DELONE MEASURES OF FINITE LOCAL COMPLEXITY AND APPLICATIONS TO SPECTRAL THEORY OF ONE-DIMENSIONAL CONTINUUM MODELS OF QUASICRYSTALS

被引：10

作者：

Klassert, Steffen ^{[1
]}

Lenz, Daniel ^{[2
]}

Stollmann, Peter ^{[1
]}

机构：

[1] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Univ Jena, Math Inst, D-07743 Jena, Germany

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 29卷 / 04期

关键词：

Quasicrystals; Delone sets; absolutely continuous spectrum; SINGULAR CONTINUOUS-SPECTRUM; ABSOLUTELY CONTINUOUS-SPECTRUM; SCHRODINGER-OPERATORS; SPACES; SETS;

D O I：

10.3934/dcds.2011.29.1553

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study measures on the real line and present various versions of what it means for such a measure to take only finitely many values. We then study perturbations of the Laplacian by such measures. Using Kotani-Remling theory, we show that the resulting operators have empty absolutely continuous spectrum if the measures are not periodic. When combined with Gordon type arguments this allows us to prove purely singular continuous spectrum for some continuum models of quasicrystals.

引用

页码：1553 / 1571

页数：19

共 39 条

[1]

[Anonymous], CRM MONOGRAPH SERIES

[2]

[Anonymous], 1990, PROBABILITY ITS APPL

[3] Deformation of delone dynamieal systems and pure point diffraction [J].