Time quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods

Communications in Mathematical Physics

Volumn 219, Issue 2, 2001, Pages 465-480

  Bambusi, Dario ^a   Graffi, Sandro ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035534944     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100426     Document Type: Article

References (22)

1. 1. Arnold, V.I.: Chapitres supplémentaires de la théorie des equations différentielles ordinaires. Moscou: Mir, 1980
2. 2. Bellissard, J.: Stability and instability in quantum mechanics. In: Trends and Developments in the Eighties, S. Albeverio and Ph. Blanchard, Editors, Singapore: World Scientific, 1985, pp. 1-106
3. 3. Combescure, M.: The quantum stability problem for tim-periodic perturbation of the harmonic oscillator. An. Inst. H. Poincaré 47, 62-82 (1987); Erratum ibidem, 451-454
4. 4. Dimassi, M., Sjöstrand, J.: Spectral Asymptotics in the Semiclassical Limit. London Math. Soc. Lecture Notes Serie 268, Cambridge: Cambridge University Press, 1999
5. 5. Duclos, P., Stovicek, P.: Floquet Hamiltonians with Pure Point Spectrum. Commun. Math. Phys. 177, 327-347 (1996)
6. 6. Duclos, P., Stovicek, P., Vittot, M.: Perturbation of an eigen-value from a dense point spectrum: A general Floquet Hamiltonian. Ann. Inst. H. Poincaré Phys. Théor. 71, 241-301 (1999)
7. 7. Gallavotti, G.: The Elements of Mechanics. Berlin-Heidelberg-New York: Springer-Verlag, 1983
8. 8. Graffi, S., Yajima, K.: Absolute Continuity of the Floquet Spectrum for a Nonlinearly Forced Harmonic Oscillator. Commun. Math. Phys. 215, 245-250 (2000)
9. 9. Hagedorn, G., Loss, M., Slawny, J.: Non-stochasticity of time-dependent quadratic Hamiltonians and the spectra of canonical transformations. J. Phys. A 19, 521-531 (1986)
10. 10. Howland, J.: Floquet Operators with Singular Spectrum, I. Ann. Inst. H. Poincaré 49, 309-323 (1989); II, ibidem, 325-334 (1989)
11. 10. Howland, J.: Floquet Operators with Singular Spectrum, I. Ann. Inst. H. Poincaré 49, 309-323 (1989); II, ibidem, 325-334 (1989)
12. 11. Jauslin, H.R., Monti, F.: Quantum Nekhoroshev theorem for quasi-periodic Floquet Hamiltonians. Rev. Math. Phys. 10, 393-428 (1998)
13. 12. Jauslin, H.R., Lebowitz, J.L.: Spectral and stability aspects of quantum chaos. Chaos 1, 114-121 (1991)
14. 13. Jorba, A., Simó, C.: On the reducibility of linear differential equations with quasiperiodic coefficients. J. Differ. Eqs. 98, 111-124 (1992)
15. 14. Joye, A.: Absence of absolutely continuous spectrum of Floquet operators. J. Stat. Phys. 75, 929-952 (1994)
16. 15. Kappeler, T., Pöschel, J.: Perturbation of KdV Equations - The KAM proof. Preprint 1997
17. 16. Kuksin, S.B.: On small-denominators equations with large variable coefficients. J. Appl. Math. Phys. (ZAMP) 48, 262-271 (1997)
18. 17. Nenciu, G.: Floquet operators without absolutely continuous spectrum. Ann. Inst. H. Poincaré 59, 91-97 (1993)
19. 18. Pöschel, J.: A KAM-Theorem for some Partial Differential Equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 23, 119-148 (1996)
20. 19. Shubin, M.A.: Pseudodifferential Operators and Spectral Theory. Berlin-Heidelberg-New York: Springer-Verlag, 1987
21. 20. Xu, J., Zheng, Q.: On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate. Proc. Am. Math. Soc. 126, 1445-1451 (1998)
22. 21. Yajima, K.: Scattering Theory for Schrödinger Operators with Potentials Periodic in Time. J. Math. Soc. Japan 29, 729-743 (1977)