A remark on quantum dynamics

Helvetica Physica Acta

Volumn 71, Issue 3, 1998, Pages 233-241

  Knill, Oliver ^a  

^a The University of Arizona   (United States)

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[No Author keywords available]

Indexed keywords

EID: 0009217076     PISSN: 00180238     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. R. Artuso, G. Casati, F. Borgonovi, L. Rebuzzini, and I. Guarneri. Fractal and dynamical properties of the kicked Harper model. Intern. J. Mod. Phys. B, 8:207-235, 1994.
2. A. Barelli, R. Fleckinger, and T. Ziman. Europhys. lett. 27:531-536, 1994.
3. A. Barelli, R. Fleckinger, and T. Ziman. Two-dimensional electron in a random magnetic field. Phys. Rev. B, 49:3340-3349, 1994.
4. C.M. Bender, L.R. Mead, and K.A. Milton. Discrete time quantum mechanics. Computers Math. Applic, 28:279-317, 1994.
5. J-M. Combes. Connections between quantum dynamics and spectral properties of time evolution operators. In Differential equations with applications to Mathematical physics, volume 192 of Mathematics in science and engineering, 1993.
6. K. Falconer. Fractal Geometry, Mathematical Foundations and Applications. John Wiley and Sons, Chichester, 1990.
7. J.P. Gaspard and P. Lambin. Generalized moments: application to solid-state physics. In Polynômes Orthogonaux et Applications, volume 1171 of Lecture Notes in Mathematics. Springer Verlag, 1984. Proceedings, Bar-le-Duc.
8. A. Gordon, S. Jitomirskaya, Y. Last, and B. Simon. Duality and singular continuous spectrum in the almost mathieu equation. preprint 1996, available in mp_arcmath.utexas.edu, 1996.
9. I. Guarneri. Spectral properties of quantum diffusion on discrete lattices. Europhys. Lett., 10:95-100, 1989.
10. M. Holschneider. Fractal wavelet dimension and localization. Commun. Math. Phys., 160:457-473, 1994.
11. S.Ya. Jitomirskaya. Almost everything about the almost Mathieu operator II. 1995. Proceedings of the XI'th international congress of Mathematical Physics, Paris July 18-23, 1994.
12. S.Ya. Jitomirskaya. Anderson localization for the almost mathieu equation II, point spectrum for λ ≥ 2. Commun. Math. Phys., 168:201-205, 1995.
13. J-P. Kahane and R. Salem. Ensembles parfaits et séries trigonométriques. Hermann, 1963.
14. R. Ketzmerick, G. Petschel, and T. Geisel. Slow decay of temporal correlations in quantum systems with cantor spectra. Phys. Rev. Lett., 69:695-698, 1992.
15. O. Knill. Discrete random electromagnetic Laplacians. (preprint available in the Mathematical Physics Preprint Archive, mp-arcmath.utexas.edu, document number: 95-195), 1995.
16. O. Knill. On the dynamics of a general unitary operator. Caltech 1996, submitted, 1996.
17. M. Kohmoto and B. Sutherland. Electronic and vibrational modes on a Penrose lattice: Localized states and band structure. Phys. Rev. B, 34:3849-3853, 1986.
18. M. Kohmoto and B. Sutherland. Electronic states on a Penrose lattice. Phys. Rev. Lett., 56:2740-2743, 1986.
19. Y. Last. Quantum dynamics and decompositions of singular continuous spectra. To appear in J. Funct. Anal. Caltech Preprint, April, 1995.
20. Y. Last. Almost everything about the almost Mathieu operator I. 1995. Proceedings of the XI'th international congress of Mathematical Physics, Paris July 18-23, 1994.
21. V. Mandelshtam. Global recursion polynomial expansions of the Green's function and time evolution operator. In To be published in Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics. Springer-Verlag, New York, 1996.
22. V.A. Mandelshtam and S.Ya. Zhitomirskaya. 1d-quasiperiodic operators. Latent symmetries. Commun. Math. Phys., 139:589-604, 1991.
23. J.L. Richardson. Visualizing quantum scattering on the CM-2 supercomputer. Comp. Phys. Comm., 63:84-94, 1991.
24. M.A. Shubin. Discrete magnetic Laplacians. Commun. Math. Phys., 164:259-275, 1994.
25. B. Simon. Operators with singular continuous spectrum: I. General operators. Annals of Mathematics, 141:131-145, 1995.
26. B. Simon. Operators with singular continuous spectrum VI, Graph Laplacians and Laplace-Beltrami operators. To appear in Proc. Amer. Math. Soc, 1995.
27. B. Simon. Spectral analysis of rank one perturbations and applications, volume 8 of CRM Proceedings and Lecture Notes, pages 109-149, 1995.
28. R.S. Strichattz. Fourier asymptotics of fractal measures. J. Func. Anal., 89:154-187, 1990.
29. G. Szegö. Orthogonal Polynomials, volume 23 of American Mathematical Society, Colloquium Publications. American Mathematical Society, 1939.