Evolution of a model quantum system under time periodic forcing: Conditions for complete ionization

Communications in Mathematical Physics

Volumn 221, Issue 1, 2001, Pages 1-26

  Costin, O ^a   Costin, R D ^a   Lebowitz, J L ^a   Rokhlenko, A ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035620092     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100455     Document Type: Article

References (37)

1. Simon, B.: Schrödinger Operators in the Twentieth Century. J. Math. Phys. 41, 3523 (2000)
2. Cycon, H.L., Froese, R.G., Kirsch, W. and Simon, B.: Schrödinger Operators. Berlin-Heidelberg-New York: Springer-Verlag, 1987
3. Pillet, C.-A.: Some results on the quantum dynamics of a particle in a Markovian potential. Commun. Math. Phys. 102, 237-254 (1985) and 105, 259 (1986)
4. Pillet, C.-A.: Some results on the quantum dynamics of a particle in a Markovian potential. Commun. Math. Phys. 102, 237-254 (1985) and 105, 259 (1986)
5. Yajima, K.: Existence of Solutions for Schrödinger Evolution Equations. Commun. Math. Phys. 110, 415-426 (1987)
6. Fring, A., Kastrykin, V. and Schrader, R.: Ionization Probabilities through Ultra-Intense Fields in the Extreme Limit. J. Phys. Math. Gen. 30, 8599-8610 (1997)
7. Soffer, A. and Weinstein, M.I.: Nonautonomous Hamiltonians. J. Stat. Phys. 93, 359-391 (1998)
8. Soffer, A. and Costin, O.: Resonance Theory for Schrödinger Operators. Submitted to Commun. Math. Phys.
9. Landau, L.D. and Lifschitz, E. M.: Quantum Mechanics - Nonrelativistic Theory. 2nd ed. New York: Pergamon, 1965
10. Cohen-Tannoudji, C., Duport-Roc, J. and Arynberg, G.: Atom-Photon Interactions. New York: Wiley, 1992
11. Fermi, E.: Notes on Quantum Mechanics. Chicago: The University of Chicago Press, 1961, p. 100
12. Koch, P.M. and van Leeuven, K.A.H.: The Importance of Resonances in Microwave "Ionization" of Excited Hydrogen Atoms. Phys. Repts. 255, 289-403 (1995)
13. Casatti, G., Chirikovand, B. and Shepelyansky, D. L.: Relevance of Classical Chaos in Quantum Mechanics: The Hydrogen Atom in a Monochromatic Field. Phys. Repts. 154, 77-123 (1987)
14. Patolige, R.M. and Shaheshaft, R.: Multiphoton Processes in an Intense Laser Field: Harmonic Generation and Total Ionization Rates for Atomic Hydrogen. Phys. Rev. A 40, 3061-3079 (1990)
15. Buchleitner, A., Delande, D. and Gay, J.-C.: Microwave Ionization of Three Dimensional Hydrogen Atoms in a Realistic Numerical Experiment. J. Opt. Soc. Am. B 12, 505-519 (1995)
16. Benenti, G., Casati, G., Maspero, G. and Shepelyansky, D.L.: Quantum Poincaré Recurrences for Hydrogen Atom in a Microwave Field. Preprint, physics/9911200
17. 2 in Strong Laser Fields, Chem. Phys. 217, 233-244 (1997)
18. Guerin, S. and Jauslin, H.-R.: Laser-Enhanced Tunneling through Resonant Intermediate Levels. Phys. Rev. A 55, 1262-1275 (1997)
19. Eberly, J.M. and Kulander, K.C.: Atomic-Stabilization by Super-Intense Lasers. Science 262 1233 (1993)
20. Su, Q., Irving, B.P. and Eberly, J.H.: Ionization Modulation in Dynamic Stabilization. Laser Physics 7, 568 (1997)
21. Figueira de Morisson Faria, C., Fring, A. and Schrader, R.: Analytical Treatment of Stabilization. Preprint, physics/9808047, v2
22. Barash, D., Orel, A.E. and Vemuri, V.R.: A Genetic Search in Frequency Space for Stabilizing Atoms by High-Intensity Laser Fields. J. Comp. Info. Tech. CIT 8, 2, 103-113 (2000)
23. Rokhlenko, A. and Lebowitz, J.L.: Ionization of a Model Atom by Perturbation of the Potential. J. Math. Phys. 41, 3511-3523 (2000)
24. Costin, O., Lebowitz, J.L. and Rokhlenko, A.: Exact Results for the Ionization of a Model Quantum System. J. Phys. A. 33, 6311-6319 (2000) physics/9905038, and work in preparation
25. Costin, O., Lebowitz, J.L. and Rokhlenko, A.: To appear in: Proceedings of the CRM meeting "Nonlinear Analysis and Renormalization Group", American Mathematical Society Publications (2000), math-ph/0002003
26. Demkov, Yu.N. and Ostrovskii, V.N.: Zero Range Potentials and Their Application in Atomic Physics. New York: Plenum, 1988; Albeverio, S., Gesztesy, F., Høegh-Krohn, R. and Holden, H.: Solvable Models in Quantum Mechanics. Berlin-Heidelberg-New York: Springer-Verlag, 1988
27. Demkov, Yu.N. and Ostrovskii, V.N.: Zero Range Potentials and Their Application in Atomic Physics. New York: Plenum, 1988; Albeverio, S., Gesztesy, F., Høegh-Krohn, R. and Holden, H.: Solvable Models in Quantum Mechanics. Berlin-Heidelberg-New York: Springer-Verlag, 1988
28. Susskind, R.M., Cowley, S.C. and Valeo, E.J.: Multiphoton Ionization in a Short Range Potential: A Nonperturbative Approach. Phys. Rev. A 42, 3090-3106 (1990)
29. Scharf, G., Sonnemoser, K. and Wreszinski, W.F.: Sensitive Multiphoton Ionization. Phys. Rev. A 44, 3250-3265 (1991)
30. LaGattuta, K.J.: Laser-Assisted Scattering from a One-Dimensional δ-function potential: An Exact Solution. Phys. Rev. A 49 No. 3, 1745-1751 (1994)
31. Nikol'skii, N.K.: Treatise on the Shift Operator. Berlin-Heidelberg-New York: Springer-Verlag, 1986
32. Reed, M. and Simon, B.: Methods of Modern Mathematical Physics, Vol. I. New York: Academic Press, 1979
33. Martin, P.A.: Scattering with Time Periodic Potentials and Cyclic States. Preprint 1999, Texas
34. Kovar, T. and Martin, P.A.: Scattering with a periodically kicked interaction and cyclic states. Preprint (1999)
35. Belissard. J.: Stability and Instability in Quantum Mechanics. In: Trends and Developments in the Eighties, Albeverio, S. and Blanchard, Ph. eds., Singapore: World Scientific, 1985, pp. 1-106
36. Jauslin, H.R. and Lebowitz, J.L.: Spectral and Stability Aspects of Quantum Chaos. Chaos 1, 114-121 (1991)
37. Costin, O. and Costin, R.D.: Rigorous WKB for Discrete Schemes with Smooth Coefficients. SIAM J. Math. Anal. 27 no. 1, 110-134 (1996)