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arXiv · 1010.5977

A Nonlinear Adiabatic Theorem for Coherent States

Rémi Carles·Clotilde Fermanian Kammerer
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Abstract

We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the nonlinear evolution preserves the separation of modes, in a scaling such that nonlinear effects are critical (the envelope equation is nonlinear). The proof relies on a fine geometric analysis of the role of spectral projectors, which is compatible with the treatment of nonlinearities. We also prove a nonlinear superposition principle for these adiabatic wave packets.

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Rémi Carles, Clotilde Fermanian Kammerer. 2010-10-28. A Nonlinear Adiabatic Theorem for Coherent States. https://doi.org/10.1088/0951-7715%2F24%2F8%2F002

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