2002/05/24 by Olivier Brodier, Peter Schlagheck, Denis Ullmo · 2 citations
Physics and Astronomy · #Coherence (philosophical gambling strategy) #Ground state #Integrable system #Nonlinear Photonic Systems #Nonlinear system #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum dynamics #Quantum tunnelling #Semiclassical physics #nlin.CD
paper · pdf · doi:10.1006/aphy.2002.6281
52 pages, 16 figures, submitted to Annals of Physics
arxiv created 2002/05/24 · openalex publication_date 2002/08/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found.