1207.5197 (Dan Li)

Harper operators, Fermi curves, and Picard-Fuchs equations    [PDF]

Dan Li

This is a continuation of the work on the spectral problem of Harper operators. We continue to discuss the local monodromy representation of the Fermi curve using the Picard-Lefschetz formula. The density of states over approximating components of the Fermi curve satisfies a Picard-Fuchs equation. A mirror map is derived based on the Picard-Fuchs equation, which gives a $q$-expansion of the energy level for the electronic model.

View original: http://arxiv.org/abs/1207.5197