On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schroedinger operators

Abstract

We show for a large class of discrete Harper-like and continuous magnetic Schrodinger 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 J. Bellissard in 1994, and give examples in favor of a recent conjecture of G. Nenciu.

15 pages, accepted for publication in Annales Henri Poincare

References in corpus (5)

• The Magnetic Weyl Calculus
• Magnetic Pseudodifferential Operators
• The Faraday effect revisited: Thermodynamic limit
• The Faraday effect revisited: General theory
• Strict Deformation Quantization for a Particle in a Magnetic Field

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