Decay of Quantum Accelerator Modes

Abstract

Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on 1/hbar, are identified, depending on the resolution of KAM substructures that is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to well describe decay whenever applicable.

16 pages, 11 encapsulated postscript figures (figures with a better resolution are available upon request to the authors); added reference for section 1

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Cited by in corpus (27)

• Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
• Dynamical tunneling in mushroom billiards
• Regular-to-chaotic tunneling rates using a fictitious integrable system
• Dynamical tunneling in molecules: Quantum routes to energy flow
• Quality factors and dynamical tunneling in annular microcavities
• Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
• Nano-wires with surface disorder: Giant localization lengths and quantum-to-classical crossover
• Experimental Observation of Resonance-Assisted Tunneling
• Observation of resonance-assisted dynamical tunneling in an asymmetric microcavity
• Chaos-assisted emission from asymmetric resonant cavity microlasers
• Dynamical tunneling of a Bose-Einstein condensate in periodically driven systems
• Effects of atomic interactions on Quantum Accelerator Modes
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Universality in the flooding of regular islands by chaotic states
• Quantum chaos of a mixed, open system of kicked cold atoms
• Complex paths for regular-to-chaotic tunneling rates
• Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
• Quantum Accelerator Modes near Higher-Order Resonances
• Applications of fidelity measures to complex quantum systems
• Fidelity for kicked atoms with gravity near a quantum resonance
• Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach
• Consequences of Flooding on Spectral Statistics
• Resonance-assisted tunneling in 4D normal-form Hamiltonians
• Coupling of bouncing-ball modes to the chaotic sea and their counting function
• Engineering transport by concatenated maps
• Spinor Dynamics of Quantum Accelerator Modes near Higher Order Resonances
• Engineered quantum tunnelling in extended periodic potentials