Nonlinear dynamics of semiclassical coherent states in periodic potentials
journal contributionposted on 2013-11-22, 00:00 authored by Remi Carles, Christof Sparber
We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities we establish a novel averaging type result in the critical case.
R. Carles is supported by the French ANR project R.A.S. (ANR-08-JCJC-0124-01). C. Sparber has been supported by the Royal Society through his University Research Fellowship.
Publisher StatementThis is a copy of an article published in the Journal of Physics A: Mathematical and Theoretical © 2012 Institute of Physics. The final publication is available at http://iopscience.iop.org/1751-8121 doi: 10.1088/1751-8113/45/24/244032
PublisherInstitute of Physics