| Quantum eigenstate can live on an invariant torus. Then the tunneling tail of eigenfunction is supported by a subset on the complexified torus which is obtained by continuing the real torus analytically in the complex domain. If the system is completely integrable, the supporting set defines the instanton. However, in general situation, the complexified torus( and so the instanton as well) is interrupted by the natural boundary. The effect of natural bounrary on the tunnelling effect have been, however, overlooked. We demonstrate a crucial significance of natural boundary in the tunnelling effect. |
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