Dynamical tunneling in mushroom billiards
arXiv:0801.2833 · doi:10.1103/PhysRevLett.100.174103
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.
4 pages, 4 figures
References in corpus (17)
- Combining directional light output and ultralow loss in deformed microdisks
- First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
- Resonance-assisted tunneling in near-integrable systems
- Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard
- Resonance-Assisted Tunneling
- Dynamical Tunneling in Mixed Systems
- On the rate of quantum ergodicity in Euclidean billiards
- Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
- Stickiness in mushroom billiards
- Regular-to-chaotic tunneling rates using a fictitious integrable system
- Quantum mushroom billiards
- Flooding of regular islands by chaotic states
- Decay of Quantum Accelerator Modes
- Spectral properties of Bunimovich mushroom billiards
- Amplitude distribution of eigenfunctions in mixed systems
- Nano-wires with surface disorder: Giant localization lengths and quantum-to-classical crossover
- Universality in the flooding of regular islands by chaotic states
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- Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
- Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
- Quality factors and dynamical tunneling in annular microcavities
- Resonances in open quantum maps
- Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
- Quantum chaotic resonances from short periodic orbits
- Chaos-assisted tunneling resonances in a synthetic Floquet superlattice
- Open Mushrooms: Stickiness revisited
- Experimental Observation of Resonance-Assisted Tunneling
- Dynamical tunneling of a Bose-Einstein condensate in periodically driven systems
- Chaos-assisted emission from asymmetric resonant cavity microlasers
- Marginally Unstable Periodic Orbits in Semiclassical Mushroom Billiards
- Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
- Statistics of time delay and scattering correlation functions in chaotic systems I. Random Matrix Theory
- Chaos-Assisted Long-Range Tunneling for Quantum Simulation
- Complex paths for regular-to-chaotic tunneling rates
- Signatures of unstable semiclassical trajectories in tunneling
- Routes towards the experimental observation of the large fluctuations due to chaos assisted tunneling effects with cold atoms
- Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
- Energy-dependent correlations in the -matrix of chaotic systems
- Thermodynamics of a time dependent and dissipative oval billiard: a heat transfer and billiard approach
- Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos
- Resonance--Assisted Tunneling in Deformed Optical Microdisks with a Mixed Phase Space
- Nonperiodic echoes from quantum mushroom billiard hats
- Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
- Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space
- Chaos-assisted tunneling in the presence of Anderson localization
- Few Islands Approximation of Hamiltonian System with divided Phase Space
- Investigating quantum transport with an initial value representation of the semiclassical propagator
- Partial Weyl Law for Billiards
- Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method
- Further results on the power-law decay of the fraction of the mixed eigenstates in kicked-top model with mixed-type classical phase space
- Resonance-assisted tunneling in 4D normal-form Hamiltonians
- Magnetic field-induced control of transport in multiterminal focusing quantum billiards
- Chaotic properties of the truncated elliptical billiard
- Bloch theorem dictated wave chaos in microcavity crystals
- Coupling of bouncing-ball modes to the chaotic sea and their counting function
- Dynamical tunnelling of a Nano-mechanical Oscillator
- Chaos and Parrondo's paradox: An overview
- Self-Similarity Among Energy Eigenstates
- Long quantum transition times due to unstable semiclassical dynamics
- Temporal flooding of regular islands by chaotic wave packets
- Universality and beyond in optical microcavity billiards with source-induced dynamics
- Chaos assisted many-body tunnelling