Nonlinear dynamics of semiclassical coherent states in periodic potentials

Rémi Carles (1) , Christof Sparber (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 UIC - Department of Mathematics, Statistics and Computer Science [Chicago]

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Rémi Carles, Christof Sparber. Nonlinear dynamics of semiclassical coherent states in periodic potentials. Journal of Physics A: Mathematical and Theoretical, 2012, 45 (24), pp.244032. ⟨10.1088/1751-8113/45/24/244032⟩. ⟨hal-00637052⟩