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

Christopher Eltschka·Peter Schlagheck
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Abstract

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.

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Christopher Eltschka, Peter Schlagheck. 2004-09-08. Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems. https://doi.org/10.1103/physrevlett.94.014101

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