Asymptotics for Fermi curves: small magnetic potential

Details Asymptotics for Fermi curves: small magnetic potential Asymptotics for Fermi curves: small magnetic potential

2010-03-02

arxiv.org/abs/1003.0586v2

Rev. Math. Phys. 22(8) (2010) 881-961

Physics

Mathematical Physics

71 pages, 1 figure

Scientific paper

10.1142/S0129055X10004107

We consider complex Fermi curves of electric and magnetic periodic fields. These are analytic curves in C^2 that arise from the study of the eigenvalue problem for periodic Schroedinger operators. We characterize a certain class of these curves in the region of C^2 where at least one of the coordinates has "large" imaginary part. The new results in this work extend previous results in the absence of magnetic field to the case of "small" magnetic field. Our theorems can be used to show that generically these Fermi curves belong to a class of Riemann surfaces of infinite genus.

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