Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
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离散周期薛定谔算子和嵌入特征值的费米簇的不可约性
DOI：
10.1007/s00039-021-00587-z
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发表时间：
2022
影响因子：
2.2
通讯作者：
Liu, Wencai
中科院分区：
文献类型：
--
作者：
Liu, Wencai
Letbe a discrete periodic Schrödinger operator on: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H_0=-\Delta +V, \end{aligned}$$\end{document}whereis the discrete Laplacian andis periodic. We prove that for any, the Fermi variety at every energy level is irreducible (modulo periodicity). For, we prove that the Fermi variety at every energy level except for the average of the potential is irreducible (modulo periodicity) and the Fermi variety at the average of the potential has at most two irreducible components (modulo periodicity). This is sharp since forand a constant potentialV, the Fermi variety atV-level has exactly two irreducible components (modulo periodicity). We also prove that the Bloch variety is irreducible (modulo periodicity) for any. As applications, we prove that whenVis a real-valued periodic function, the level set of any extrema of any spectral band functions, spectral band edges in particular, has dimension at mostfor any, and finite cardinality for. We also show thatdoes not have any embedded eigenvalues provided thatvdecays super-exponentially
Letbe a discrete periodic Schrödinger operator on: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H_0=-\Delta +V, \end{aligned}$$\end{document}whereis the discrete Laplacian andis periodic. We prove that for any, the Fermi variety at every energy level is irreducible (modulo periodicity). For, we prove that the Fermi variety at every energy level except for the average of the potential is irreducible (modulo periodicity) and the Fermi variety at the average of the potential has at most two irreducible components (modulo periodicity). This is sharp since forand a constant potentialV, the Fermi variety atV-level has exactly two irreducible components (modulo periodicity). We also prove that the Bloch variety is irreducible (modulo periodicity) for any. As applications, we prove that whenVis a real-valued periodic function, the level set of any extrema of any spectral band functions, spectral band edges in particular, has dimension at mostfor any, and finite cardinality for. We also show thatdoes not have any embedded eigenvalues provided thatvdecays super-exponentially
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DOI：
10.1080/03605302.2014.978015
发表时间：
2014-04
影响因子：
1.9
作者：
C. Kenig;L. Silvestre;Jenn-Nan Wang
通讯作者：
C. Kenig;L. Silvestre;Jenn-Nan Wang
具有维格纳-冯·诺依曼势的周期性薛定谔算子的谱密度零点
影响因子：
0.8
作者：
S. Naboko;S. Simonov
通讯作者：
S. Simonov
周期性势的维格纳-冯·诺依曼扰动：带中的光谱奇点
影响因子：
0.8
作者：
P. Kurasov;S. Naboko
通讯作者：
S. Naboko
关于离散周期算子的谱带
影响因子：
2.4
作者：
N. Filonov;I. Kachkovskiy
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I. Kachkovskiy
离散贝特-索末菲猜想
DOI：
--
发表时间：
2017
期刊：
影响因子：
--
作者：
R. Han;S. Jitomirskaya
通讯作者：
S. Jitomirskaya