 02524 Pavel Exner and Katerina Nemcova
 Magnetic layers with periodic point perturbations
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Dec 18, 02

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Abstract. We study spectral properties of a spinless quantum
particle confined to an infinite planar layer with hard walls
which interacts with a periodic lattice of point perturbations and
a homogeneous magnetic field perpendicular to the layer. It is
supposed that the lattice cell contains a finite number of
impurities and the flux through the cell is rational. Using the
LandauZak transformation, we convert the problem into
investigation of the corresponding fiber operators which is
performed by means of Krein's formula. This yields an explicit
description of the spectral bands which may be absolutely
continuous or degenerate, depending on the parameters of the
model.
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