Spin dynamics: A paradigm for time optimal control on compact Lie groups

DOI10.1007/s10898-005-6015-6zbMath1138.81058OpenAlexW1973742313MaRDI QIDQ2457913

Gunther Dirr, K. Hüper, Martin Kleinsteuber, Yanqun Liu, Uwe R. Helmke

Publication date: 23 October 2007

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1885/34964

zbMATH Keywords

Lie groupsGlobal optimizationBilinear systemsQuantum systemsNMR spectroscopySpin dynamicsTime optimal control

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Molecular physics (81V55) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items

Optimal control of spins by analytical Lie algebraic derivatives ⋮ Dynamic programming and viscosity solutions for the optimal control of quantum spin systems ⋮ Lie Theory for Quantum Control ⋮ Lie-semigroup structures for reachability and control of open quantum systems: Kossakowski-Lindblad generators form Lie wedge to Markovian channels ⋮ Symmetry principles in quantum systems theory ⋮ A method for solving exact-controllability problems governed by closed quantum spin systems

Cites Work

• Unnamed Item
• Unnamed Item
• Completely integrable gradient flows
• A hybrid descent method for global optimization
• Gradient flows computing the C-numerical range with applications in NMR spectroscopy
• Control theory from the geometric viewpoint.
• Notions of controllability for bilinear multilevel quantum systems
• Lie groups beyond an introduction