Universality in the flooding of regular islands by chaotic states

Abstract

We investigate the structure of eigenstates in systems with a mixed phase space in terms of their projection onto individual regular tori. Depending on dynamical tunneling rates and the Heisenberg time, regular states disappear and chaotic states flood the regular tori. For a quantitative understanding we introduce a random matrix model. The resulting statistical properties of eigenstates as a function of an effective coupling strength are in very good agreement with numerical results for a kicked system. We discuss the implications of these results for the applicability of the semiclassical eigenfunction hypothesis.

arXiv comment11 pages, 12 figures

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• The driven Harper model
• Complex paths for regular-to-chaotic tunneling rates
• Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos
• Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space
• Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
• Consequences of Flooding on Spectral Statistics
• Coupling of bouncing-ball modes to the chaotic sea and their counting function
• Temporal flooding of regular islands by chaotic wave packets
• Level-dynamic approach to the excited spectra of the Jahn-Teller model - kink-train lattice and 'glassy' quantum phase