HP Labs Technical Reports
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Universal Twinkling Exponents for Spectral Fluctuations Associated with Mixed Chaology
Berry, M.V.; Keating, J.P.; Schomerus, H.
HPLBRIMS200004
Keyword(s): spectral statistics; mixed systems; bifurcations
Abstract: Please Note. This abstract contains mathematical formulae which cannot be represented here. For systems that are neither fully integrable nor fully chaotic, bifurcations of periodic orbits give rise to semiclassically emergent singularities in the fluctuating part N_{f1} of the energylevel counting function. The bifurcations dominate the spectral moments M_{m}(h) = á (N_{f1})^{2m} ñ in the limit h® 0. We show that M_{m}(h) ~ constant / h^{v}_{m} , and calculate the twinkling exponents v_{m} as the results of a competition between bifurcations with different codimensions and repetition numbers.
Notes: M.V. Berry, H H Wills Physics Laboratory, Tyndall Ave, Bristol BS8 1TL, UK. H. Schomerus, InstituutLorentz, Universiteit Leiden, 2300RA Leiden, The
Netherlands
22 Pages
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