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Abstract: 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 eigenvalueproblem for periodic Schroedinger operators. We characterize a certain class ofthese 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 inthe absence of magnetic field to the case of -small- magnetic field. Ourtheorems can be used to show that generically these Fermi curves belong to aclass of Riemann surfaces of infinite genus.



Author: Gustavo de Oliveira

Source: https://arxiv.org/



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