Absolute continuity of the spectrum of the periodic Schr\"odinger operator in a layer and in a smooth cylinder

Nikolay Filonov; Ilya Kachkovskiy

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arXiv · 1011.1394

Absolute continuity of the spectrum of the periodic Schr\"odinger operator in a layer and in a smooth cylinder

Nikolay Filonov·Ilya Kachkovskiy

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Abstract

We consider the Schr\"odinger operator $H = -\Delta + V$ in a layer or in a $d$-dimensional cylinder. The potential $V$ is assumed to be periodic with respect to some lattice. We establish the absolute continuity of $H$, assuming $V \in L_{p, \loc}$, where $p$ is a real number greater than $d/2$ in the case of a layer, and $p > \max (d/2, d-2)$ for the cylinder.

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BibTeX RIS

Nikolay Filonov, Ilya Kachkovskiy. 2010-11-05. Absolute continuity of the spectrum of the periodic Schr\"odinger operator in a layer and in a smooth cylinder. https://arxiv.org/abs/1011.1394

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