Approximations of Symbolic Substitution Systems in One Dimension

IF 2.3 4区 化学 Q3 CHEMISTRY, MULTIDISCIPLINARY
Lior Tenenbaum
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引用次数: 0

Abstract

Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schrödinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra approximate the spectrum of the limiting operator (of the quasicrystal). This naturally leads to study the convergence of the underlying dynamical systems. We treat dynamical systems which are based on one‐dimensional substitutions. We first find natural candidates of dynamical subsystems to approximate the substitution dynamical system. Subsequently, we offer a characterization of their convergence and provide estimates for the rate of convergence. We apply the proposed theory to some guiding examples.

Abstract Image

一维符号替换系统的近似值
根据已知的周期晶体理论,准晶体的周期近似是分析由准晶体产生的薛定谔算子谱的有力工具。也就是说,我们要寻找其频谱近似于(准晶体的)极限算子频谱的周期算子。这自然会引出对底层动力系统收敛性的研究。我们处理基于一维置换的动力系统。我们首先找到了近似置换动力系统的自然候选动力子系统。随后,我们对它们的收敛性进行了描述,并提供了收敛速率的估计值。我们将提出的理论应用于一些指导性实例。
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来源期刊
Israel Journal of Chemistry
Israel Journal of Chemistry 化学-化学综合
CiteScore
6.20
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: The fledgling State of Israel began to publish its scientific activity in 1951 under the general heading of Bulletin of the Research Council of Israel, which quickly split into sections to accommodate various fields in the growing academic community. In 1963, the Bulletin ceased publication and independent journals were born, with Section A becoming the new Israel Journal of Chemistry. The Israel Journal of Chemistry is the official journal of the Israel Chemical Society. Effective from Volume 50 (2010) it is published by Wiley-VCH. The Israel Journal of Chemistry is an international and peer-reviewed publication forum for Special Issues on timely research topics in all fields of chemistry: from biochemistry through organic and inorganic chemistry to polymer, physical and theoretical chemistry, including all interdisciplinary topics. Each topical issue is edited by one or several Guest Editors and primarily contains invited Review articles. Communications and Full Papers may be published occasionally, if they fit with the quality standards of the journal. The publication language is English and the journal is published twelve times a year.
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