Nonlinear coherent states and Ehrenfest time for Schrodinger equation
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| Description: |
Carles, R (Montpellier 2)
Wednesday 15 December 2010, 14:00-15:00 |
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| Created: | 2010-12-16 13:46 | ||||
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| Collection: | Partial Differential Equations in Kinetic Theories | ||||
| Publisher: | Isaac Newton Institute | ||||
| Copyright: | Carles, R | ||||
| Language: | eng (English) | ||||
| Distribution: |
World
(downloadable)
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| Explicit content: | No | ||||
| Aspect Ratio: | 16:9 | ||||
| Screencast: | No | ||||
| Bumper: | UCS Default | ||||
| Trailer: | UCS Default | ||||
| Abstract: | We consider the propagation of wave packets for the nonlinear Schrodinger equation, in the semi-classical limit. We establish the existence of a critical size for the initial data, in terms of the Planck constant: if the initial data are too small, the nonlinearity is negligible up to the Ehrenfest time. If the initial data have the critical size, then at leading order the wave function propagates like a coherent state whose envelope is given by a nonlinear equation, up to a time of the same order as the Ehrenfest time. We also prove a nonlinear superposition principle for these nonlinear wave packets. |
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