This website requires JavaScript.

Spectral and Combinatorial Aspects of Cayley-Crystals

Fabian R. LuxEmil Prodan
Dec 2022
摘要
Owing to their interesting spectral properties, the synthetic crystals overlattices other than regular Euclidean lattices, such as hyperbolic and fractalones, have attracted renewed attention, especially from materials andmeta-materials research communities. They can be studied under the umbrella ofquantum dynamics over Cayley graphs of finitely generated groups. In this work,we investigate numerical aspects related to the quantum dynamics over suchCayley graphs. Using an algebraic formulation of the "periodic boundarycondition" due to Lueck [Geom. Funct. Anal. 4, 455-481 (1994)], we devise apractical and converging numerical method that resolves the true bulk spectrumof the Hamiltonians. Exact results on the matrix elements of the resolvent,derived from the combinatorics of the Cayley graphs, give us the means tovalidate our algorithms and also to obtain new combinatorial statements. Ourresults open the systematic research of quantum dynamics over Cayley graphs ofa very large family of finitely generated groups, which includes the free andFuchsian groups.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答