Energy Minimization Problem in Two-Level Dissipative Quantum Control: Meridian Case

We analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky–Lindblad equation. According to the Pontryagin maximum principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the value...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 195; no. 3; pp. 311 - 335
Main Authors Bonnard, B., Cots, O., Shcherbakova, N.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.12.2013
Springer
Springer Verlag (Germany)
Subjects
Computer Science
Control systems
Distributed, Parallel, and Cluster Computing
Mathematics
Mathematics and Statistics
Nuclear magnetic resonance spectroscopy
Pontryagin Maximum Principle
Integrable Case
Spherical Case
Conjugate Point
Dissipation Parameter
Optimal Control
Quantum Systems
Optimality Conditions
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Summary:We analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky–Lindblad equation. According to the Pontryagin maximum principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous analysis from [5] concerning 2D solutions in the case where the Hamiltonian dynamics are integrable.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-013-1582-4