Dynamical tunneling across the separatrix

Abstract

The strong enhancement of tunneling couplings typically observed in tunneling splittings in the quantum map is investigated. We show that the transition from instanton to noninstanton tunneling, which is known to occur in tunneling splittings in the space of the inverse Planck constant, takes place in a parameter space as well. By applying the absorbing perturbation technique, we find that the enhancement invoked as a result of local avoided crossings and that originating from globally spread interactions over many states should be distinguished and that the latter is responsible for the strong and persistent enhancement. We also provide evidence showing that the coupling across the separatrix in phase-space is crucial in explaining the behavior of tunneling splittings by performing the wave-function-based observation. In the light of these findings, we examine the validity of the resonance-assisted tunneling theory.

References in corpus (20)

• Floquet engineering with quasienergy bands of periodically driven optical lattices
• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
• Resonance-assisted tunneling in near-integrable systems
• Resonance-Assisted Tunneling
• Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
• Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
• Julia set describes quantum tunneling in the presence of chaos
• Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
• Tunneling rate fluctuations induced by non-linear resonances: a quantitative treatment based on semiclassical arguments
• Influence of classical resonances on chaotic tunnelling
• On dynamical tunneling and classical resonances
• Instantons revisited: dynamical tunnelling and resonant tunnelling
• Resonance-assisted tunneling in three degrees of freedom without discrete symmetry
• The Poincare-Birkhoff theorem in Quantum Mechanics
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Complex paths for regular-to-chaotic tunneling rates
• Origin of the enhancement of tunneling probability in the nearly integrable system
• Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
• Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach
• Correspondence between classical and quantum resonances