J. Bellissard, I. Guarneri, H. Schulz-Baldes
Phase-averaged transport for quasiperiodic Hamiltonians
(406K, ps)
ABSTRACT. For a class of discrete quasi-periodic Schroedinger operators
defined by covariant re- presentations 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.