Nonlinear dynamics of semiclassical coherent states in periodic potentials

Abstract

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.

14 pages, to appear in J. Phys. A

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• Quadratic Quantum Hamiltonians revisited
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• Analysis of Hartree equation with an interaction growing at the spatial infinity