Séminaire informel : Kin’Ya Takahashi (Kyoto University)


10:00 - 11:00

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Noninstanton tunneling for a periodically perturbed rounded-rectangular potential


Kin’Ya Takahashi (Kyoto University)


We study tunneling probabilities with changing Planck’s constant for a periodically perturbed rounded rectangular potential, for which instanton tunneling is substantially prohibited. The periodical perturbation creates an energy ladder of harmonic channels at En = EI + n hbar ω. Harmonic channels above the potential height V0 induce multi-quanta absorption tunneling (MQAT), and the harmonic channel just above V0 dominantly contributes to noninstanton tunneling. The replacement of the dominant harmonic channel makes a sawtooth structure with changing 1/hbar. The sawtooth structure made by the tunneling probability in the potential region is accompanied by resonance peaks due to the resonance states above the potential. The sawtooth structure is also observed with changing ω. Thus, this is the essential nature of MQAT. We introduce an effective formula to characterize the profile of the sawtooth structure. Furthermore, the sawtooth structure can be reproduced by the complex semiclassical method except for small neighborhoods the switching regions including resonance peaks. The Melnikov method, i.e., approximate semiclassical method, provides the essentially same formula as mentioned above.

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