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Warianty tytułu
Języki publikacji
Abstrakty
The objective of this article is to present techniques of geometric time-optimal control developed to analyze the control of two-level dissipative quantum systems. Combined with numerical simulations they allow to compute the time-minimal control using a shooting method. The robustness with respect to initial conditions and dissipative parameters is also analyzed using a continuation method.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
1053--1080
Opis fizyczny
Bibliogr. 25 poz., wykr.
Twórcy
autor
autor
- Institut de Mathematiques de Bourgogne, UMR CNRS 5584 9 Avenue Alain Savary, BP 47 870, F-21078 Dijon Cedex, France
Bibliografia
- ALLGOWER, E. and GEORG. K. (1990) Numerical Continuation Methods: An Introduction. Springer-Verlag, New York.
- ALTAFINI, C.A. (2002) Controllabillity properties for finite dimensional quantum Markovian master equations. J. Math. Phys. 44, 2357-2372.
- BAO, D., ROBLES, C. and SHEN, Z. (2004) Zermelo navigation on Riemannian manifolds. J. Differential Geom. 66 (3), 377-435.
- BONNARD, B., CAILLAU, J.-B. and TRELAT, E. (2007) Second-order optimality conditions in the smooth case and applications in optimal control. ESAIM : COCV. 13, 2, 207-236.
- BONNARD, B., CAILLAU, J.-B., SINCLAIR, R. and TANAKA, M. (2009) Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Ann. Inst. H. Poincare Anal. Non Lineaire 26, 1081-1098.
- BONNARD, B. and CHYBA, M. (2003) Singular Trajectories and Their Role in Control Theory. Mathematiques & Appl. 40. Springer-Verlag, Berlin.
- BONNARD, B., CHYBA, M. and SUGNY, D. (2009) Time-minimal control of dissipative two-level quantum systems: the generic case. IEEE Trans. AC., 54 (11), 2598-2610.
- BONNARD, B. and KUPKA, I. (1993) Théorie des singularités de l’application entrée/sortie et optimalité des trajectoires singulières dans le probleme du temps minimal. Forum Mathematicum 5, 111-159.
- BONNARD, B. and SUGNY, D. (2008) Optimal control theory with applications in space and quantum dynamics. AIMS. Series in Applied Math., submitted.
- BONNARD, B. and SUGNY, D. (2009a) Time-minimal control of dissipative two-level quantum systems: the integrable case. SIAM J. Control Optim. 48 (3), 1289-1308.
- BONNARD, B. and SUGNY, D. (2009b) Optimal control theory with applications in space and quantum mechanics. AIMS. Series in Applied Maths., submitted.
- BOSCAIN, U. and PICCOLI, B. (2004) Optimal Syntheses for Control Systems on 2-D Manifolds. Mathématiques & Applications 43. Springer-Verlag, Berlin.
- BOSCAIN, U. et al. (2002) Optimal control in laser-induced population transfer for two- and three-level quantum systems. J. Math. Phys. 43 (5), 2107.
- CARATHÉODORY, C. (1982) Calculus of Variations and Partial Differential Equations of First Order. Chelsea Publishing company, New-York.
- COTCOT Conditions of Order Two: Conjugate Times, http://apo.enseeiht.fr /cotcot.
- EKELAND, I. (1978) Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations. Inst. Hautes Etudes Sci. Publ. Math. 47, 5-32.
- GORINI, V., KOSSAKOWSKI, A. and SUDARSHAN, E.C.G. (1976) Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821-825.
- KHANEJA, N., BROCKETT, R.W. and GLASER, S.J. (2001) Time optimal control of spin systems. Phys. Rev. A 63, 032308.
- KHANEJA, N., GLASER, S.J. and BROCKETT, R.W. (2002) Sub-Riemannian geometry and time optimal control of three spin systems: Coherence transfer and quantum gates. Phys. Rev. A 65, 032301.
- KOSSAKOWSKI, A. (1973) On the general form of the generator of a dynamical semi-group for the spin 1/2 system. Bull. Acad. Pol. Sciences, Ser. Sciences Math., Ast., Phys. 21, 7, 649-653.
- LEE, E. and MARKUS, L. (1967) Foundations of Optimal Control Theory. John Wiley, New York.
- LINDBLAD, G. (1976) On the generators of quantum dynamical semi-groups. Comm. Math. Phys. 48, 119.
- PONTRYAGIN, L. et al. (1961) The Mathematical Theory of Optimal Processes. John Wiley, New York.
- SUGNY, D., KONTZ, C. and JAUSLIN, H.R. (2007) Time-optimal control of two-level dissipative quantum systems. Phys. Rev. A 76, 023419.
- VIEILLARD, T. et al. (2008) Field-free molecular alignment of CO2 mixtures in presence of collisional relaxation. J. Raman Spectrosc. 39, 694-699.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0046-0007