We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.
COBISS.SI-ID: 60794881
In this work we study level spacing distribution in classically mixed-type quantum systems. In the asymptotic regime of the sufficiently small effective Planck constant the Berry and Robnik (1984) picture applies, which is very well established. We present a new universal semiempirical theory of the level spacing distribution in a regime away from the Berry-Robnik regime, by describing both the dynamical localization effects of chaotic eigenstates, and the tunneling effects. The theory works extremely well in the 2D mixed-type billiard system introduced by Robnik (1983).
COBISS.SI-ID: 64947713
We study ensembles of real non-Gaussian random matrices and their spectral statistics, for dimensions N=2 up to N infinity, namely: box distribution, exponential, Lorentz, and singular times exponential. For N=2 we have explicit exact results, for N>2 numerical results. BZHW theory predicts, that for infinite N the statistics is always the same as for Gaussian matrices, if (i) the distribution of the eigenvalues is smooth and (ii) on finite interval. We show that the transition is fast, if conditions are satisfied, otherwise not.
COBISS.SI-ID: 1618791
We have studied the energy evolution in the time-dependent linear oscillator, which is in the sense of mathematical physics equivalent to the stationary Schroedinger equation. We are interested in the applicability of the WKB method, which we have developed and obtained explicit analytic results up to all orders. We are interested in application in higher dimensions.
COBISS.SI-ID: 62111745