Absolutely Continuous Spectrum for Quantum Trees

被引：3

作者：

Anantharaman, Nalini ^{[1
]}

Ingremeau, Maxime ^{[2
]}

Sabri, Mostafa ^{[3
]}

Winn, Brian ^{[4
]}

机构：

[1] Univ Strasbourg, CNRS, IRMA, UMR 7501, F-67000 Strasbourg, France

[2] Univ Cote Azur, Lab JA Dieudonne, CNRS, UMR 7351,UNS, F-06108 Nice, France

[3] Cairo Univ, Fac Sci, Dept Math, Giza 12613, Egypt

[4] Loughborough Univ, Dept Math Sci, Loughborough LE11 3TU, Leics, England

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2021年 / 383卷 / 01期

关键词：

ANDERSON MODEL; GRAPHS; OPERATORS;

D O I：

10.1007/s00220-021-03994-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.

引用

页码：537 / 594

页数：58

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