Phase-averaged transport for quasi-periodic Hamiltonians

Communications in Mathematical Physics

Volumn 227, Issue 3, 2002, Pages 515-539

  Bellissard, Jean ^a   Guarneri, Italo ^b,c,d   Schulz Baldes, Hermann ^e  

^a UNIVERSITÉ PAUL SABATIER   (France)

^b UNIVERSITY OF INSUBRIA   (Italy)

^c Istituto Nazionale per la Fisica della Materia Milan   (Italy)

^d INFN SEZIONE DI PAVIA   (Italy)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036628279     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200642     Document Type: Article

References (32)

1. [BSB] Barbaroux, J.-M., Schulz-Baldes, H.: Anomalous transport in presence of salf-similar spectra. Annales I.H.P. Phys. Théo. 71, 539-559 (1999)
2. [BGT] Barbaroux, J.M., Germinet, F., Tcheremchantsev, S.: Nonlinear variation of diffusion exponents in quantum dynamics, C.R. Acad. Sci. Paris 330, série 1, 409-414 (2000): Fractal Dimensions and the Phenomenon of Intermittency in Quantum Dynamics. Duke Math. J. 110, 161-193 (2001)
3. [BGT] Barbaroux, J.M., Germinet, F., Tcheremchantsev, S.: Nonlinear variation of diffusion exponents in quantum dynamics, C.R. Acad. Sci. Paris 330, série 1, 409-414 (2000): Fractal Dimensions and the Phenomenon of Intermittency in Quantum Dynamics. Duke Math. J. 110, 161-193 (2001)
4. [Bel] Bellissard, J.: K-theory of C*-algebrus in solid state physics. In: Statistical Mechanics and Field Theory: Mathematical Aspects, Lecture Notes in Physics 257, edited by T. Dorlas, M. Hugenholtz, M. Winnink, Berlin: Springer-Verlag, 1986, pp. 99-156; Gap labelling theorems for Schrödinger operators. In: From Number Theory to Physics. Berlin: Springer, 1992, pp. 538-630
5. [Bel] Bellissard, J.: K-theory of C*-algebrus in solid state physics. In: Statistical Mechanics and Field Theory: Mathematical Aspects, Lecture Notes in Physics 257, edited by T. Dorlas, M. Hugenholtz, M. Winnink, Berlin: Springer-Verlag, 1986, pp. 99-156; Gap labelling theorems for Schrödinger operators. In: From Number Theory to Physics. Berlin: Springer, 1992, pp. 538-630
6. [Bel94] Bellissard, J.: Lipshitz continuity of gap boundaries for Hofstadter-like spectra. Commun. Math. Phys. 160, 599-613 (1994)
7. [Com] Combes, J.-M.: In: Differential Equations with Applications to Mathematical Physics. Ames, W.F., Harrell, E.M., Herod J.V., eds. Boston: Academic Press, 1993
8. [Con] Connes, A.: Noncommutative Geometry. London: Academic Press, 1994
9. [DS] Deift, P., Simon, B.: Almost periodic Schrödinger operators. III. The absolutely continuous spectrum in one dimension. Commun. Math. Phys. 90, 389-411 (1983)
10. [Gua] Guarneri, I.: Spectral properties of quantum diffusion on discrete lattices. Europhys. Lett. 10, 95-100 (1989): On an estimate concerning quantum diffusion in the presence of a fractal spectrum. Europhys. Lett. 21, 729-733 (1993)
11. [Gua] Guarneri, I.: Spectral properties of quantum diffusion on discrete lattices. Europhys. Lett. 10, 95-100 (1989): On an estimate concerning quantum diffusion in the presence of a fractal spectrum. Europhys. Lett. 21, 729-733 (1993)
12. [GM] Guarneri, I., Mantica, G.: Multifractal Energy Spectra and Their Dynamical Implications. Phys. Rev. Lett. 73, 3379-3383 (1994)
13. [GSB1] Guarneri, I., Schulz-Baldes, H.: Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar spectra. Rev. Math. Phys. 11, 1249-1268 (1999)
14. [GSB2] Guarneri, I., Schulz-Baldes, H.: Lower bounds on wave packet propagation by packing dimensions of spectral measures. Elect. J. Math. Phys. 5 (1999)
15. [GSB3] Guarneri, I., Schulz-Baldes, H.: Intermittent lower bound on quantum diffusion. Lett. Math. Phys. 49, 317-324 (1999)
16. [Har] Harper, P. G.: Single Band Motion of Conduction Electrons in a Uniform Magnetic Field. Proc. Phys. Soc. Lond. A 68, 874-878 (1955)
17. [Her] Herman, M. R.: Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Publications I.H.E.S. 49, 5-233 (1979)
18. [Jit] Jitomirskaya, S.: Metal-Insulator Transition for the Almost Mathieu Operator. Ann. of Math. 150, 1159-1175 (1999)
19. [Las] Last, Y.: Quantum Dynamics and decomposition of singular continuous spectra. J. Funct. Anal. 142, 402-445 (1996)
20. [KKKG] Ketzmerick, R., Kruse, K., Kraut, S. and Geisel, T.: What determines the spreading of a wave packet?. Phys. Rev. Lett. 79, 1959-1962 (1997)
21. [KL] Kiselev, A., Last, Y.: Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains. Duke Math. J. 102, 125-150 (2000)
22. [Man] Mantica, G.: Quantum intermittency in almost periodic systems derived from their spectral properties. Physica D 103, 576-589 (1997); Wave Propagation in Almost-Periodic Structures. Physica D 109, 113-127 (1997)
23. [Man] Mantica, G.: Quantum intermittency in almost periodic systems derived from their spectral properties. Physica D 103, 576-589 (1997); Wave Propagation in Almost-Periodic Structures. Physica D 109, 113-127 (1997)
24. [Per] Perelomov, A.: Generalized Coherent States and Their Applications. Berlin: Springer, 1986
25. [Pie] Piéchon, F.: Anomalous Diffusion Properties of Wave Packets on Quasiperiodic Chains. Phys. Rev. Lett. 76, 4372-4375 (1996)
26. [Ram] Rammal, R.: Landau level spectrum of Bloch electron in a honeycomb lattice. J. Phys. France 46, 1345-1354 (1985)
27. [Rie] Rieffel, M. A.: C*-algebras associated with irrational rotations. Pac. J. Math. 93, 415-429 (1981)
28. [RP] Rüdinger, A., Piéchon, F.: Hofstadter rules and generalized dimensions of the spectrum of Harper's equation. J. Phys. A 30, 117-128 (1997)
29. [Sak] Sakai, S.: C*-algebras and W*-algebras. Berlin: Springer, 1971
30. [SBB] Schulz-Baldes, H., Bellissard. J. Anomalous transport: A mathematical framework. Rev. Math. Phys. 10, 1-46 (1998)
31. [Sei] Seip, K.: Density theorems for sampling and interpolation in the Bargmann-Fock space I. J. Reine Angew. Math. 429, 91-106 (1992)
32. [TK] Tang, C., Kohmoto, M.: Global scaling properties of the spectrum for a quasiperiodic Schrödinger equation. Phys. Rev. B 34, 2041-2044 (1986)