Hamiltonian identification for quantum systems : well-posedness and numerical approaches
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 378-395.

This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the solution. A numerical approach is also introduced with an illustration of its efficiency on a test problem.

DOI : https://doi.org/10.1051/cocv:2007013
Classification : 93B30,  65K10
Mots clés : inverse problem, quantum systems, hamiltonian identification, optimal identification
     author = {Bris, Claude Le and Mirrahimi, Mazyar and Rabitz, Herschel and Turinici, Gabriel},
     title = {Hamiltonian identification for quantum systems : well-posedness and numerical approaches},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {378--395},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {2},
     year = {2007},
     doi = {10.1051/cocv:2007013},
     zbl = {1123.93040},
     mrnumber = {2306642},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2007013/}
Bris, Claude Le; Mirrahimi, Mazyar; Rabitz, Herschel; Turinici, Gabriel. Hamiltonian identification for quantum systems : well-posedness and numerical approaches. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 378-395. doi : 10.1051/cocv:2007013. http://www.numdam.org/articles/10.1051/cocv:2007013/

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