Phase-averaged transport for quasiperiodic Hamiltonians - Bellissard, Jean; Guarneri, Italo; Schulz-Baldes, Hermann (Communications in Mathematical Physics, 2002)
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.
UnivIS-Import:2015-03-09:Pub.2002.nat.dma.pma22.phasea