标题： 对雷蒙德著作的综述：强耦合常数下的Sturmian哈密顿量——周期逼近与间隙标签 显示英文标题

标题： A review of a work by Raymond: Sturmian Hamiltonians with a large coupling constant -- periodic approximations and gap labels

摘要： 我们回顾L. Raymond于1995年的研究。 本次回顾旨在使这项工作更易理解，并提供了某些陈述和证明的改编版本。 此外，本回顾为完全解决R. Band、S. Beckus和R. Loewy在论文arXiv:2402.16703中提出的Sturmian哈密顿量的Dry Ten Martini问题提供了适用的框架。 一个Sturmian哈密顿量是一个一维Schrödinger算子，其势能是一个Sturmian序列乘以一个耦合常数，$V\in\mathbb{R}$。 这种算子的谱通常通过指定周期算子的谱来近似。 如果$V>4$，则周期算子的谱带表现出一种特定的组合结构。 这种结构提供了一个积分态密度的公式。 利用这一点，可以证明如果$V>4$，则所有由间隙标记定理预测的间隙都存在。 显示英文摘要

摘要： We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an applicable framework for the complete solution of the Dry Ten Martini Problem for Sturmian Hamiltonians as appears in the work arXiv:2402.16703 by R. Band, S. Beckus and R. Loewy. A Sturmian Hamiltonian is a one-dimensional Schr\"odinger operator whose potential is a Sturmian sequence multiplied by a coupling constant, $V\in\mathbb{R}$. The spectrum of such an operator is commonly approximated by the spectra of designated periodic operators. If $V>4$, then the spectral bands of the periodic operators exhibit a particular combinatorial structure. This structure provides a formula for the integrated density of states. Employing this, it is shown that if $V>4$, then all the gaps, as predicted by the gap labelling theorem, are there.