| Language |
English
|
| From |
2011/11/11 14:00
|
| To |
2011/11/11 17:00
|
| Place | Room 609, Building No.6, Faculty of Science, Kyoto University |
| Seminar Name | Kyoto Dynamical Systems Seminar |
| Title |
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)) |
| Field |
Geometry
Analysis
Other
|
| Speakers | 藤家 雪朗 |
| Affiliation | 立命館大学理工学部 |
| Abstract | 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)
|
| Link | http://www.math.kyoto-u.ac.jp/dynamics/ |
|