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...
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| Online Access: | https://dx.doi.org/10.48550/arxiv.1604.01573 https://arxiv.org/abs/1604.01573 |
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ftdatacite:10.48550/arxiv.1604.01573 2023-05-15T17:07:14+02:00 Schrödinger operators with random $δ$ magnetic fields Mine, Takuya Nomura, Yuji 2016 https://dx.doi.org/10.48550/arxiv.1604.01573 https://arxiv.org/abs/1604.01573 unknown arXiv https://dx.doi.org/10.1007/s00023-017-0559-0 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Mathematical Physics math-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2016 ftdatacite https://doi.org/10.48550/arxiv.1604.01573 https://doi.org/10.1007/s00023-017-0559-0 2022-04-01T11:41:24Z 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. Text laptev DataCite Metadata Store (German National Library of Science and Technology) |
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Open Polar |
| collection |
DataCite Metadata Store (German National Library of Science and Technology) |
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ftdatacite |
| language |
unknown |
| topic |
Mathematical Physics math-ph FOS Physical sciences |
| spellingShingle |
Mathematical Physics math-ph FOS Physical sciences Mine, Takuya Nomura, Yuji Schrödinger operators with random $δ$ magnetic fields |
| topic_facet |
Mathematical Physics math-ph FOS Physical sciences |
| description |
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. |
| format |
Text |
| author |
Mine, Takuya Nomura, Yuji |
| author_facet |
Mine, Takuya Nomura, Yuji |
| author_sort |
Mine, Takuya |
| title |
Schrödinger operators with random $δ$ magnetic fields |
| title_short |
Schrödinger operators with random $δ$ magnetic fields |
| title_full |
Schrödinger operators with random $δ$ magnetic fields |
| title_fullStr |
Schrödinger operators with random $δ$ magnetic fields |
| title_full_unstemmed |
Schrödinger operators with random $δ$ magnetic fields |
| title_sort |
schrödinger operators with random $δ$ magnetic fields |
| publisher |
arXiv |
| publishDate |
2016 |
| url |
https://dx.doi.org/10.48550/arxiv.1604.01573 https://arxiv.org/abs/1604.01573 |
| genre |
laptev |
| genre_facet |
laptev |
| op_relation |
https://dx.doi.org/10.1007/s00023-017-0559-0 |
| op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
| op_doi |
https://doi.org/10.48550/arxiv.1604.01573 https://doi.org/10.1007/s00023-017-0559-0 |
| _version_ |
1766062583423434752 |