Nonlinear coherent states and Ehrenfest time for Schrodinger equation

Rémi Carles (1) , Clotilde Fermanian Kammerer (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Rémi Carles, Clotilde Fermanian Kammerer. Nonlinear coherent states and Ehrenfest time for Schrodinger equation. Communications in Mathematical Physics, 2011, 301 (2), pp.443-472. ⟨10.1007/s00220-010-1154-0⟩. ⟨hal-00440273⟩