Abstract
We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu.
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Communicated by Jean Bellissard.
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Cornean, H.D. On the Lipschitz Continuity of Spectral Bands of Harper-Like and Magnetic Schrödinger Operators. Ann. Henri Poincaré 11, 973–990 (2010). https://doi.org/10.1007/s00023-010-0048-1
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DOI: https://doi.org/10.1007/s00023-010-0048-1