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.
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 Nf1 of the energy-level counting function. The bifurcations dominate the spectral moments Mm(h) = á (Nf1)2m ñ in the limit h® 0. We show that Mm(h) ~ constant / hvm , and calculate the twinkling exponents vm 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, Instituut-Lorentz, Universiteit Leiden, 2300RA Leiden, The
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