Simultaneous approximate tracking of density matrices for a system of Schroedinger equations

Details Simultaneous approximate tracking of density matrices for a system of Schroedinger equations Simultaneous approximate tracking of density matrices for a system of Schroedinger equations

2009-02-22

arxiv.org/abs/0902.3798v1

Mathematics

Optimization and Control

11 pages

Scientific paper

We consider a non-resonant system of finitely many bilinear Schroedinger equations with discrete spectrum driven by the same scalar control. We prove that this system can approximately track any given system of trajectories of density matrices, up to the phase of the coordinates. The result is valid both for bounded and unbounded Schroedinger operators. The method used relies on finite-dimensional control techniques applied to Lie groups. We provide also an example showing that no approximate tracking of both modulus and phase is possible

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