Eigenvalue estimates for the Aharonov-Bohm operator in a domain
We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generalized diamagnetic inequality which was proposed by Erdos, Loss and Vougalter. Numerical studies complement these results. R...
| Main Authors: | , |
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| Format: | Report |
| Language: | unknown |
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2017
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| Online Access: | https://doi.org/10.48550/arXiv.0710.1089 |
| Summary: | We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generalized diamagnetic inequality which was proposed by Erdos, Loss and Vougalter. Numerical studies complement these results. Received by the editors February 5, 2007. (Submitted on 4 Oct 2007) The authors would like to thank A. Laptev for the setting of the problem and helpful remarks. The first author is grateful to E. H. Lieb and R. Seiringer for their hospitality at Princeton University and thanks them, H. Kalf and M. Loss for fruitful discussions. Submitted - 0710.1089.pdf |
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