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arXiv · 1207.5197

Harper operators, Fermi curves, and Picard-Fuchs equations

Dan Li
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Abstract

This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard-Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A $q$-expansion of the energy level can be derived from a mirror map as in the B-model.

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Dan Li. 2013-10-27. Harper operators, Fermi curves, and Picard-Fuchs equations. https://doi.org/10.1007/s11005-013-0676-8

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