Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

Phys Rev Lett. 2005 Jan 14;94(1):014101. doi: 10.1103/PhysRevLett.94.014101. Epub 2005 Jan 6.


We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems. In a similar way as for near-integrable tunneling, such resonances induce couplings between regular states within the islands and states that are supported by the chaotic sea. On the basis of this mechanism, we derive a semiclassical expression for the average tunneling rate, which yields good agreement in comparison with the exact quantum tunneling rates calculated for the kicked rotor and the kicked Harper.