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 (7)

• Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
• Influence of classical resonances on chaotic tunnelling
• On dynamical tunneling and classical resonances
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Origin of the enhancement of tunneling probability in the nearly integrable system
• Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach
• Correspondence between classical and quantum resonances