Harper operators, Fermi curves, and Picard-Fuchs equations
Mathematical Physics
2015-06-05 v2 math.MP
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 -expansion of the energy level can be derived from a mirror map as in the B-model.
Keywords
Cite
@article{arxiv.1207.5197,
title = {Harper operators, Fermi curves, and Picard-Fuchs equations},
author = {Dan Li},
journal= {arXiv preprint arXiv:1207.5197},
year = {2015}
}
Comments
v2, 13 pages, minor changes have been made