A Nonlinear Adiabatic Theorem for Coherent States

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.

21 pages, no figure

References in corpus (1)

• Nonlinear coherent states and Ehrenfest time for Schrodinger equation

Cited by in corpus (6)

• Adiabatic Lindbladian Evolution with Small Dissipators
• Propagation of Wave Packets for Systems Presenting Codimension 1 Crossings
• Nonlinear dynamics of semiclassical coherent states in periodic potentials
• Propagation of Coherent States through Conical Intersections
• Nonlinear Propagation of Coherent States through Avoided Energy Level Crossing
• A generic framework of adiabatic approximation for nonlinear evolutions II