磁薛定谔算子与二维弯曲带中的势能支持

IF 1.1 3区数学 Q1 MATHEMATICS Mediterranean Journal of Mathematics Pub Date : 2024-05-02 DOI:10.1007/s00009-024-02651-y

Juan Bory-Reyes, Diana Barseghyan, Baruch Schneider

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引用次数: 0

摘要

我们考虑了磁薛定谔算子（H=(i \nabla +A)^2- V\ ），该算子的非负势能 V 支持在一个条带上，该条带是直线条带的局部变形，磁场 \(B:=\textrm{rot}(A)\) 被假定为非零且局部的。我们证明磁场不会改变这个系统的基本谱，并研究了 H 的离散谱为空的充分条件。

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Magnetic Schrödinger Operator with the Potential Supported in a Curved Two-Dimensional Strip

We consider the magnetic Schrödinger operator \(H=(i \nabla +A)^2- V\) with a non-negative potential V supported over a strip which is a local deformation of a straight one, and the magnetic field \(B:=\textrm{rot}(A)\) is assumed to be non-zero and local. We show that the magnetic field does not change the essential spectrum of this system, and investigate a sufficient condition for the discrete spectrum of H to be empty.

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.