PRACTICAL TESTS WITH IRREGULAR AND REGULAR FINITE SPECTRA OF A PROPOSED STATISTICAL MEASURE FOR QUANTUM CHAOS

Using the first N = 668 measured eigenfrequencies of a two-dimensional (2D) microwave cavity, we test experimentally the properties of a qua ntity W(x) proposed by Aurich, Bolte, and Steiner [Phys. Rev. Lett. 73 , 1356 (1994)] as a statistical measure for quantum chaos in spectra. Our data confirm that the distribution of W(x) for the spectrum of the classically irregular cavity has a statistically significant Gaussian form. We also calculate spectra of classically regular 2D cavities (r ectangular and square) up to comparable values of N and calculate thei r IV(x) distributions. Finding that their distributions, too, are clos e to Gaussian form, we conclude that one should not expect to be able to use the distribution of W(x) as an effective experimental tool for deciding whether a given fi,lite quantum spectrum corresponds to a cla ssically irregular (chaotic) or regular (integrable) system.