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Nonlinear dynamics of semiclassical coherent states in periodic potentials
journal contribution
posted on 2013-11-22, 00:00 authored by Remi Carles, Christof SparberWe 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.
Funding
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.
History
Publisher Statement
This 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: 10.1088/1751-8113/45/24/244032Publisher
Institute of PhysicsLanguage
- en_US