离散周期Schrödinger算符的费米等谱性

IF 3.1 1区数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2023-09-10 DOI:10.1002/cpa.22161

Wencai Liu

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引用次数: 9

摘要

让 Γ = q 1 Z ⊕ q 2 Z ⊕ ... ⊕ q d Z $Gamma =q_1\mathbb {Z}\oplus q_2 \mathbb {Z}\oplus \ldots \oplus q_d\mathbb {Z}$ ，其中 q l∈ Z + $q_l\in \mathbb {Z}_+$ , l = 1 , 2 , ... , d $l=1,2,\ldots ,d$ , 是成对的共素数。让 Δ + V $\Delta +V$ 是离散薛定谔算子，其中 Δ 是 Z d $\mathbb {Z}^d$ 上的离散拉普拉奇，势 V : Z d → C $V:\mathbb {Z}^d\rightarrow \mathbb {C}$ 是Γ周期的。我们证明了离散周期薛定谔算子在任意维度 d ≥ 3 $d\ge 3$ 的三个刚度定理：

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Fermi isospectrality for discrete periodic Schrödinger operators

Let $Γ = q_{1} Z \oplus q_{2} Z \oplus … \oplus q_{d} Z$ , where $q_{l} \in Z_{+}$ , $l = 1, 2, …, d$ , are pairwise coprime. Let $Δ + V$ be the discrete Schrödinger operator, where Δ is the discrete Laplacian on $Z^{d}$ and the potential $V : Z^{d} \to C$ is Γ-periodic. We prove three rigidity theorems for discrete periodic Schrödinger operators in any dimension $d \geq 3$ :

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.