We calculate explicitly the first correlation functions, to leading orders in their energy arguments, for both unitary and orthogonal symmetry classes. The results agree with corresponding predictions from random matrix theory, thereby giving solid support to the conjecture of universality. [ABSTRACT FROM AUTHOR]

We investigate entanglement production in a generic normal conductor, connected to two single-channel left leads and two single-channel right leads. We consider the joint statistics of the number of entangled pairs produced during a given time and amount of entanglement carried by them. We find a constraint that implies that more entangled states are less likely to be detected. Namely, if C is the concurrence and N is the squared norm of the entangled state, then production occurs only if N(1+C)<1. For the particular case of a chaotic cavity working as quantum entangler, we obtain explicit expressions for the joint distribution of C and N, both for systems with and without time-reversal symmetry. [ABSTRACT FROM AUTHOR]

We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly nonideal; that is, it contains tunnel barriers characterized by tunneling probabilities Γ i . Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in 1-Γ i valid for an arbitrary number of channels and obtain explicit formulas up to second order for the average and variance of the conductance and for the average shot noise. Higher moments of the conductance are considered to leading order. [ABSTRACT FROM AUTHOR]

We develop a semiclassical approach for the statistics of the time delay in quantum chaotic systems in the presence of a tunnel barrier, for broken time-reversal symmetry. Results are obtained as asymptotic series in powers of the reflectivity of the barrier, with coefficients that are rational functions of the channel number. Exact expressions, valid for arbitrary reflectivity and channel number, are conjectured and numerically verified for specific families of statistical moments.

The M-dimensional scattering matrix S(E) which connects incoming to outgoing waves in a chaotic systyem is always unitary, but shows complicated dependence on the energy. This is partly encoded in correlators constructed from traces of powers of S(E+ε)S^{†}(E-ε), averaged over E, and by the statistical properties of the time delay operator, Q(E)=-iℏS^{†}dS/dE. Using a semiclassical approach for systems with broken time-reversal symmetry, we derive two kinds of expressions for the energy correlators: one as a power series in 1/M whose coefficients are rational functions of ε, and another as a power series in ε whose coefficients are rational functions of M. From the latter we extract an explicit formula for Tr(Q^{m}) which is valid for all m and is in agreement with random matrix theory predictions.

We study the dynamical entanglement between the spin and the spatial degrees of freedom for a spin- 1/2 charged particle in a square billiard, subject to a nonhomogeneous magnetic field, a system which is classically nonintegrable. This system has three degrees of freedom, one of them being strictly quantum, and we consider initial states which are coherent states with spin in the x direction. The center of the coherent state can be chosen to lie on classically chaotic or regular initial conditions. We show that for chaotic initial conditions the entanglement is rather fast and increases monotonically, while for the regular ones it may present strong recoherences, whose period is related to the classical motion. We also show that this system exhibits special initial conditions which entangle even faster than a typical chaotic one.