Interpolating ensembles of random unitary matrices

We investigate transitions between ensembles of unitary random matrices modeling changes of statistical properties of quantum chaotic systems which are periodically time dependent. The transitions simulating change of integrability are modeled with the help of numerically generated one-parameter families of ensembles interpolating between an ensemble of diagonal unitary matrices and a circular unitary or circular orthogonal ensemble. In an analogous manner we described transitions between circular orthogonal and unitary ensembles corresponding to the time-reversal symmetry-breaking perturbation of a chaotic system. In all cases we present results concerning statistics of the quasi-energy levels and eigenvectors. \textcopyright{} 1996 The American Physical Society.