no. 2
On quantum twist maps and spectral properties of Floquet operators
Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 2, pp. 139-157. 
@article{AIHPA_1998__68_2_139_0,
     author = {Karner, Gunther},
     title = {On quantum twist maps and spectral properties of {Floquet} operators},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {139--157},
     publisher = {Gauthier-Villars},
     volume = {68},
     number = {2},
     year = {1998},
     mrnumber = {1618660},
     zbl = {0902.58036},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1998__68_2_139_0/}
}
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Karner, Gunther. On quantum twist maps and spectral properties of Floquet operators. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 2, pp. 139-157. http://archive.numdam.org/item/AIHPA_1998__68_2_139_0/

[1] J. Bellissard and A. Barelli, Dynamical localization, mathematical framework, preprint, 1991. | MR

[2] J. Bellissard, Stability and instability in quantum mechanics, In: Trends and developments in the eighties, S. ALBEVERIO and Ph. BLANCHARD Eds., Singapore, World Scientific, 1985. | MR | Zbl

[3] H.R. Jauslin and J.L. Lebowitz, Spectral and stability aspects of quantum chaos, Chaos, Vol. 1, 1991, pp. 114-137. | MR | Zbl

[4] Ya G. Sinai, Some mathematical problems in the theory of quantum chaos, Physica, Vol. A 163, 1990, pp. 197-204. | MR | Zbl

[5] L. Geisler Iii and J.S. Howland, Spectra of quasienergies, preprint, 1995. | MR | Zbl

[6] M. Combescure, Recurrent versus diffusive dynamics for a kicked quantum system, Ann. Inst. H. Poincaré, Vol. A 57, 1992, pp. 67-79. | Numdam | MR | Zbl

[7] G. Karner, The dynamics of the quantum standard map, preprint, 1996. | MR

[8] G. Casati and L. Molinari, Quantum chaos with time-periodic Hamiltonians, Prog. Theo. Phys., Suppl. Vol. 98, 1989, pp. 287-307. | MR

[9] H.R. Jauslin, Stability and chaos in classical and quantum Hamiltonian systems, In: Proc. II Granada seminar on computational physics, Singapore, World Scientific, 1993. | MR

[10] E. Merbacher, Quantum mechanics, New York, Wiley, 1961. | Zbl

[11] V. Enss and K. Veselić, Bound states and propagating states for time-dependent Hamiltonians, Ann. Inst. H. Poincaré, Vol. 39, 1983, pp. 159-191. | Numdam | MR | Zbl

[12] N.I. Akhiezer and I.M. Glazman, Theory of linear operators in Hilbert spaces, London, Pitman, 1981.

[13] Y. Last, Quantum dynamics and decomposition of singular continuous spectra, preprint, 1995 and A. Joye, Private communication. | MR

[14] J.M. Combes, Connections between quantum dynamics and spectral properties of time-evolution operators, In: Differential equations with applications to mathematical physics, W. F. AMES, E. M. HARRELL II, and J. V. HEROD Eds., New York, Academic Press, 1993. | MR | Zbl

[15] G. Karner, The simplified Fermi accelerator in classical and quantum mechanics, J. Stat. Phys., Vol. 77, 1994, pp. 867-879. | MR | Zbl

[16] A.J. Lichtenberg and M.A. Lieberman, Fermi acceleration revisited, Physica, Vol. 1 D, 1980, pp. 291-305. | MR

[17] G. Karner, The Schrödinger equation on time-dependent domains. 1. Time-periodic case, preprint, 1996.

[18] G. Karner and M. Mukherjee, A new characterization of irrational numbers of constant type, preprint, 1996.

[19] S. Lang, Introduction to diophantine approximations, Reading, Addison-Wesely, 1966. | MR | Zbl

[20] M. Mukherjee, Irrational numbers of constant type and diophantine conditions, preprint, 1995.

[21] G. Birkhoff and G.C. Rota, Ordinary differential equations, 3rd ed., New York, Wiley, 1978. | MR | Zbl

[22] K. Ireland and M. Rosen, A classical introduction to modern number theory, 2nd ed., New York, Springer, 1993. | MR

[23] J.S. Howland, Private communication.

[24] G. Casati and I. Guarneri, Non-recurrent behaviour in quantum mechanics, Commun. Math. Phys., 95, 1984, pp. 121-127. | MR | Zbl