A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance
Joint Authors
Sugny, Dominique
Bonnard, Bernard
Glaser, Steffen J.
Source
Advances in Mathematical Physics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-29, 29 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-16
Country of Publication
Egypt
No. of Pages
29
Main Subjects
Abstract EN
We present a geometric framework to analyze optimal control problems of uncoupled spin 1/2 particles occurring in nuclear magnetic resonance.
According to the Pontryagin's maximum principle, the optimal trajectories are solutions of a pseudo-Hamiltonian system.
This computation is completed by sufficient optimality conditions based on the concept of conjugate points related to Lagrangian singularities.
This approach is applied to analyze two relevant optimal control issues in NMR: the saturation control problem, that is, the problem of steering in minimum time a single spin 1/2 particle from the equilibrium point to the zero magnetization vector, and the contrast imaging problem.
The analysis is completed by numerical computations and experimental results.
American Psychological Association (APA)
Bonnard, Bernard& Glaser, Steffen J.& Sugny, Dominique. 2012. A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance. Advances in Mathematical Physics،Vol. 2012, no. 2012, pp.1-29.
https://search.emarefa.net/detail/BIM-503828
Modern Language Association (MLA)
Bonnard, Bernard…[et al.]. A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance. Advances in Mathematical Physics No. 2012 (2012), pp.1-29.
https://search.emarefa.net/detail/BIM-503828
American Medical Association (AMA)
Bonnard, Bernard& Glaser, Steffen J.& Sugny, Dominique. A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance. Advances in Mathematical Physics. 2012. Vol. 2012, no. 2012, pp.1-29.
https://search.emarefa.net/detail/BIM-503828
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-503828