非周期量子系统II的谱连续性。1D中的周期近似
Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D
摘要：
在固体物理中，具有收敛谱的周期近似的存在性和构造对于相应的薛定谔算子的谱研究是至关重要的。在即将出版的著作[9]（arXiv：1709.00975）中，这项任务被归结为豪斯多夫拓扑中潜在动力系统的周期近似的存在性和构造。因此，一维系统承认这种近似完全分类在本工作中。此外，明确的结构提供了动力系统定义的原始替换覆盖所有研究的例子，如斐波那契序列或Golay-Rudin-Shapiro序列。一个主要的工具是通过字典上的局部模式拓扑以及描述局部结构的GAP图来描述Hausdorff拓扑。讨论了间隙图中分支点与缺陷的联系。
英文摘要：
The existence and construction of periodic approximations with convergent spectra is crucial in solid state physics for the spectral study of corresponding Schrödinger operators. In a forthcoming work [9] (arXiv:1709.00975) this task was boiled down to the existence and construction of periodic approximations of the underlying dynamical systems in the Hausdorff topology. As a result the one-dimensional systems admitting such approximations are completely classified in the present work. In addition explicit constructions are provided for dynamical systems defined by primitive substitutions covering all studied examples such as the Fibonacci sequence or the Golay-Rudin-Shapiro sequence. One main tool is the description of the Hausdorff topology by the local pattern topology on the dictionaries as well as the GAP-graphs describing the local structure. The connection of branching vertices in the GAP-graphs and defects is discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
