Schrödinger operators with random $δ$ magnetic fields
We shall consider the Schrödinger operators on $\mathbf{R}^2$ with random $δ$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $δ$-fields, we prove the spectrum coincides with $[0,\infty)$ and the integrated density of states (IDS) decays exponentially at the bottom...
| Main Authors: | , |
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| Format: | Text |
| Language: | unknown |
| Published: |
arXiv
2016
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.1604.01573 https://arxiv.org/abs/1604.01573 |
| Summary: | We shall consider the Schrödinger operators on $\mathbf{R}^2$ with random $δ$ magnetic fields. Under some mild conditions on the positions and the fluxes of the $δ$-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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