Universality in the flooding of regular islands by chaotic states

2007/01/31 by Arnd Bäcker, Roland Ketzmerick, Alejandro Monastra +1 · 4 citations
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Theoretical and Computational Physics #nlin.CD

paper · pdf · doi:10.1103/physreve.75.066204

published as Phys. Rev. E 75, 066204 (2007) · 11 pages, 12 figures

openalex publication_date 2007/06/07 · arxiv created 2007/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Flooding of Chaotic Eigenstates into Regular Phase Space Islands
• Directed chaotic transport in Hamiltonian ratchets
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces

Cited by

• Dynamical Tunneling in Mushroom Billiards
• Complex paths for regular-to-chaotic tunnelling rates
• Nanowires with surface disorder: Giant localization length and dynamical tunneling in the presence of directed chaos
• Direct regular-to-chaotic tunneling rates using the fictitious-integrable-system approach