Absence of positive eigenvalues of magnetic Schr\'odinger operators

Autor:	Avramska-Lukarska, Silvana, Hundertmark, Dirk, Kovarik, Hynek
Rok vydání:	2020
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: accepted for publication in Calculus of Variations & PDE
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.07294 Zobrazit plný text záznamu View this record from Arxiv