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Chaotic Dynamics

arXiv:chao-dyn/9412007 (chao-dyn)
[Submitted on 14 Dec 1994]

Title:Spectral Statistics in the Quantized Cardioid Billiard

Authors:A. Baecker, F. Steiner (II. Institut fuer Theoretische Physik, Universitaet Hamburg), P. Stifter (Abteilung fuer Quantenphysik, Universitaet Ulm)
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Abstract: The spectral statistics in 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.
Comments: 20 pages, uu-encoded ps.Z-file
Subjects: Chaotic Dynamics (nlin.CD)
Report number: DESY 94-213
Cite as: arXiv:chao-dyn/9412007
  (or arXiv:chao-dyn/9412007v1 for this version)
  https://doi.org/10.48550/arXiv.chao-dyn/9412007
Journal reference: Phys. Rev. E 52 (1995) pp. 2463--2472
Related DOI: https://doi.org/10.1103/PhysRevE.52.2463

Submission history

From: Arnd Baecker [view email]
[v1] Wed, 14 Dec 1994 19:14:12 UTC (160 KB)
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