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arXiv · 1604.01573

Schr\"odinger operators with random $\delta$ magnetic fields

Takuya Mine·Yuji Nomura
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Abstract

We shall consider the Schr\"odinger operators on $\mathbf{R}^2$ with random $\delta$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $\delta$-fields, we prove the spectrum coincides with $[0,\infty)$ and the integrated density of states (IDS) decays exponentially at the bottom of the spectrum (Lifshitz tail), by using the Hardy type inequality by Laptev-Weidl. We also give a lower bound for IDS at the bottom of the spectrum.

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Takuya Mine, Yuji Nomura. 2016-04-06. Schr\"odinger operators with random $\delta$ magnetic fields. https://doi.org/10.1007/s00023-017-0559-0

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