Quantum Nekhoroshev theorem for quasi-periodic Floquet Hamiltonians

Reviews in Mathematical Physics

Volumn 10, Issue 3, 1998, Pages 393-428

  Monti, F ^a   Jauslin, H R ^a  

^a UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032222022     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X98000124     Document Type: Article

References (23)

1. J. Bellissard, "Stability and chaotic behaviour of quantum rotators" in Stochastic Processes in Classical and Quantum Systems, Ascona, eds. S. Albeverio, G. Casati and D. Merlini, Springer-Verlag, 1986.
2. J. Bellissard, "Stability and instability in quantum mechanics" in Trends and Developments in the Eighties, eds. S. Albeverio and Ph. Blanchard, World Scientific, (1985) 1-106.
3. J. Bellissard, "Small divisors in quantum mechanics" in Chaotic Behaviour in Quantum Systems, ed. G. Casati, Nato series B120 Plenum, 1985.
4. G. Benettin and G. Gallavotti, "Stability of motions near resonances in quasi-integrable Hamiltonian systems", J. Stat. Phys. 44 (1986) 293-338.
5. P. M. Blekher, H. R. Jauslin and J. L. Lebowitz, "Floquet spectrum for two-level systems in quasi-periodic time-dependent fields", J. Stat. Phys. 68 (1992) 271-310.
6. H. P. Breuer and M. Holthaus, "Quantum phases and Landau-Zener transitions in oscillating fields", Phys. Lett. A140 (1989) 507-512.
7. S. Chelkowski, A. D. Bandrauk and P. B. Corkum, "Efficient molecular dissociation by a chirped ultrashort infrared laser pulse", Phys. Rev. Lett. 65 (1990) 2355-2358.
8. M. Combescure, "The quantum stability problem for time-periodic perturbations of the harmonic oscillator", Ann. Inst. Henri Poincaré 47 (1987) 63-83; (1987) 451-454.
9. M. Combescure, "The quantum stability problem for time-periodic perturbations of the harmonic oscillator", Ann. Inst. Henri Poincaré 47 (1987) 63-83; (1987) 451-454.
10. M. Combescure, "The quantum stability problem for some class of time-dependent Hamiltonians", Ann. Physics 185 (1988) 86-110.
11. A. Delshams and P. Gutiérrez, "Effective stability and KAM Theory", J. Diff. Eq. 128 (1996) 415-490.
12. P. Duclos and P. Šťovíček, "Floquet Hamiltonians with pure point spectrum", Commun. Math. Phys. 177 (1996) 327-347.
13. V. Enss and K. Veselić, "Bound states and propagating states for time-dependent Hamiltonians", Ann. Inst. Henri Poincaré A39 (1983) 159-191.
14. S. Guérin, "Complete dissociation by chirped laser pulses designed by adiabatic Floquet analysis", Phys. Rev. A56 (1997) 1458-1462.
15. S. Guérin and H. R. Jauslin, "Laser-enhanced tunneling through resonant intermediate levels", Phys. Rev. A55 (1997) 1262-1275.
16. H. R. Jauslin and J. L. Lebowitz, "Spectral and stability aspects of quantum chaos", Chaos 1 (1991) 114-121.
17. À. Jorba, R. Ramírez-Ros and J. Villanueva, "Effective reducibility of quasi-periodic linear equations close to constant coefficients", SIAM J. Math. Anal. 28 (1997) 178-188.
18. T. Kato, "Linear evolution equations of "Hyperbolic" type", J. Fac. Sci. Univ. Tōkyō Sect. IA Math. 17 (1970) 241-258.
19. T. Kato, "Perturbation theory for linear operators", reprint of the 2nd ed., Springer-Verlag, 1995.
20. P. Lochak, "Canonical perturbation theory via simultaneous approximation", Russian Math. Surveys 47 (1992) 57-133.
21. N. N. Nekhoroshev, "An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems", Russian Math. Surveys 32 (1977) 1-65.
22. J. Pöschel, "Nekhoroshev estimates for quasi-convex Hamiltonian systems", Math. Z. 213 (1993) 187-216.
23. K. Yosida, "Functional analysis", reprint of the 6th ed., Springer-Verlag, 1995.