Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues

Details Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues

2011-02-15

arxiv.org/abs/1102.3063v1

Mathematics

Optimization and Control

Scientific paper

In this paper we present a constructive method to control the bilinear Schr\"odinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if the latter are conical (as it happens generically). We provide sharp estimates of the relation between the error and the controllability time.

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