Convergent perturbative solutions of the Schrödinger equation for two-level systems with Hamiltonians depending periodically on time

Annales Henri Poincare

Volumn 2, Issue 5, 2001, Pages 963-1005

  Barata, J C A ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

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EID: 0035540797     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-001-8601-6     Document Type: Article

References (23)

1. J. C. A. Barata, On Formal Quasi-Periodic Solutions of the Schrödinger Equation for a Two-Level System with a Hamiltonian Depending Quasi-Periodically on Time, Rev. Math. Phys. 12, 25-64 (2000).
2. J. C. A. Barata and W. F. Wreszinski. Strong Coupling Theory of Two Level Atoms in Periodic Fields, Phys. Rev. Lett. 84, 2112-2115 (2000).
3. W. F. Wreszinski, Atoms and Oscillators in Quasi-Periodic External Fields, Helv. Phys. Acta 70, 109-123 (1997).
4. W. F. Wreszinski and S. Casmeridis, Models of Two Level Atoms in Quasi-periodic External Fields, J. Stat. Phys. 90, 1061 (1998).
5. I. I. Rabi, Space Quantization in a Gyrating Magnetic Field, Phys. Rev. 31, 652-654 (1937).
6. F. Bloch and A. Siegert, Magnetic Resonance for Nonrotating Fields, Phys. Rev. 57, 522-527 (1940).
7. S. H. Autler and C. H. Townes, Stark Effect in Rapidly Varying Fields, Phys. Rev. 100, 703-722 (1955).
8. L. H. Eliasson, Absolutely Convergent Series Expansions for Quasi Periodic Motions, Mathematical Physics Electronic Journal 2, No. 4 (1996). URL: http://www.ma.utexas.edu/mpej/MPEJ.html
9. L. H. Eliasson, Floquet Solutions for the 1-Dimensional Quasi-Periodic Schrödinger Equation, Comm. Math. Phys. 146, 447-482 (1992).
10. G. Gentile and V. Mastropietro, Methods for the Analysis of the Lindstedt Series for KAM Tori and Renormalizability in Classical Mechanics. A Review with Some Applications, Rev. Math. Phys. 8, 393-444 (1996).
11. G. Benfatto, G. Gentile and V. Mastropietro, Electrons in a Lattice with an Incommensurate Potential, J. Stat. Phys. 89, 655-708 (1997).
12. M. Frasca, Duality in Perturbation Theory and the Quantum Adiabatic Approximation, Phys. Rev. A. 58, 3439-3442 (1998).
13. W. Scherer, Superconvergent Perturbation Method in Quantum Mechanics, Phys. Rev. Lett. 74, 1495 (1995).
14. J. Feldman and E. Trubowitz, Renormalization in Classical Mechanics and Many Body Quantum Field Theory, Journal d'Analyse Mathématique 58, 213 (1992).
15. H. R. Jauslin, Stability and Chaos in Classical and Quantum Hamiltonian Systems, P. Garrido and J. Marro (editors). II Granada Seminar on Computational Physics - World Scientific, Singapore, (1993).
16. Yitzhak Katznelson, An Introduction to Harmonic Analysis, Dover Publications, Inc. (1978).
17. C. Corduneanu, Almost Periodic Functions. Interscience Publishers - John Wiley & Sons (1968).
18. Michael Reed and Barry Simon, Methods of Modern Mathematical Physics Vol. 2. Fourier Analysis , Self-Adjointness, Academic Press, New York (1972-1979)
19. Heindrich Dörrie, 100 Great Problems of Elementary Mathematics. Their History and Solution, Dover Publications, Inc. (1965). Originally published in German under the title of "Triumph der Mathematik. Hunderte berühmte Probleme aus zwei Jahrtausenden mathematischer Kultur''. Physica-Verlag, Würzburg (1958).
20. Heindrich Dörrie, 100 Great Problems of Elementary Mathematics. Their History and Solution, Dover Publications, Inc. (1965). Originally published in German under the title of "Triumph der Mathematik. Hunderte berühmte Probleme aus zwei Jahrtausenden mathematischer Kultur''. Physica-Verlag, Würzburg (1958).
21. Ronald L. Graham, Donald E. Knuth and Oren Patashnik, Concrete Mathematics - A Foundation for Computer Science, Addison-Wesley Publishing Company. (1994).
22. Harro Heuser, Gewöhnliche Differentialgleichungen, B. G. Teubner. Stuttgart (1991).
23. Harry Hochstadt, The Functions of Mathematical Physics, Dover Publications, Inc. (1986).