Edge Switching Transformations of Quantum Graphs

被引：6

作者：

Aizenman, M. ^{[1
,2
]}

Schanz, H. ^{[3
]}

Smilansky, U. ^{[4
]}

Warzel, S. ^{[5
]}

机构：

[1] Princeton Univ, Dept Phys, Princeton, NJ 08540 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08540 USA

[3] Univ Appl Sci Magdeburg Stendal, Inst Mech Engn, D-39114 Magdeburg, Germany

[4] Weizmann Inst Sci, Dept Phys Complex Syst, IL-7610001 Rehovot, Israel

[5] Tech Univ Munich, Zentrum Math, Boltzmannstr 3, D-85747 Garching, Germany

来源：

ACTA PHYSICA POLONICA A | 2017年 / 132卷 / 06期

基金：

美国国家科学基金会;

关键词：

ONE HEAR; CHAOS; SHAPE;

D O I：

10.12693/APhysPolA.132.1699

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schrodinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {E-n}(n=1)(infinity) and {(E) over bar (n)}(n=1)(infinity) correspondingly, are level-2 interlaced, so that En-2 <= (E) over bar (n) <= En+2. The proofs are guided by considerations of the quantum graphs' discrete analogs.

引用

页码：1699 / 1703

页数：5

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