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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 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.

Wave scattering in chaotic systems can be characterized by its spectrum of resonances, z(n)=E(n)-iΓ(n)/2, where E(n) is related to the energy and Γ(n) 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 Γ(n) become larger than some γ. However, rare cases with Γ<γ 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.

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.