Controllability of the discrete-spectrum Schrodinger equation driven by an external fieldReport as inadecuate




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1 IECN - Institut Élie Cartan de Nancy 2 CORIDA - Robust control of infinite dimensional systems and applications IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est 3 IAC 4 INRIA Lorraine 5 SISSA - ISAS - Scuola Internazionale Superiore di Studi Avanzati - International School for Advanced Studies 6 Le2i - Laboratoire Electronique, Informatique et Image

Abstract : We prove approximate controllability of the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials.





Author: Thomas Chambrion - Paolo Mason - Mario Sigalotti - Ugo Boscain -

Source: https://hal.archives-ouvertes.fr/



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