Anomalous quantum transport in presence of self-similar spectra
J.-M. Barbaroux; H. Schulz-Baldes
Annales de l'I.H.P. Physique théorique (1999)
- Volume: 71, Issue: 5, page 539-559
- ISSN: 0246-0211
Access Full Article
topHow to cite
topBarbaroux, J.-M., and Schulz-Baldes, H.. "Anomalous quantum transport in presence of self-similar spectra." Annales de l'I.H.P. Physique théorique 71.5 (1999): 539-559. <http://eudml.org/doc/76844>.
@article{Barbaroux1999,
author = {Barbaroux, J.-M., Schulz-Baldes, H.},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {5},
pages = {539-559},
publisher = {Gauthier-Villars},
title = {Anomalous quantum transport in presence of self-similar spectra},
url = {http://eudml.org/doc/76844},
volume = {71},
year = {1999},
}
TY - JOUR
AU - Barbaroux, J.-M.
AU - Schulz-Baldes, H.
TI - Anomalous quantum transport in presence of self-similar spectra
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 5
SP - 539
EP - 559
LA - eng
UR - http://eudml.org/doc/76844
ER -
References
top- [1] J.-M. Barbaroux, Dynamique quantique des Milieux désordonnés, Ph.D. Thesis, Toulon, 1997.
- [2] J.-M. Barbaroux, J.M. Combes and R. Montcho, Remarks on the relation between quantum dynamics and fractal spectra, J. Math. Anal. Appl.213 (1997) 698-722. Zbl0893.47048MR1470878
- [3] J. Bellissard, Stability and instability in quantum mechanics, in: S. Albeverio and Ph. Blanchard (Eds.), Trends and Developments in the Eighties, World Scientific, Singapore, 1985. Zbl0584.35024MR853743
- [4] T. Bohr and D. Rand, The entropy function for characteristic exponents, Physica D 25 (1987) 387-398. Zbl0643.58006MR887471
- [5] R. Bowen, Equilibrium states and the ergodic theory of anosov diffeomorphisms, Lect. Notes Math., Vol. 470, Springer, Berlin, 1975. Zbl0308.28010MR442989
- [6] A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, Jones and Barlett, Boston, London, 1993. Zbl0793.60030MR1202429
- [7] I. Guarneri, 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] I. Guarneri and G. Mantica, Multifractal energy spectra and their dynamical implications, Phys. Rev. Lett.73 (1994) 3379-3383.
- [9] I. Guarneri, Singular continuous spectra and discrete wave packet dynamics, J. Math. Phys.37 (1996) 5195-5206. Zbl0894.46051MR1411626
- [10] I. Guarneri and H. Schulz-Baldes, Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar spectra, Rev. Math. Phys., to appear. Zbl0969.81018MR1734713
- [11] H. Hiramoto and S. Abe, Dynamics of an electron in quasiperiodic systems. I. Fibonacci model, J. Phys. Soc. Japan57 (1988) 230-240; Dynamics of an electron in quasiperiodic systems. II. Harper model, J. Phys. Soc. Japan57 (1988) 1365-1372.
- [12] Y. Last, Quantum dynamics and decomposition of singular continuous spectra, J. Funct. Anal.142 (1996) 402-445. Zbl0905.47059MR1423040
- [13] G. Mantica, 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. Zbl0925.58041
- [14] D. Mayou, 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] F. Piéchon, Anomalous diffusion properties of wave packets on quasiperiodic chains, Phys. Rev. Lett.76 (1996) 4372-4375.
- [16] D. Ruelle, Thermodynamic Formalism, Addison-Wesley, Reading, MA, 1978. MR511655
- [17] H. Schulz-Baldes and J. Bellissard, Anomalous transport: A mathematical framework, Rev. Math. Phys.10 (1998) 1-46. Zbl0908.47066MR1606847
- [18] H. Schulz-Baldes and J. Bellissard, A kinetic theory for quantum transport in aperiodic media, J. Stat. Phys.91 (1998) 991-1027. Zbl0960.82029MR1637278
- [19] G. Servizi, G. Turchetti and S. Vaienti, Generalized dynamical variables and measures for the Julia sets, Nuovo Cimento101 B (1988) 285-307. MR962588
- [20] C. Sire, B. Passaro and V. Benza, Anomalous diffusion and conductivity in octagonal tiling models, Phys. Rev. B46 (1992) 13751-13754.
- [21] A. Sütó, 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. Zbl0624.34017MR900502
- [22] H. Stahl and V. Totik, General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992. Zbl0791.33009MR1163828
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.