On quantum twist maps and spectral properties of Floquet operators

 Access to full text

 Full (PDF)

1. [1] J. Bellissard and A. Barelli, Dynamical localization, mathematical framework, preprint, 1991. MR1155875
2. [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. Zbl0584.35024MR853743
3. [3] H.R. Jauslin and J.L. Lebowitz, Spectral and stability aspects of quantum chaos, Chaos, Vol. 1, 1991, pp. 114-137. Zbl0899.58059MR1135898
4. [4] Ya G. Sinai, Some mathematical problems in the theory of quantum chaos, Physica, Vol. A 163, 1990, pp. 197-204. Zbl0713.58057MR1043648
5. [5] L. Geisler III and J.S. Howland, Spectra of quasienergies, preprint, 1995. MR1438922
6. [6] M. Combescure, Recurrent versus diffusive dynamics for a kicked quantum system, Ann. Inst. H. Poincaré, Vol. A 57, 1992, pp. 67-79. Zbl0766.58061MR1176358
7. [7] G. Karner, The dynamics of the quantum standard map, preprint, 1996. MR1267705
8. [8] G. Casati and L. Molinari, Quantum chaos with time-periodic Hamiltonians, Prog. Theo. Phys., Suppl. Vol. 98, 1989, pp. 287-307. MR1033467
9. [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. MR1349116
10. [10] E. Merbacher, Quantum mechanics, New York, Wiley, 1961. Zbl0102.42701
11. [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. Zbl0532.47007MR722684
12. [12] N.I. Akhiezer and I.M. Glazman, Theory of linear operators in Hilbert spaces, London, Pitman, 1981. Zbl0467.47001
13. [13] Y. Last, Quantum dynamics and decomposition of singular continuous spectra, preprint, 1995 and A. Joye, Private communication. MR1423040
14. [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. Zbl0797.35136MR1207148
15. [15] G. Karner, The simplified Fermi accelerator in classical and quantum mechanics, J. Stat. Phys., Vol. 77, 1994, pp. 867-879. Zbl0839.60075MR1301465
16. [16] A.J. Lichtenberg and M.A. Lieberman, Fermi acceleration revisited, Physica, Vol. 1 D, 1980, pp. 291-305. Zbl1194.37092MR602112
17. [17] G. Karner, The Schrödinger equation on time-dependent domains. 1. Time-periodic case, preprint, 1996. 
18. [18] G. Karner and M. Mukherjee, A new characterization of irrational numbers of constant type, preprint, 1996. Zbl0893.11004
19. [19] S. Lang, Introduction to diophantine approximations, Reading, Addison-Wesely, 1966. Zbl0144.04005MR209227
20. [20] M. Mukherjee, Irrational numbers of constant type and diophantine conditions, preprint, 1995. 
21. [21] G. Birkhoff and G.C. Rota, Ordinary differential equations, 3rd ed., New York, Wiley, 1978. Zbl0377.34001MR507190
22. [22] K. Ireland and M. Rosen, A classical introduction to modern number theory, 2nd ed., New York, Springer, 1993. Zbl0712.11001MR661047
23. [23] J.S. Howland, Private communication. 
24. [24] G. Casati and I. Guarneri, Non-recurrent behaviour in quantum mechanics, Commun. Math. Phys., 95, 1984, pp. 121-127. Zbl0581.46062MR757057