Resonance-assisted tunneling in near-integrable systems

Abstract

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasi-degenerate eigenvalues from the purely exponential decrease with 1 / hbar obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the KAM tori, allows to quantitatively reproduce the behavior of the eigenvalue splittings.

4 pages, 2 figures, gzipped tar file, to appear in Phys. Rev. Lett, text slightly condensed compared to first version

References in corpus (2)

• First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
• Quantum Resonances of Kicked Rotor and SU(q) group

Cited by in corpus (63)

• Non-dispersive wave packets in periodically driven quantum systems
• Resonance-Assisted Tunneling
• Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
• Dynamical tunneling in mushroom billiards
• Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
• Regular-to-chaotic tunneling rates using a fictitious integrable system
• Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective
• Dynamical tunneling in molecules: Quantum routes to energy flow
• Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling
• Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
• Chaos-assisted tunneling resonances in a synthetic Floquet superlattice
• Signatures of chaotic tunnelling
• Experimental verification of a one-parameter scaling law for the quantum and "classical" resonances of the atom-optics kicked rotor
• Influence of classical resonances on chaotic tunnelling
• Observation of resonance-assisted dynamical tunneling in an asymmetric microcavity
• Quantum Computation of a Complex System : the Kicked Harper Model
• Semiclassical Study on Tunneling Processes via Complex-Domain Chaos
• On dynamical tunneling and classical resonances
• Analysis of dynamical tunnelling experiments with a Bose-Einstein condensate
• Scaling perspective on Intramolecular vibrational energy flow: analogies, insights, and challenges
• Local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse oscillator
• Resonance-assisted tunneling in three degrees of freedom without discrete symmetry
• Dynamical tunneling of a Bose-Einstein condensate in periodically driven systems
• The Poincare-Birkhoff theorem in Quantum Mechanics
• NOON states with ultracold bosonic atoms via resonance- and chaos-assisted tunneling
• Sharp tunneling peaks in a parametric oscillator: quantum resonances missing in the rotating wave approximation
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Dynamical tunneling in molecules: role of the classical resonances and chaos
• Chaos-Assisted Long-Range Tunneling for Quantum Simulation
• Resonance-assisted decay of nondispersive wave packets
• Dynamical tunnelling with ultracold atoms in magnetic microtraps
• Complex paths for regular-to-chaotic tunneling rates
• Origin of the enhancement of tunneling probability in the nearly integrable system
• A Statistical Theory of Designed Quantum Transport Across Disordered Networks
• Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
• Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
• Creating triple-NOON states with ultracold atoms via chaos-assisted tunneling
• Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
• Avoided crossings in driven systems
• Quantum suppression of chaotic tunneling
• Resonance--Assisted Tunneling in Deformed Optical Microdisks with a Mixed Phase Space
• Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach
• Consequences of Flooding on Spectral Statistics
• Quantum-Chaotic Evolution Reproduced from Effective Integrable Trajectories
• Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems
• Integrable approximation of regular regions with a nonlinear resonance chain
• Dynamical Tunneling in Many-Dimensional Chaotic Systems
• Quantum Dynamical Tunneling Breaks Classical Conserved Quantities
• 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
• Quality factors of deformed dielectric cavities
• Small Phase Space Structures and their Relevance to Pulsed Quantum Evolution: the Stepwise Ionization of the Excited Hydrogen Atom in a Microwave Pulse
• Universal wave functions structure in mixed systems
• Quantum Enhancement of Thermalization
• Recovery of chaotic tunneling due to destruction of dynamical localization by external noise
• Dynamical tunneling across the separatrix
• Resonance- and Chaos-Assisted Tunneling
• Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard
• Computing Quantum Mean Values in the Deep Chaotic Regime
• Chaos assisted many-body tunnelling
• Quasi-integrability and nonlinear resonances in cold atoms under modulation
• Multimode NOON-state generation with ultracold atoms via geodesic counterdiabatic driving
• Arnold web and dynamical tunneling in a four-site Bose-Hubbard model