Spectral and scattering theory for Schrödinger operators on perturbed topological crystals
Spectral and scattering theory for Schrödinger operators on perturbed topological crystals
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扰动拓扑晶体薛定谔算子的光谱和散射理论
DOI：
10.1142/s0129055x18500095
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发表时间：
2016
影响因子：
1.8
通讯作者：
S. Richard
中科院分区：
文献类型：
--
作者：
D. Parra;S. Richard
本文研究了扰动周期离散图上薛定谔算子的谱和散射理论。考虑的扰动有两种类型：无论是一个乘法算子的短程或长程功能，或短程型修改的顶点和边缘上的图定义的措施。谱理论用于描述基本算子的谱的性质。对于短程扰动，也证明了局域波算子的存在性和渐近完备性。
In this paper, we investigate the spectral and the scattering theory of Schrodinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or a long-range function, or a short-range type modification of the measure defined on the vertices and on the edges of the graph. Mourre theory is used for describing the nature of the spectrum of the underlying operators. For short-range perturbations, existence and asymptotic completeness of local wave operators are also proved.
反演问题、离散 Schrodenger 算子的迹公式
DOI：
--
发表时间：
2012
期刊：
Ann. Henri Poincare
影响因子：
--
作者：
Kazufumi Kimoto;Sho Matsumoto and Masato Wakayama;T. Ikeda;近藤武夫・中邑賢龍;H.Nakamura;H. isozaki and E. Korotyaev
通讯作者：
H. isozaki and E. Korotyaev