Hamiltonian identification for quantum systems: well-posedness and numerical approaches

Claude Le Bris; Mazyar Mirrahimi; Herschel Rabitz; Gabriel Turinici

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 2, page 378-395
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Le Bris, Claude, et al. "Hamiltonian identification for quantum systems: well-posedness and numerical approaches." ESAIM: Control, Optimisation and Calculus of Variations 13.2 (2007): 378-395. <http://eudml.org/doc/250051>.

@article{LeBris2007,
abstract = { 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. },
author = {Le Bris, Claude, Mirrahimi, Mazyar, Rabitz, Herschel, Turinici, Gabriel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Inverse problem; quantum systems; Hamiltonian identification; optimal identification; Hamiltonian identification; Schrödinger equation; identification},
language = {eng},
month = {5},
number = {2},
pages = {378-395},
publisher = {EDP Sciences},
title = {Hamiltonian identification for quantum systems: well-posedness and numerical approaches},
url = {http://eudml.org/doc/250051},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Le Bris, Claude
AU - Mirrahimi, Mazyar
AU - Rabitz, Herschel
AU - Turinici, Gabriel
TI - Hamiltonian identification for quantum systems: well-posedness and numerical approaches
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/5//
PB - EDP Sciences
VL - 13
IS - 2
SP - 378
EP - 395
AB - 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.
LA - eng
KW - Inverse problem; quantum systems; Hamiltonian identification; optimal identification; Hamiltonian identification; Schrödinger equation; identification
UR - http://eudml.org/doc/250051
ER -

References

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