| 発表言語 |
英語
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| 開催日 |
2011年11月11日 14時00分
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| 終了日 |
2011年11月11日 17時00分
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| 開催場所 | 京都大学理学部6号館609号室 |
| セミナー名 | 京都力学系セミナー |
| タイトル |
Width of semi-classical resonances created by homoclinic orbits (joint work with J.-F.Bony (Bordeaux I), T.Ramond (Paris XI), M.Zerzeri (Paris XIII)) |
| 分野 |
幾何
解析
その他
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| 講演者名 | 藤家 雪朗 |
| 講演者所属 | 立命館大学理工学部 |
| 概要 | We consider Schroedinger operators and the corresponding classical Hamiltonian with a real potential decaying at infinity. In the semi-classical limit, the set of trapped orbits on an energy surface for a positive energy is closely related to the semi-classical distribution of ``resonances" in a complex neighborhood of this energy. Resonances are defined to be the poles of the resolvent, or equivalently the complex eigenvalues of the Schroedinger operator modified near infinity. Their imaginary part (width) represents the inverse of the life time of quantum particles. It is then expected that the width is large if the trapped orbits are "filamentary". We will talk about an estimate from below of resonances created by homoclinic orbits. Since classical particles stay for a long time near the hyperbolic fixed point, the width of resonances is essentially determined by the behavior of quantum particles near this point. The method is relies on our previous work about the propagation of microlocal solutions from the incoming stable manifold to the outgoing one (J.Funct.Anal.252(1), 2007)
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| リンク | https://www.math.kyoto-u.ac.jp/dynamics/ |
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