Phase-Averaged Transport¶for Quasi-Periodic Hamiltonians
- Cite this article as:
- Bellissard, J., Guarneri, I. & Schulz-Baldes, H. Commun. Math. Phys. (2002) 227: 515. doi:10.1007/s002200200642
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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.