标题： 沿无限扩展扰动的量子晶格输运 显示英文标题

标题： Quantum lattice transport along an infinitely extended perturbation

摘要： 我们考虑一个周期性量子图，其形式为矩形晶格，在顶点处具有强度为$\gamma$的$\delta$耦合，该顶点被扰动，将无限直线顶点数组中的后者改变为$\widetilde\gamma\ne\gamma$。 我们分析系统的带状谱，并证明当$\widetilde\gamma>\gamma>0$时，它作为集合保持不变，而对于其他所有组合，在未扰动系统的某些或所有间隙中会出现额外的带。 我们还证明，对于随机选择的正能，扰动附近存在指数局域态的概率等于$\frac12$。 显示英文摘要

摘要： We consider a periodic quantum graph in the form of a rectangular lattice with the $\delta$-coupling of strength $\gamma$ in the vertices perturbed by changing the latter at an infinite straight array of vertices to a $\widetilde\gamma\ne\gamma$. We analyze the band spectrum of the system and show that it remains preserved as a set provided $\widetilde\gamma>\gamma>0$ while for all the other combinations additional band appear in some or all gaps of the unperturbed system. We also prove that for a randomly chosen positive energy, the probability of existence of a state exponentially localized in the vicinity of the perturbation equals $\frac12$.