Dynamical Tunneling in Mushroom Billiards

2008/01/31 by Arnd Bäcker, A. Bäcker, Roland Ketzmerick +12 · 6 citations
Mathematics · Physics and Astronomy · #Chaotic #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Dynamical billiards #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hamiltonian system #Integrable system #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum tunnelling #Statistical physics #nlin.CD

paper · pdf · doi:10.1103/physrevlett.100.174103

published as Phys. Rev. Lett. 100, 174103 (2008) · 4 pages, 4 figures

openalex publication_date 2008/05/01 · arxiv created 2008/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.

Citations

• Flooding of Chaotic Eigenstates into Regular Phase Space Islands
• First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
• Universality in the flooding of regular islands by chaotic states
• Regular-to-Chaotic Tunneling Rates Using a Fictitious Integrable System
• Semiclassical Description of Tunneling in Mixed Systems: Case of the Annular Billiard
• Stickiness in mushroom billiards

Cited by

• Chaos and Quantum Tunneling
• Chaos and Parrondo's paradox: An overview
• 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
• Signatures of unstable semiclassical trajectories in tunneling