@article{AIHPA_1999__71_5_539_0, author = {Barbaroux, Jean-Marie and Schulz-Baldes, H.}, title = {Anomalous quantum transport in presence of self-similar spectra}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {71}, year = {1999}, pages = {539-559}, mrnumber = {1728189}, zbl = {01421478}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1999__71_5_539_0} }
Barbaroux, J.-M.; Schulz-Baldes, H. Anomalous quantum transport in presence of self-similar spectra. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) pp. 539-559. http://gdmltest.u-ga.fr/item/AIHPA_1999__71_5_539_0/
[1] Dynamique quantique des Milieux désordonnés, Ph.D. Thesis, Toulon, 1997.
,[2] Remarks on the relation between quantum dynamics and fractal spectra, J. Math. Anal. Appl. 213 (1997) 698-722. | MR 1470878 | Zbl 0893.47048
, and ,[3] Stability and instability in quantum mechanics, in: S. Albeverio and Ph. Blanchard (Eds.), Trends and Developments in the Eighties, World Scientific, Singapore, 1985. | MR 853743 | Zbl 0584.35024
,[4] The entropy function for characteristic exponents, Physica D 25 (1987) 387-398. | MR 887471 | Zbl 0643.58006
and ,[5] Equilibrium states and the ergodic theory of anosov diffeomorphisms, Lect. Notes Math., Vol. 470, Springer, Berlin, 1975. | MR 442989 | Zbl 0308.28010
,[6] Large Deviation Techniques and Applications, Jones and Barlett, Boston, London, 1993. | MR 1202429 | Zbl 0793.60030
and ,[7] Spectral properties of quantum diffusion on discrete lattices, Europhys. Lett. 10 (1989) 95-100; On an estimate concerning quantum diffusion in the presence of a fractal spectrum, Europhys. Lett. 21 (1993) 729-733.
,[8] Multifractal energy spectra and their dynamical implications, Phys. Rev. Lett. 73 (1994) 3379-3383.
and ,[9] Singular continuous spectra and discrete wave packet dynamics, J. Math. Phys. 37 (1996) 5195-5206. | MR 1411626 | Zbl 0894.46051
,[10] Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar spectra, Rev. Math. Phys., to appear. | MR 1734713 | Zbl 0969.81018
and ,[11] Dynamics of an electron in quasiperiodic systems. I. Fibonacci model, J. Phys. Soc. Japan 57 (1988) 230-240; Dynamics of an electron in quasiperiodic systems. II. Harper model, J. Phys. Soc. Japan 57 (1988) 1365-1372.
and ,[12] Quantum dynamics and decomposition of singular continuous spectra, J. Funct. Anal. 142 (1996) 402-445. | MR 1423040 | Zbl 0905.47059
,[13] Quantum intermittency in almost periodic systems derived from their spectral properties, Physica D 103 (1997) 576-589; Wave propagation in almost-periodic structures, Physica D 109 (1997) 113-127. | Zbl 0925.58041
,[14] Introduction to the theory of electronic properties of quasicrystals, in: F. Hippert and D. Gratias (Eds.), Lectures on Quasicrystals, Les Éditions de Physique, Les Ulis, 1994, 417-462.
,[15] Anomalous diffusion properties of wave packets on quasiperiodic chains, Phys. Rev. Lett. 76 (1996) 4372-4375.
,[16] Thermodynamic Formalism, Addison-Wesley, Reading, MA, 1978. | MR 511655
,[17] Anomalous transport: A mathematical framework, Rev. Math. Phys. 10 (1998) 1-46. | MR 1606847 | Zbl 0908.47066
and ,[18] A kinetic theory for quantum transport in aperiodic media, J. Stat. Phys. 91 (1998) 991-1027. | MR 1637278 | Zbl 0960.82029
and ,[19] Generalized dynamical variables and measures for the Julia sets, Nuovo Cimento 101 B (1988) 285-307. | MR 962588
, and ,[20] Anomalous diffusion and conductivity in octagonal tiling models, Phys. Rev. B 46 (1992) 13751-13754.
, and ,[21] The spectrum of a quasiperiodic Schrödinger operator, Commun. Math. Phys. 111 (1987) 409-415; Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian, J. Stat. Phys. 56 (1989) 525- 530. | MR 900502 | Zbl 0624.34017
,[22] General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992. | MR 1163828 | Zbl 0791.33009
and ,