二维周期结构中波导束缚态的缺失
谱理论
2015-03-19 v4 数学物理
math.MP
摘要
我们在由完全周期背景结构和线缺陷形式扰动组成的二维介质中研究 Helmholtz 型谱问题。该缺陷沿一条坐标轴排列，在该方向上具有周期性（与背景周期相同），并在另一方向上有界。该设定模拟了所谓的“软壁”波导问题。我们证明不存在束缚态，即所研究算子的谱不包含点谱。
关键词
引用
@article{arxiv.1111.4578,
title = {Absence of bound states for waveguides in 2D periodic structures},
author = {Vu Hoang and Maria Radosz},
journal= {arXiv preprint arXiv:1111.4578},
year = {2015}
}
备注
This is an updated version of our paper (in slightly different form in Journal of Mathematical Physics). An anonymous reviewer kindly made us aware that ref. 10 is not applicable in our situation. An application of the theorem in ref. 10 would have proved the absence of singular continuous spectrum also. Our result on the absence of point spectrum is not affected by this