DEFECT MODES AND HOMOGENIZATION OF PERIODIC SCHRODINGER OPERATORS
DEFECT MODES AND HOMOGENIZATION OF PERIODIC SCHRODINGER OPERATORS
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DOI：
10.1137/100807302
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发表时间：
2011-01-01
影响因子：
2
通讯作者：
Weinstein, M. I.
中科院分区：
文献类型：
--
作者：
Hoefer, M. A.;Weinstein, M. I.
本文考虑算子H-ε = -Delta + V（x）+ ε（2）Q（ε x）的离散本征值，其中V（x）是周期的，Q（y）定域在R-d上，d ≥ 1.当λ> 0且足够小时，离散本征值可以从周期薛定谔算子的谱带边缘分叉（出现）到谱隙中，H-0 = -Delta（x）竖线V（x）。分支的性质取决于齐次化Schrodinger算子L-A，L-Q = -del（y）中心点Adel（y）+ Q（y）.这里，A表示与谱带边缘相关的逆有效质量矩阵，谱带边缘是分叉的位置。
We consider the discrete eigenvalues of the operator H-epsilon = -Delta + V(x) + epsilon(2)Q(epsilon x), where V(x) is periodic and Q(y) is localized on R-d, d >= 1. For epsilon > 0 and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schrodinger operator, H-0 = -Delta(x) vertical bar V(x), into spectral gaps. The nature of the bifurcation depends on the homogenized Schrodinger operator L-A,L-Q = -del(y) center dot A del(y) + Q(y). Here, A denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation.