Spectral properties of a limit-periodic Schrodinger operator in dimension two

被引:8
|
作者
Karpeshina, Yulia [1 ]
Lee, Young-Ran [2 ]
机构
[1] Univ Alabama Birmingham, Dept Math, Birmingham, AL 35294 USA
[2] Sogang Univ, Dept Math, Seoul 121742, South Korea
来源
基金
美国国家科学基金会; 新加坡国家研究基金会;
关键词
DENSITY-OF-STATES; INTEGRATED DENSITY; PERTURBATIONS; EQUATION;
D O I
10.1007/s11854-013-0014-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the Schrodinger operator H = -Delta + V(x) in dimension two, V(x) being a limit-periodic potential. We prove that the spectrum of H contains a semiaxis, and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves exp() at the high energy region. Second, the isoenergetic curves in the space of momenta corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.
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页码:1 / 84
页数:84
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