Resonance-assisted tunneling in near-integrable systems

Area of Science:

• Quantum mechanics
• Classical mechanics
• Mathematical physics

Background:

• Dynamical tunneling describes quantum transitions between classically isolated regions.
• Near-integrable systems exhibit complex behavior influenced by both regular and chaotic dynamics.
• The kicked Harper model is a standard testbed for studying quantum dynamics in periodically driven systems.

Purpose of the Study:

• To investigate dynamical tunneling in near-integrable regimes.
• To analyze the influence of classical resonances on wave function decay.
• To develop a semiclassical framework for predicting eigenvalue splitting.

Main Methods:

• Studying the kicked Harper model.
• Analyzing wave function decay in classically forbidden regions.
• Developing a semiclassical model incorporating resonance substructure.

Main Results:

• Classical resonances modify exponential wave function decay.
• Eigenvalue splitting deviates significantly from integrable predictions.
• The semiclassical framework accurately reproduces observed eigenvalue splitting behavior.

Conclusions:

• Classical resonances play a crucial role in dynamical tunneling.
• The developed semiclassical model provides quantitative predictions for eigenvalue splitting.
• Understanding these mechanisms is key for quantum chaos studies.