Explicitly solvable extremals of time optimal control for 2-level quantum systems. (English) Zbl 0992.81016
Summary: In this letter we study the time optimal control problem for amplitude-bounded 2-level quantum systems. Properties of minimum-time controls are characterized and explicit construction of part of extremals are provided.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
References:
| [1] | Law, C.; Eberly, J., Phys. Rev. Lett., 76, 1055 (1995) |
| [2] | Reck, M.; Zeilinger, A., Phys. Rev. Lett., 73, 58 (1994) |
| [3] | Ramakrishna, V.; Flores, K. L.; Rabitz, H.; Ober, R. J., (Proc. of 39th IEEE Conference on Decision and Control, 1 (2000)), 955 |
| [4] | Ramakrishna, V.; Ober, R. J.; Flores, K. L.; Rabitz, H. |
| [5] | Ramakrishna, V.; Flores, K. L.; Rabitz, H.; Ober, R. J., Phys. Rev. A, 62, 053409 (2001) |
| [6] | D’Alessandro, D.; Dahleh, M., IEEE Trans. Automat. Control, 46, 866 (2001) · Zbl 0993.81070 |
| [7] | D’Alessandro, D., J. Math. Phys., 42, 9 (2001) |
| [8] | Khaneja, N.; Brockett, R.; Glaser, S. J., Phys. Rev. A, 63, 2308 (2001) |
| [9] | Khaneja, N.; Glaser, S. J., Chem. Phys., 267, 11 (2001) |
| [10] | Fleming, H.; Rishel, R. W., Deterministic and Stochastic Optimal Control (1975), Springer · Zbl 0323.49001 |
| [11] | Jurdjević, V.; Sussmann, H. J., J. Diff. Equations, 12, 313 (1972) · Zbl 0237.93027 |
| [12] | Baillieul, J., J. Optim. Theory Appl., 25, 519 (1978) · Zbl 0368.49013 |
| [13] | Jurdjevic, V., Geometric Control Theory (1997), Cambridge University Press · Zbl 0940.93005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
