HISLOP, Peter D.; POPOFF, Nicolas; RAYMOND, Nicolas; SUNDQVIST, Mikael

doi:10.1142/S0218202516500056

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HISLOP, Peter D.
University of Kentucky

POPOFF, Nicolas
Équipe EDP et Physique Mathématique

RAYMOND, Nicolas
Institut de Recherche Mathématique de Rennes [IRMAR]

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Article de revue

Ce document a été publié dans

Mathematical Models and Methods in Applied Sciences. 2016, vol. 26, n° 1, p. 161-184

World Scientific Publishing

Résumé en anglais

We complete the analysis of the band functions for two-dimensional magnetic Schrödinger operators with piecewise constant magnetic fields. The discontinuity of the magnetic field can create edge currents that flow along the discontinuity that have been described by physicists. Properties of these edge currents are directly related to the behavior of the band functions. The effective potential of the fiber operator is an asymmetric double well (eventually degenerated) and the analysis of the splitting of the bands incorporates the asymmetry. If the magnetic field vanishes, the reduced operator has essential spectrum and we provide an explicit description of the band functions located below the essential spectrum. For non degenerate magnetic steps, we provide an asymptotic expansion of the band functions at infinity. We prove that when the ratio of the two magnetic fields is rational, a splitting of the band functions occurs and has a natural order, predicted by numerical computations.< Réduire

Mots clés en anglais

magnetic Schrödinger operators

edge currents

band functions

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194527

DOI

http://dx.doi.org/10.1142/S0218202516500056

Project ANR

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251