A review of geometric optimal control for quantum systems in nuclear magnetic resonance
type: Item
instance of: scholarly article
title: A review of geometric optimal control for quantum systems in nuclear magnetic resonance
zbMATH Open document ID: 1238.81181
DOI: 10.1155/2012/857493
author: Steffen J. Glaser
author: Dominique Sugny
author: Bernard Bonnard
published in: Advances in Mathematical Physics
publication date: 2012-03-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 81V35
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 70E05
Mathematics Subject Classification ID: 49S05
zbMATH DE Number: 6012978
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/857493
OpenAlex ID: W1966510950
Wikidata QID: Q58699603
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description: scientific article; zbMATH DE number 6012978