Relating diffraction and spectral data of aperiodic tilings: Towards a Bloch theorem

被引：6

作者：

Akkermans, Eric ^{[1
]}

Don, Yaroslav ^{[1
]}

Rosenberg, Jonathan ^{[2
]}

Schochet, Claude L. ^{[3
]}

机构：

[1] Technion, Dept Phys, IL-3200003 Haifa, Israel

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[3] Technion, Dept Math, IL-3200003 Haifa, Israel

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2021年 / 165卷

基金：

以色列科学基金会;

关键词：

Bloch theorem; tiling; diffraction spectrum; Cech cohomology; K-theory for C*-algebras; Gap labeling; ROTATION NUMBER; TOPOLOGICAL INVARIANTS; DYNAMICAL-SYSTEMS; INTEGER GROUP; GAP; OPERATORS; COHOMOLOGY; ELECTRONS; ALGEBRAS; CURRENTS;

D O I：

10.1016/j.geomphys.2021.104217

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by Cech cohomology of the tiling space) and the spectral properties (of Hamiltonians defined on such tilings) defined by K-theory, and to show their equivalence in dimensions <= 3. A theorem makes precise the conditions for this relationship to hold. It can be viewed as an extension of the "Bloch Theorem" to a large class of aperiodic tilings. The idea underlying this result is based on the relationship between cohomology and K-theory traces and their equivalence in low dimensions. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：23

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