HP Labs Technical Reports

Universal Twinkling Exponents for Spectral Fluctuations Associated with Mixed Chaology

Berry, M.V.; Keating, J.P.; Schomerus, H.

HPL-BRIMS-2000-04

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 energy-level 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, Instituut-Lorentz, Universiteit Leiden, 2300RA Leiden, The Netherlands

22 Pages

Back to Index