Lyapunov control of a quantum particle in a decaying potential

Abstract : A Lyapunov-based approach for the trajectory generation of an N-dimensional Schrödinger equation in whole RN is proposed. For the case of a quantum particle in an N-dimensional decaying potential the convergence is precisely analyzed. The free system admitting a mixed spectrum, the dispersion through the absolutely continuous part is the main obstacle to ensure such a stabilization result. Whenever, the system is completely initialized in the discrete part of the spectrum, a Lyapunov strategy encoding both the distance with respect to the target state and the penalization of the passage through the continuous part of the spectrum, ensures the approximate stabilization.
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Mazyar Mirrahimi. Lyapunov control of a quantum particle in a decaying potential. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2009, 26 (5), pp.1743-1765. ⟨10.1016/j.anihpc.2008.09.006⟩. ⟨hal-00793568⟩

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