Quantum chaos in extended systems: Spreading wave packets and avoided band crossings (Q2760012)

Classical nonintegrable quantum systems have distributions of energy levels which generically conform with the random-matrix theory predictions. In case of a pure point spectrum, a parameter dependence of the Hamiltonian leads to avoided level crossings. In general, however, the spectrum of a quantum system needs not to have a pure component only. In this case, by varying an external parameter, one arrives at avoided band crossings. This issue is studied in some detail for a kicked Harper model.NEWLINENEWLINENEWLINESince changes in the spectrum of the Hamiltonian have a profound impact on the dynamics, the role played by the eigenfunctions in the asymptotic wave packet evolution is exemplified.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00065].