Nonlinear dynamics of semiclassical coherent states in periodic potentials

Details Nonlinear dynamics of semiclassical coherent states in periodic potentials Nonlinear dynamics of semiclassical coherent states in periodic potentials

2011-10-30

arxiv.org/abs/1110.6633v1

Physics

Mathematical Physics

14 pages, to appear in J. Phys. A

Scientific paper

We consider nonlinear Schrodinger 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 Schrodinger model with effective mass. In the case of nonlocal nonlinearities we establish a novel averaging type result in the critical case.

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