On scaling in relation to singular spectra

Communications in Mathematical Physics

Volumn 184, Issue 3, 1997, Pages 567-577

  Hof, A ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031518894     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050073     Document Type: Article

References (37)

1. Aaronson, J. and Keane, M.: The visits to zero of some deterministic random walks. Proc. Lond. Math. Soc. (3) 44, 535-553 (1982)
2. Aubry, S., Godrèche, C. and Luck, J.M.: A structure intermediate between quasi-periodic and random. Europhys. Lett. 46, 39-643 (1987)
3. Aubry, S., Godrèche, C. and Luck, J.M.: Scaling properties of a structure intermediate between quasiperiodic and random. J. Stat. Phys. 51, 1033-1074 (1988)
4. Barbaroux, J.M., Combes, J.M. and Montchio, R.: Remarks on the relation between quantum dynamics and fractal spectra, preprint Marseille CPT-96/P.3303
5. Berbee, H.: Recurrence and transience for random walks with stationary increments. Z. Wahr. Verw. Geb. 56, 531-536 (1981)
6. Bunimovich, L., Jauslin, H.R., Lebowitz, J.L., Pellegrenotti, A. and Nielaba, P.: Diffusive energy growth in classical and quantum driven oscillators. J. Stat. Phys. 62, 793-817 (1991)
7. Combes, J.M.: Connections between quantum dynamics and spectral properties of time evolution operators. In W.F. Ames, E.M Harrell, and J.V. Herod, editors, Differential Equations with Applications to Mathematical Physics. New York: Academic Press, Inc., 1993
8. Combescure, M.: Recurrent versus diffusive dynamics for a kicked quantum oscillator. Ann. Inst. Henri Poincaré Phys. Théor. 57, 67-87 (1992)
9. Cornfeld, I.P., Fomin, S.V. and Sinai, Ya.G.: Ergodic Theory, Vol. 115 of Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Berlin-Heidelberg-New York: Springer-Verlag, 1982
10. de Oliveira, C.R.: Numerical study of the long-time behaviour of quantum systems driven by Thue-Morse forces. Application to two-level systems. Europhys. Lett. 31, 63-68 (1995)
11. Dekking, F.M.: On transience and recurrence of generalized random walks. Z. Wahr. Verw. Geb. 61, 459-465 (1982)
12. Dekking, F.M.: Marches automatiques. J. de Théorie de Nombres de Bordeaux 5, 93-100 (1993)
13. Dekking, F.M.: Random and automatic walks. In F. Axel and D. Gratias, editors, Beyond Quasicrystals. Les Éditions de Physique, Berlin-Heidelber-New York: Springer-Verlag, 1995
14. Dekking, F.M. and Mendès France, M.: Uniform distribution modulo one: A geometric point of view. J. Reine Angew. Math. 329, 143-153 (1981)
15. del Rio, R., Jitomirskaya, S., Last, Y. and Simon, B.: Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization. J. Analyse Math. 69, 153-200 (1996)
16. Dumont, J.M. and Thomas, A.: Systèmes de numération et fonctions fractales relatifs aux substitutions. Theor. Comp. Science 65, 153-169 (1989)
17. Goodson, G.R. and Whitman, P.N.: On the spectral properties of a class of special flows. J. Lond. Math. Soc. 21, 567-576 (1980)
18. Guarneri, I.: Spectral properties of quantum diffusion on discrete lattices. Europhys. Lett. 10, 95-100 (1989)
19. Guarneri, I.: On an estimate concerning quantum diffusion in the presence of a fractal spectrum. Europhys. Lett. 21, 729-733 (1993)
20. Guarneri, I. and Mantica, G.: On the asymptotic properties of quantum dynamics in the presence of a fractal spectrum. Ann. Inst. Henri Poincaré Phys. Théor. 61, 369-379 (1994)
21. Hof, A.: On diffraction by aperiodic structures. Commun. Math. Phys. 169, 25-43 (1995)
22. Hof, A.: On a "Structure intermediate between quasiperiodic and random". J. Stat. Phys. 84, 309-320 (1996)
23. Hof, A.: Diffraction by aperiodic structures. In R.V. Moody and J. Patera, editors, Proceedings of the NATO Advanced Study Institute on the Mathematics of Aperiodic Long Range Order. Kluwer Academic Publishers. To appear
24. Jitomirskaya, S. and Last, Y.: Dimensional Hausdorff properties of singular continuous spectra. Phys. Rev. Lett. 76, 1765-1769 (1996)
25. Katznelson, Y.: An Introduction to Harmonic Analysis. New York; John Wiley & Sons, 1968
26. Last, Y.: Quantum dynamics and decompositions of singular continuous spectra. J. Func. Anal. 142, 406-445 (1996)
27. Liardet, P.: Regularities of distribution. Comp. Math. 61, 267-293 (1987)
28. Luck, J.M.: Cantor spectra and scaling of gap widths in deterministic aperiodic systems. Phys. Rev. B 39, 5834-5849 (1989)
29. Luck, J.M., Orland, H. and Smilansky, U.: On the response of a two-level quantum system to a class of time-dependent quasiperiodic perturbations. J. Stat. Phys. 53, 551-564 (1988)
30. Pikovsky, A.S. and Feudel, U.: Correlations and spectra of strange non-chaotic attractors. J. Phys. A: Math. Gen. 27, 5209-5219 (1994)
31. Pikovsky, A.S., Zaks, M.A., Feudel, U. and Kurths, J.: Singular continuous spectra in dissipative dynamics. Phys. Rev. B 52. 285-296 (1995)
32. Queffélec, M.: Substitution Dynamical Systems - Spectral Analysis, Vol. 1294 Lect. Notes in Mathematics. Berlin-Heidelberg-New York: Springer-Verlag, 1987
33. Robinson, Jr., E.A.: On uniform convergence in the Wiener-Wintner theorem. J. Lond. Math. Soc. 49, 493-501 (1994)
34. Rogers, C.A.: Hausdorff measures. Cambridge: Cambridge University Press, 1970
35. Strichartz, R.S.: Fourier asymptotics of fractal measures. J. Func. Anal. 89, 154-187 (1990)
36. Wen, Z.-X. and Wen, Z.-Y: Marches sur les arbres homogènes suivant une suite substitutive. Sém. Téor. Nombres, Bordeaux 4, 155-186 (1992)
37. Zygmund, A.: Trigonometric Series. Cambridge: Cambridge University Press, 1959