Fermi isospectrality for discrete periodic Schrödinger operators

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2023-09-10 DOI:10.1002/cpa.22161

Wencai Liu

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引用次数: 9

Abstract

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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离散周期Schrödinger算符的费米等谱性

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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