Article details

Title:: Spectral statistics in the quantized cardioid billiard
Authors:: A. Bäcker, F. Steiner and P. Stifter
Journal:: Phys. Rev. E 52 (1995) 2463-2472
Abstract:: The spectral statistics of the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good agreement with the GOE distribution of random-matrix theory. In case of the number variance and rigidity we observe agreement with the random-matrix model for short-range correlations only, whereas for long-range correlations both statistics saturate in agreement with semiclassical expectations. Furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal Gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes. By means of the Gutzwiller trace formula the trace of the cosine-modulated heat kernel is studied. Since the billiard boundary is focusing there are conjugate points giving rise to zeros at the locations of the periodic orbits instead of exclusively Gaussian peaks.
Download:: Please refer to the above published version.
(The preprint version of this article can be obtained as
DESY report 94-213 or chao-dyn/9412007 (1994))