Weighted CLR type bounds in two dimensions
- Creators
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Frank, Rupert1
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Laptev, Ari2
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Read, Larry3
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1.
California Institute of Technology
- 2. Imperial College London
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3.
Ludwig-Maximilians-Universität München
Abstract
We derive weighted versions of the Cwikel–Lieb–Rozenblum inequality for the Schrödinger operator in two dimensions with a nontrivial Aharonov–Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a class of long-range potentials that saturate our bounds in the strong coupling limit. We also extend our analysis to the two-dimensional Schrödinger operator acting on antisymmetric functions and obtain similar results.
Copyright and License
© Copyright 2024 by the authors
Acknowledgement
The first author was partially supported through US National Science Foundation grant DMS-1954995, as well as through the Excellence Strategy of the German Research Foundation grant EXC-2111-390814868 and through German Research Foundation project TRR 352 - Project-ID 470903074. The second author was supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement 075-10-2021-093, Project MTH-RND-2124).The third author was partially supported through German Research Foundation project TRR 352 - Project-ID 470903074.
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Additional details
- National Science Foundation
- DMS-1954995
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft
- TRR 352 - Project-ID 470903074
- The Ministry of Education and Science of the Russian Federation
- Project MTH-RND-2124
- Publication Status
- Published