L. Sirko et Pm. Koch, PRACTICAL TESTS WITH IRREGULAR AND REGULAR FINITE SPECTRA OF A PROPOSED STATISTICAL MEASURE FOR QUANTUM CHAOS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(1), 1996, pp. 21-24
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.