Absence of positive eigenvalues of magnetic Schr\"odinger operators
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Publication:6336841
DOI10.1007/S00526-022-02397-ZarXiv2003.07294MaRDI QIDQ6336841
Silvana Avramska-Lukarska, Hynek Kovařík, Dirk Hundertmark
Publication date: 16 March 2020
Abstract: We study sufficient conditions for the absence of positive eigenvalues of magnetic Schr"odinger operators in . In our main result we prove the absence of eigenvalues above certain threshold energy which depends explicitly on the magnetic and electric field. A comparison with the examples of Miller--Simon shows that our result is sharp as far as the decay of the magnetic field is concerned. As applications, we describe several consequences of the main result for two-dimensional Pauli and Dirac operators, and two and three dimensional Aharonov--Bohm operators.
General topics in linear spectral theory for PDEs (35P05) PDEs in connection with quantum mechanics (35Q40) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)
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