Renormalization techniques for inflation systems and some of their applications.

IF 2.1 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2026-07-01 Epub Date: 2026-05-26 DOI:10.1107/S2053273326003918

Michael Baake, Franz Gähler, Anna Klick, Neil Mañibo, Jan Mazáč

引用次数: 0

Abstract

Exact renormalization techniques are important and powerful, particularly for inflation-generated systems. We review recent results in this direction. We recall the necessary notions for inflation systems and show the renormalization principle, which allows us to obtain exact values of highly erratic functions, such as window covariograms. We apply these techniques to compute the diffraction pattern of the new monotile tilings with arbitrary precision. We also recall a recent invariant for a system with pure-point spectrum, the orbit separation dimension, and its relation to renormalization. Lastly, we recall results beyond the pure-point spectrum setting and show how renormalization and Lyapunov exponents can be used to exclude the presence of absolutely continuous parts of the spectra.

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膨胀系统的重整化技术及其一些应用。

精确的重整化技术是重要和强大的，特别是对于膨胀生成的系统。我们回顾了这方面的最新成果。我们回顾了膨胀系统的必要概念，并展示了重整化原理，它允许我们获得高度不稳定函数的精确值，例如窗口协方差。我们应用这些技术以任意精度计算了新的单片瓷砖的衍射图样。我们还回顾了最近的一个具有纯点谱的系统的不变量，轨道分离维数，以及它与重整化的关系。最后，我们回顾了纯点光谱设置之外的结果，并展示了如何使用重整化和李雅普诺夫指数来排除光谱中绝对连续部分的存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.