直线上支持静电δ壳势的Dirac算子的谱跃迁。

IF 0.8 3区数学 Q2 MATHEMATICS

Integral Equations and Operator Theory Pub Date : 2022-01-01 Epub Date: 2022-08-30 DOI:10.1007/s00020-022-02711-6

Jussi Behrndt, Markus Holzmann, Matěj Tušek

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引用次数: 4

摘要

本文研究了具有强度η∈R的静电δ壳相互作用的二维狄拉克算子A η在直线上的支承。我们观察到在临界相互作用强度η =±2时，自由狄拉克算符a0的谱隙内的a η的连续谱突然坍缩为一个单点。

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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Spectral Transition for Dirac Operators with Electrostatic δ -Shell Potentials Supported on the Straight Line.

In this note the two dimensional Dirac operator $A_{η}$ with an electrostatic $δ$ -shell interaction of strength $η \in R$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths $η = \pm 2$ the continuous spectrum of $A_{η}$ inside the spectral gap of the free Dirac operator $A_{0}$ collapses abruptly to a single point.

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来源期刊

Integral Equations and Operator Theory 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Integral Equations and Operator Theory (IEOT) is devoted to the publication of current research in integral equations, operator theory and related topics with emphasis on the linear aspects of the theory. The journal reports on the full scope of current developments from abstract theory to numerical methods and applications to analysis, physics, mechanics, engineering and others. The journal consists of two sections: a main section consisting of refereed papers and a second consisting of short announcements of important results, open problems, information, etc.