论文标题
2D晶格中连续体中的离散嵌入式模式
Discrete embedded modes in the continuum in 2D lattices
论文作者
论文摘要
我们使用潜在的工程方法和冯·诺伊曼（Von Neumann）研究了方形晶格的准孔子带内构建散装和表面嵌入式模式（EMS）的问题。基于一维（1D）晶格的先前结果，并利用可分离性，我们产生了二维包络函数的示例以及产生它们的二维（2D）电位。 2D嵌入式模式像伸展指数一样衰减，具有作为权力定律的支撑潜力。可分离性过程可能会导致1D杂质状态（在1D频段之外）会产生2D嵌入式模式（在频段内）。嵌入式模式可以添加潜力的随机扰动。但是，此过程引入了频段内的其他局部模式，并引起了扰动模式定位的一般趋势。
We study the problem of constructing bulk and surface embedded modes (EMs) inside the quasi-continuum band of a square lattice, using a potential engineering approach à la Wigner and von Neumann. Building on previous results for the one-dimensional (1D) lattice, and making use of separability, we produce examples of two-dimensional envelope functions and the two-dimensional (2D) potentials that produce them. The 2D embedded mode decays like a stretched exponential, with a supporting potential that decays as a power law. The separability process can cause that a 1D impurity state (outside the 1D band) can give rise to a 2D embedded mode (inside the band). The embedded mode survives the addition of random perturbations of the potential; however, this process introduces other localized modes inside the band, and causes a general tendency towards localization of the perturbed modes.
