Communications in Mathematical Physics

, Volume 227, Issue 3, pp 515–539

Phase-Averaged Transport¶for Quasi-Periodic Hamiltonians

  • Jean Bellissard
  • Italo Guarneri
  • Hermann Schulz-Baldes

DOI: 10.1007/s002200200642

Cite this article as:
Bellissard, J., Guarneri, I. & Schulz-Baldes, H. Commun. Math. Phys. (2002) 227: 515. doi:10.1007/s002200200642


For a class of discrete quasi-periodic Schrödinger operators defined by covariant representations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is proven. This result is established under a Diophantine condition on the incommensuration parameter. The relevant class of operators is distinguished by invariance with respect to symmetry automorphisms of the rotation algebra. It includes the critical Harper (almost-Mathieu) operator. As a by-product, a new solution of the frame problem associated with Weyl–Heisenberg–Gabor lattices of coherent states is given.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean Bellissard
    • 1
  • Italo Guarneri
    • 3
  • Hermann Schulz-Baldes
    • 6
  1. 1.Université Paul-Sabatier, 118 route de Narbonne, 31062 Toulouse, FranceFR
  2. 2.Institut Universitaire de FranceFR
  3. 3.Università dell'Insubria a Como, via Valleggio 11, 22100 Como, ItalyIT
  4. 4.Istituto Nazionale per la Fisica della Materia, via Celoria 16, 20133 Milano, ItalyIT
  5. 5.Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, 27100 Pavia, ItalyIT
  6. 6.University of California at Irvine, CA 92697, USAUS

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