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Harper operator, Fermi curves and Picard-Fuchs equation. (English) Zbl 1302.74199

Summary: This paper is a continuation of the work on the spectral problem of the 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 is derived from a mirror map as in the B-model.

MSC:

74S25 Spectral and related methods applied to problems in solid mechanics
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