Quantum Chaos and Spectral Transitions in the Kicked Harper Model

In contrast to bounded systems, quantum chaos in extended systems may be associated with fractal spectra, metal-insulator transitions due to avoided band crossings, and spreading wave packets. In this lecture we point out the role of avoided band crossings for spectral transitions in the example of the kicked Harper model. We explain the coexistence of localized and extended eigenfunctions off the critical line as well as changes of the fractal dimension on the critical line. Avoided band crossings thus provide a common cause for various phenomena observed numerically in the spectrum of the kicked Harper model.