## 抄録

We consider a simple model which is a caricature of a crystal interacting with a radiation field. The model has two bands of continuous spectrum and the particle can pass from the upper one to the lower by radiating a photon, the coupling between the excited and deexcited states being of a Friedrichs type. Under suitable regularity and analyticity assumptions we find the continued resolvent and show that for weak enough coupling it has a curve-type singularity in the lower halfplane which is a deformation of the upper-band spectral cut. We then find a formula for the decay amplitude and show that for a fixed energy it is approximately exponential at intermediate times, while the tail has a power-like behaviour.

本文言語 | 英語 |
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ページ（範囲） | 753-786 |

ページ数 | 34 |

ジャーナル | Journal of the Mathematical Society of Japan |

巻 | 56 |

号 | 3 |

DOI | |

出版ステータス | 出版済み - 2004 |

外部発表 | はい |

## All Science Journal Classification (ASJC) codes

- 数学 (全般)