Investigation of the quantum Cantori regime in quarter-stadium billiards

We study experimentally and numerically the regime of quantum cantori in quarter-stadium billiards. Experimentally, a quarter-stadium billiard is simulated by a thin quarter-stadium microwave cavity. Using a field perturbation technique and a circular wave expansion method we reconstruct the eigenfunctions of the quarter-stadium microwave billiard with the parameter epsilon=0.1 in the cantori regime N=7-63. The quarter-stadium billiards with epsilon=0.1 and 0.05, respectively, are also investigated numerically. We show that in the quantum cantori regime the rescaled localization length of the eigenfunctions fluctuates around a value that depends on the parameter epsilon.