# 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

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topLe 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 -

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