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arXiv · 2003.07294

Absence of positive eigenvalues of magnetic Schr\"odinger operators

Silvana Avramska-Lukarska·Dirk Hundertmark·Hynek Kovarik
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Abstract

We study sufficient conditions for the absence of positive eigenvalues of magnetic Schr\"odinger operators in $\mathbb{R}^d,\, d\geq 2$. 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.

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Silvana Avramska-Lukarska, Dirk Hundertmark, Hynek Kovarik. 2020-03-16. Absence of positive eigenvalues of magnetic Schr\"odinger operators. https://arxiv.org/abs/2003.07294

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