Controllability of the Schrödinger equation via intersection of eigenvalues

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 1080-1085

  Adami, Riccardo ^a   Boscain, Ugo ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b SISSA   (Italy)

Author keywords

like interactions; Adiabatic theory; Controllability of PDEs; Quantum control

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; INTERSECTIONS; MATHEMATICAL OPERATORS; QUANTUM THEORY; SPECTRUM ANALYSIS;

ADIABATIC THEORY; CONTROLLABILITY OF PDE; DISCRETE SPECTRUM; QUANTUM CONTROL;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33847209264     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582301     Document Type: Conference Paper

References (20)

1. R. Adami and A. Teta, A class of nonlinear Schrödinger equations with concentrated nonlinearity, J. Funct. Anal. 180, no. 1, 148-175, 2001.
2. S. Albeverio, F. Gesztesy, R. Høgh-Kroh and H. Holden, Solvable models in quantum mechanics. Second edition. With an appendix by Pavel Exner, AMS Chelsea Publishing, Providence, RI, 2005.
3. S. Albeverio and P. Kurasov, Singular perturbations of differential operators, Solvable Schro"dinger type operators, London Mathematical Society Lecture Note Series, 271. Cambridge University Press, Cambridge, 2000.
4. Y. Avron, R. Seiler and L. G. Jaffe, Adiabatic theorems and applications to the quantum Hall effect, Commun. Math. Phys. 110, 33-49, 1987.
5. U. Boscain, G. Charlot, Resonance of Minimizers for n-level Quantum Systems with an Arbitrary Cost, ESAIM: Control, Optimisation and Calculus of Variations 10, 593-614 (2004).
6. O. Costin, R.D. Costin, J.L. Lebowitz, A. Rokhlenko, Evolution of a Model Quantum System under Time Periodic Forcing: Conditions for Complete Ionization, Commun. Math. Phys. 221, 1-26, 2001.
7. E. Fermi, Sul moto del neutroni nelle sostanze idrogenate, Ric. Sci. 7, 13-52, 1936 (in italian).
8. S. Guérin and H. Jauslin, "Control of Quantum Dynamics By Laser Pulses: Adiabatic Floquet Theory", Advances in Chemical Physics, Volume 125, 2003
9. G.A. Hagedorn, "Molecular propagation through electron energy level crossings", American Mathematical Society. Memoirs no.536, 1994.
10. T. Kato, On the adiabatic theorems of quantum mechanics, Phys. Soc. Japan 5, 435-439, 1950.
11. T. Kato, Perturbation Theory for Linear Operators, Classics in mathematics, Springer, Berlin 1995.
12. N. Khaneja, R. Brockett and S. J. Glaser Time optimal control in spin systems, Phys. Rev. A v.63, (2001).
13. E.H. Lieb, M. Loss, "Analysis", American Mathematical Society, series: Graduate studies in mathematics, v.14. (2001).
14. G. Nenciu, On the adiabatic theorem of quantum mechanics, J. Phys A 13, L15-L18, 1980.
15. M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press, New York-London, 1978.
16. P. Rouchon. Control of a quantum particle in a moving potential well. In IFAC 2nd Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, April 2003.
17. Shore, Bruce W., The theory of coherent atomic excitation. New York, NY, Wiley, 1990.
18. M.R. Sayapova, D.R. Yafaev, The Evolution Operator for Time Dependent Potentials of Zero Radius, Proceedings of the Steklov Institute of Mathematics, Issue 2, 1984.
19. S. Teufel, "Adiabatic perturbation theory in quantum dynamics." Lecture Notes in Mathematics 1821, Springer-Verlag, Berlin, Heidelberg, New York (2003).
20. L. P. Yatsenko, S. Guérin and H. R. Jauslin, Topology of adiabatic passage, Phys. Rev. A 65, 043407 (7 pages), 2002.