Control of Heisenberg spin systems; Lie algebraic decompositions and action-angle variables

Proceedings of the IEEE Conference on Decision and Control

Volumn 4, Issue , 2003, Pages 4174-4178

  Vaidya, Umesh ^a   D'Alessandro, Domenico ^c   Mezić, Igor ^a,b  

^a University of California   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

CONTROL PROBLEMS; LIE ALGEBRA; SPIN SYSTEMS;

FEEDBACK CONTROL;

EID: 1542349229     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. F. Albertini and D. D'Alessandro, Notions of controllability for multilevel bilinear quantum mechanical systems, IEEE Transactions on Automatic Control, Vol. 48, No. 8, pg. 1399-1403.
2. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer Verlag, Heidelberg 1979.
3. K. J. Åström and K. Furuta, Swinging up a pendulum by energy control, Automatica 36, 2000, pp. 287-295.
4. D. D'Alessandro, Algorithms for quantum control based on decompositions of Lie groups, in Proceedings 39-th conference on Decision and Control, Sidney, Australia, Dec. 2000, pg. 967-968.
5. D. D'Alessandro, Optimal evaluation of generalized Euler angles with applications to classical and quantum control, arXiv: quant-ph/0110120.
6. D. D'Alessandro, Controllability of one spin and two homonuclear spins, Mathematics of Control, Signals and Systems, (2003) 16:1-25.
7. D. D'Alessandro, The optimal control problem on SO(4) and its applications to quantum control, IEEE Transactions on Automatic Control, Vol. 47, no. 1, January 2002.
8. D. D'Alessandro, Directions in the theory of quantum control, in Multidisciplinary Research in Control: The Mohammed Dahleh Legacy, L. Giarre' and B. Bamieh eds., Lecture Notes in Control and Information Sciences, Springer.
9. D. D'Alessandro and M. Dahleh, Optimal control of two-level quantum systems, IEEE Transactions on Automatic Control, Vol. 46, No. 6, June 2001, pg. 867-877.
10. W. A. de Graaf, Lie Algebras, Theory and Algorithms, North-Holland Mathematical Library, 56, Amsterdam, 2000.
11. R. R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford University Press, 1987.
12. S. Grivopoulos and B. Bamieh, New iterative algorithms for approximate controllability of bilinear systems with applications to quantum control, in Proceedings of the 41-st Conference on Decision and Control, Las Vegas, NV, Dec. 2002.
13. G. M. Huang, T. J. Tarn and J. W. Clark, On the controllability of quantum mechanical systems, J. Math. Phys. 24, 11, November 1983, pg. 2608-2618.
14. V. Jurdjević and H. J. Sussmann, Control systems on Lie groups, Journal of Differential Equations, 12, 1972, 313-329.
15. N. Khaneja, R. Brockett, S. J. Glaser, Time Optimal Control of Spin Systems, Physical Review A, 63, 2001, 032308.
16. V. Ramakrishna, K. L. Flores, H. Rabitz, R. J. Ober, Quantum control by decompositions of SU(2), Physical Review A, 62,053409, 2000
17. V. Ramakrishna, R. J. Ober, K. L. Flores and H. Rabitz, Control of a coupled two spin systems without hard pulses, preprint, http://arXiv, quant-ph 0012019.
18. A. Raymond, Electron Paramagnetic Resonance; Techniques and Applications, Interscience Publishers, New York 1968.
19. J. J. Sakurai, Modern Quantum Mechanics, Addison-Wesley Pub. Co., Reading, Mass. 1994.
20. S. Schirmer, Quantum Control using Lie group decompositions, in Proceedings of the 40-th Conference on Decision and Control, Orlando Florida, Dec. 2001.
21. H-J Schmidt and M. Luban, Continuous families of isospectral Heisenberg spin systems and the limits of inference from measurement, Journal of Physics A: Mathematical and General, 34 (2001) 2839-2858.
22. P. Vettori, On the convergence of a feedback control strategy for multilevel quantum systems, in Proceedings Mathematical Theory of Networks and Systems, University of Notre Dame, August 2002.
23. W. Zhu and H. Rabitz, A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator, Journal of Chemical Physics, Vol. 109, No. 2, p. 385, 1998.
24. U. Vaidya and I. Mezić, Controllability for a class of area preserving twist maps, Submitted to Physica D
25. I. Mezić, Controllability of Hamiltonian system with drift: Action-Angle variables and ergodic partition Proceedings of CDC 2003