Green's function as a defect state in a boundary value problem
Green's function as a defect state in a boundary value problem
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DOI：
10.1103/physrevb.103.195142
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发表时间：
2021-02
影响因子：
3.7
通讯作者：
J. H. Rivero;L. Ge
中科院分区：
文献类型：
--
作者：
J. H. Rivero;L. Ge
引入了边值问题中格林函数作为辅助公式中唯一特征态的新观点。在这种处理中，格林函数可以被视为存在δ函数势的缺陷状态，δ函数势的高度取决于格林函数本身。这种方法在一维和二维亥姆霍兹方程问题中得到了说明，重点是开放和具有非厄米势的系统。然后，我们将以这种方式获得的格林函数与绕过拓扑晶格缺陷的手性边缘状态进行类比，从而揭示了格林函数在源位置的局部最小值。
A new perspective of the Green’s function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green’s function can be perceived as a defect state in the presence of a δ-function potential, the height of which depends on the Green’s function itself. This approach is illustrated in one-dimensional and two-dimensional Helmholtz equation problems, with an emphasis on systems that are open and have a non-Hermitian potential. We then draw an analogy between the Green’s function obtained this way and a chiral edge state circumventing a defect in a topological lattice, which shines light on the local minimum of the Green’s function at the source position.