Vertex coupling interpolation in quantum chain graphs

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-09-17 DOI:10.1063/5.0208361

Pavel Exner, Jan Pekař

引用次数: 0

Abstract

We analyze the band spectrum of the periodic quantum graph in the form of a chain of rings connected by line segments with the vertex coupling which violates the time reversal invariance, interpolating between the δ coupling and the one determined by a simple circulant matrix. We find that flat bands are generically absent and that the negative spectrum is nonempty even for interpolation with a non-attractive δ coupling; we also determine the high-energy asymptotic behavior of the bands.

查看原文本刊更多论文

量子链图中的顶点耦合插值

我们分析了由线段连接的环链形式的周期量子图的频带谱，其顶点耦合违反了时间反转不变性，在δ耦合和由简单环形矩阵确定的耦合之间进行插值。我们发现，平坦带一般是不存在的，而且即使在使用无吸引力的 δ 耦合进行插值时，负谱也是非空的；我们还确定了带的高能渐近行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.