Statistics – Applications
Scientific paper
Aug 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrva..44.1491c&link_type=abstract
Physical Review A (ISSN 1050-2947), vol. 44, Aug. 1, 1991, p. 1491-1499. Research supported by DFG.
Statistics
Applications
10
Chaos, Cosmology, Hamiltonian Functions, Quantum Mechanics, Half Planes, Poincare Spheres, Universe, Solutions Of Wave Equations: Bound States, Semiclassical Theories And Applications
Scientific paper
A noncompact chaotic billiard on a two-dimensional space of constant negative curvature, the infinite equilateral triangle describing anisotropy oscillations in the very early universe, is studied quantum-mechanically. A Weyl formula with a logarithmic correction term is derived for the smoothed number of states function. For one symmetry class of the eigenfunctions, the level spacing distribution, the spectral rigidity Delta3, and the Sigma2 statistics are determined numerically using the finite matrix approximation. Systematic deviations are found both from the Gaussian orthogonal ensemble (GOE) and the Poissonian ensemble. However, good agreement with the GOE is found if the fundamental triangle is deformed in such a way that it no longer tiles the space.
Csord'as Andr'as
Graham Robert
Sz'epfalusy P'eter
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