EXPERIMENTAL STUDIES OF CHAOS AND LOCALIZATION IN QUANTUM WAVE-FUNCTIONS

Wave functions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wave functi ons display universal density distributions and density autocorrelatio ns in agreement with expressions derived from a 0D nonlinear sigma mod el of supersymmetry, which coincides with random matrix theory. In con trast, disordered wave functions show deviations from this universal b ehavior due to Anderson localization. A systematic behavior of the dis tribution function is studied as a function of the localization length , and can be understood in the framework of a 1D version of the nonlin ear sigma model.