三维磁性Schrödinger操作器，电势支撑在一个管中

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-09-17 DOI:10.1007/s43034-025-00473-x

Diana Barseghyan, Juan Bory-Reyes, Baruch Schneider

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引用次数: 0

摘要

在本文中，我们研究了$\mathbb {R}^3$中的以下磁Schrödinger算子：$$H=(i \nabla +A)^2- \tilde{V},$$中，$\tilde{V}$是沿直线的局部变形曲线建立的管道上的非负势支撑，$B:=\textrm{curl}(A)$是一个非零的局部（即紧支承）磁场。我们证明了磁场不改变系统的本质谱，并建立了离散谱为空的充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Three-dimensional magnetic Schrödinger operator with the potential supported in a tube

In this paper, we study the following magnetic Schrödinger operator in $\mathbb {R}^3$:

$$H=(i \nabla +A)^2- \tilde{V},$$

where $\tilde{V}$ is non-negative potential supported over the tube built along a curve which is a local deformation of a straight one, and $B:=\textrm{curl}(A)$ is a non-zero and local (i.e., a compact supported) magnetic field. We prove that the magnetic field does not alter the essential spectrum of this system and establish a sufficient condition for the discrete spectrum to be empty.

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.