Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models

Abstract

Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunneling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalisation.

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Cited by in corpus (11)

• Excited-state quantum phase transitions
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Origin of the enhancement of tunneling probability in the nearly integrable system
• Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
• Complex density of continuum states in resonant quantum tunneling
• Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems
• Integrable approximation of regular regions with a nonlinear resonance chain
• Universal wave functions structure in mixed systems
• Continuum analogues of excited-state quantum phase transitions
• Dynamical tunneling across the separatrix
• Quantum signatures and semiclassical limitations in the transmission of Fock states