Nonlinear coherent states and Ehrenfest time for Schrodinger equation
arXiv:0912.1939 · doi:10.1007/s00220-010-1154-0
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.
27 pages
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Cited by in corpus (10)
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- A Nonlinear Adiabatic Theorem for Coherent States
- Semiclassical Propagation of Coherent States for the Hartree equation
- On semi-classical limit of nonlinear quantum scattering
- Separation of scales: Dynamical approximations for composite quantum systems
- Semiclassical wave packet dynamics for Hartree equations
- Propagation of Wave Packets for Systems Presenting Codimension 1 Crossings
- Nonlinear dynamics of semiclassical coherent states in periodic potentials
- Soliton dynamics for the generalized Choquard equation
- Interaction of coherent states for Hartree equations