Abstract:
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.
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Received: 30 May 2001 / Accepted: 2 January 2002
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Bellissard, J., Guarneri, I. & Schulz-Baldes, H. Phase-Averaged Transport¶for Quasi-Periodic Hamiltonians. Commun. Math. Phys. 227, 515–539 (2002). https://doi.org/10.1007/s002200200642
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DOI: https://doi.org/10.1007/s002200200642