Complex-path prediction of resonance-assisted tunneling in mixed systems

Area of Science:

• Quantum mechanics
• Classical dynamics
• Statistical physics

Background:

• Understanding quantum chaos is crucial for various physical systems.
• Tunneling phenomena in mixed phase space systems are complex and not fully understood.
• Nonlinear resonance chains significantly influence system dynamics.

Purpose of the Study:

• To develop a semiclassical prediction for regular-to-chaotic tunneling.
• To incorporate the effect of nonlinear resonance chains in tunneling predictions.
• To provide a method for predicting tunneling rates based on classical phase space properties.

Main Methods:

• Semiclassical analysis of tunneling paths in phase space.
• Identification of direct and resonance-assisted tunneling pathways.
• Analytical evaluation of resonance-assisted contributions.
• Comparison with numerical results for the standard map.

Main Results:

• Complex tunneling paths identified in the phase space.
• Analytical prediction for resonance-assisted tunneling developed.
• Excellent agreement between predicted and numerically determined tunneling rates for the standard map.
• The method relies on a few key properties of the classical phase space.

Conclusions:

• The semiclassical approach provides an accurate prediction of regular-to-chaotic tunneling.
• The method is applicable to systems with nonlinear resonance chains.
• The findings have potential applications in predicting ionization rates and quality factors.