Nonlinear coherent states and Ehrenfest time for Schrodinger equation

Details Nonlinear coherent states and Ehrenfest time for Schrodinger equation Nonlinear coherent states and Ehrenfest time for Schrodinger equation

2009-12-10

arxiv.org/abs/0912.1939v1

Communications in Mathematical Physics 301, 2 (2011) 443-472

Mathematics

Analysis of PDEs

27 pages

Scientific paper

10.1007/s00220-010-1154-0

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.

Affiliated with

Also associated with

No associations

Rating

Nonlinear coherent states and Ehrenfest time for Schrodinger equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonlinear coherent states and Ehrenfest time for Schrodinger equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear coherent states and Ehrenfest time for Schrodinger equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-594661