@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},
volume = {69},
year = {1998},
pages = {139-157},
mrnumber = {1618660},
zbl = {0902.58036},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1998__68_2_139_0}
}
Karner, Gunther. On quantum twist maps and spectral properties of Floquet operators. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) pp. 139-157. http://gdmltest.u-ga.fr/item/AIHPA_1998__68_2_139_0/
[1] and , Dynamical localization, mathematical framework, preprint, 1991. | MR 1155875
[2] , Stability and instability in quantum mechanics, In: Trends and developments in the eighties, S. ALBEVERIO and Ph. BLANCHARD Eds., Singapore, World Scientific, 1985. | MR 853743 | Zbl 0581.35078 | Zbl 0584.35024
[3] and , Spectral and stability aspects of quantum chaos, Chaos, Vol. 1, 1991, pp. 114-137. | MR 1135898 | Zbl 0899.58059
[4] , Some mathematical problems in the theory of quantum chaos, Physica, Vol. A 163, 1990, pp. 197-204. | MR 1043648 | Zbl 0713.58057
[5] and , Spectra of quasienergies, preprint, 1995. | MR 1438922 | Zbl 0897.46015
[6] , Recurrent versus diffusive dynamics for a kicked quantum system, Ann. Inst. H. Poincaré, Vol. A 57, 1992, pp. 67-79. | Numdam | MR 1176358 | Zbl 0766.58061
[7] , The dynamics of the quantum standard map, preprint, 1996. | MR 1267705
[8] and , Quantum chaos with time-periodic Hamiltonians, Prog. Theo. Phys., Suppl. Vol. 98, 1989, pp. 287-307. | MR 1033467
[9] , Stability and chaos in classical and quantum Hamiltonian systems, In: Proc. II Granada seminar on computational physics, Singapore, World Scientific, 1993. | MR 1349116
[10] , Quantum mechanics, New York, Wiley, 1961. | Zbl 0102.42701
[11] and , Bound states and propagating states for time-dependent Hamiltonians, Ann. Inst. H. Poincaré, Vol. 39, 1983, pp. 159-191. | Numdam | MR 722684 | Zbl 0532.47007
[12] and , Theory of linear operators in Hilbert spaces, London, Pitman, 1981.
[13] , Quantum dynamics and decomposition of singular continuous spectra, preprint, 1995 and , Private communication. | MR 1423040
[14] , 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 1207148 | Zbl 0797.35136
[15] , The simplified Fermi accelerator in classical and quantum mechanics, J. Stat. Phys., Vol. 77, 1994, pp. 867-879. | MR 1301465 | Zbl 0839.60075
[16] and , Fermi acceleration revisited, Physica, Vol. 1 D, 1980, pp. 291-305. | MR 602112
[17] , The Schrödinger equation on time-dependent domains. 1. Time-periodic case, preprint, 1996.
[18] and , A new characterization of irrational numbers of constant type, preprint, 1996.
[19] , Introduction to diophantine approximations, Reading, Addison-Wesely, 1966. | MR 209227 | Zbl 0144.04005
[20] , Irrational numbers of constant type and diophantine conditions, preprint, 1995.
[21] and , Ordinary differential equations, 3rd ed., New York, Wiley, 1978. | MR 507190 | Zbl 0377.34001
[22] and , A classical introduction to modern number theory, 2nd ed., New York, Springer, 1993. | MR 661047
[23] , Private communication.
[24] and , Non-recurrent behaviour in quantum mechanics, Commun. Math. Phys., 95, 1984, pp. 121-127. | MR 757057 | Zbl 0581.46062