Volume 13, Number 2, April-June 2007
|Page(s)||378 - 395|
|Published online||12 May 2007|
Hamiltonian identification for quantum systems: well-posedness and numerical approaches
Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.
2 CERMICS-ENPC, 6 & 8 Av. B. Pascal, 77455 Marne la Vallée Cedex, France; firstname.lastname@example.org
3 École des Mines de Paris, CAS, 60 Bd Saint-Michel, 75272 Paris Cedex 06, France; email@example.com
4 Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009; firstname.lastname@example.org
5 CEREMADE, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France; Gabriel.Turinici@dauphine.fr
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.
Mathematics Subject Classification: 93B30 / 65K10
Key words: Inverse problem / quantum systems / Hamiltonian identification / optimal identification
© EDP Sciences, SMAI, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.