no. 5
Anomalous quantum transport in presence of self-similar spectra
Annales de l'I.H.P. Physique théorique, Tome 71 (1999) no. 5, pp. 539-559. 
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     author = {Barbaroux, J.-M. and Schulz-Baldes, H.},
     title = {Anomalous quantum transport in presence of self-similar spectra},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {539--559},
     publisher = {Gauthier-Villars},
     volume = {71},
     number = {5},
     year = {1999},
     mrnumber = {1728189},
     zbl = {01421478},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1999__71_5_539_0/}
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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) no. 5, pp. 539-559. http://archive.numdam.org/item/AIHPA_1999__71_5_539_0/

[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. | MR | Zbl

[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. | MR | Zbl

[4] T. Bohr and D. Rand, The entropy function for characteristic exponents, Physica D 25 (1987) 387-398. | MR | Zbl

[5] R. Bowen, Equilibrium states and the ergodic theory of anosov diffeomorphisms, Lect. Notes Math., Vol. 470, Springer, Berlin, 1975. | MR | Zbl

[6] A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, Jones and Barlett, Boston, London, 1993. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[11] H. Hiramoto and S. Abe, 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.

[12] Y. Last, Quantum dynamics and decomposition of singular continuous spectra, J. Funct. Anal. 142 (1996) 402-445. | MR | Zbl

[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. | Zbl

[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. | MR

[17] H. Schulz-Baldes and J. Bellissard, Anomalous transport: A mathematical framework, Rev. Math. Phys. 10 (1998) 1-46. | MR | Zbl

[18] H. Schulz-Baldes and J. Bellissard, A kinetic theory for quantum transport in aperiodic media, J. Stat. Phys. 91 (1998) 991-1027. | MR | Zbl

[19] G. Servizi, G. Turchetti and S. Vaienti, Generalized dynamical variables and measures for the Julia sets, Nuovo Cimento 101 B (1988) 285-307. | MR

[20] C. Sire, B. Passaro and V. Benza, Anomalous diffusion and conductivity in octagonal tiling models, Phys. Rev. B 46 (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. | MR | Zbl

[22] H. Stahl and V. Totik, General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992. | MR | Zbl