Universal twinkling exponents for spectral fluctuations associated with mixed chaology

Citation
Mv. Berry et al., Universal twinkling exponents for spectral fluctuations associated with mixed chaology, P ROY SOC A, 456(1999), 2000, pp. 1659-1668
Citations number
30
Categorie Soggetti
Multidisciplinary
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
ISSN journal
13645021 → ACNP
Volume
456
Issue
1999
Year of publication
2000
Pages
1659 - 1668
Database
ISI
SICI code
1364-5021(20000708)456:1999<1659:UTEFSF>2.0.ZU;2-5
Abstract
For systems that are neither fully integrable nor fully chaotic, bifurcatio ns of periodic orbits give rise to semiclassically emergent singularities i n the fluctuating part N-fl of the energy-level counting function. The bifu rcations dominate the spectral moments M-m((h) over bar)= [(N-fl)(2m)] in the limit (h) over bar --> 0. We argue that M-m((h) over bar) similar to const./(h) over bar(nu m), and calculate the twinkling exponents nu(m) as the result of a competition between bifurcations with different codimension s and repetition numbers.