1997/07/03 by Steffen D. Frischat, E. Doron, Eyal Doron · 83 citations
Mathematics · Physics and Astronomy · #Amplitude #Chaotic #Cold Atom Physics and Bose-Einstein Condensates #Dynamical billiards #Geometry #Mathematics #Nonlinear Photonic Systems #Parameter space #Phase space #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Quantum tunnelling #Space (punctuation) #Standard map #Statistical physics #Symmetry (geometry) #chao-dyn #cond-mat #nlin.CD
paper · pdf · doi:10.1103/physreve.57.1421
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 57(2), 1421-1443 (American Physical Society) · 28 pages, Latex, 16 EPS figures
arxiv created 1997/07/03 · openalex publication_date 1998/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering, e.g., the annular billiard we decompose tunneling-related energy splittings and shifts into sums over paths in phase space. We show that tunneling transport is dominated by chaos-assisted paths that tunnel into and out of the chaotic layer via the ``beach'' regions sandwiched between the regular islands and the chaotic sea. Level splittings are shown to fluctuate on two scales as functions of energy or an external parameter: they display a dense sequence of peaks due to resonances with states supported by the chaotic sea, overlaid on top of slow modulations arising from resonances with states supported by the ``beaches.'' We obtain analytic expressions that enable us to assess the relative importance of tunneling amplitudes into the chaotic sea versus its internal transport properties. Finally, we average over the statistics of the chaotic region, and derive the asymptotic tail of the splitting distribution function under rather general assumptions concerning the fluctuation properties of chaotic states.