离散周期Schrödinger算符的费米等谱性

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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Let <math>\n <semantics>\n <mrow>\n <mi>Δ</mi>\n <mo>+</mo>\n <mi>V</mi>\n </mrow>\n <annotation>$\\Delta +V$</annotation>\n </semantics></math> be the discrete Schrödinger operator, where Δ is the discrete Laplacian on <math>\n <semantics>\n <msup>\n <mi>Z</mi>\n <mi>d</mi>\n </msup>\n <annotation>$\\mathbb {Z}^d$</annotation>\n </semantics></math> and the potential <math>\n <semantics>\n <mrow>\n <mi>V</mi>\n <mo>:</mo>\n <msup>\n <mi>Z</mi>\n <mi>d</mi>\n </msup>\n <mo>→</mo>\n <mi>C</mi>\n </mrow>\n <annotation>$V:\\mathbb {Z}^d\\rightarrow \\mathbb {C}$</annotation>\n </semantics></math> is Γ-periodic. We prove three rigidity theorems for discrete periodic Schrödinger operators in any dimension <math>\n <semantics>\n <mrow>\n <mi>d</mi>\n <mo>≥</mo>\n <mn>3</mn>\n </mrow>\n <annotation>$d\\ge 3$</annotation>\n </semantics></math>: \n\n </p>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2023-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Fermi isospectrality for discrete periodic Schrödinger operators\",\"authors\":\"Wencai Liu\",\"doi\":\"10.1002/cpa.22161\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <math>\\n <semantics>\\n <mrow>\\n <mi>Γ</mi>\\n <mo>=</mo>\\n <msub>\\n <mi>q</mi>\\n <mn>1</mn>\\n </msub>\\n <mi>Z</mi>\\n <mi>⊕</mi>\\n <msub>\\n <mi>q</mi>\\n <mn>2</mn>\\n </msub>\\n <mi>Z</mi>\\n <mi>⊕</mi>\\n <mtext>…</mtext>\\n <mi>⊕</mi>\\n <msub>\\n <mi>q</mi>\\n <mi>d</mi>\\n </msub>\\n <mi>Z</mi>\\n </mrow>\\n <annotation>$\\\\Gamma =q_1\\\\mathbb {Z}\\\\oplus q_2 \\\\mathbb {Z}\\\\oplus \\\\ldots \\\\oplus q_d\\\\mathbb {Z}$</annotation>\\n </semantics></math>, where <math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>q</mi>\\n <mi>l</mi>\\n </msub>\\n <mo>∈</mo>\\n <msub>\\n <mi>Z</mi>\\n <mo>+</mo>\\n </msub>\\n </mrow>\\n <annotation>$q_l\\\\in \\\\mathbb {Z}_+$</annotation>\\n </semantics></math>, <math>\\n <semantics>\\n <mrow>\\n <mi>l</mi>\\n <mo>=</mo>\\n <mn>1</mn>\\n <mo>,</mo>\\n <mn>2</mn>\\n <mo>,</mo>\\n <mtext>…</mtext>\\n <mo>,</mo>\\n <mi>d</mi>\\n </mrow>\\n <annotation>$l=1,2,\\\\ldots ,d$</annotation>\\n </semantics></math>, are pairwise coprime. 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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

ACS Applied Electronic Materials Multiple-

CiteScore

7.20

自引率

4.30%

发文量

567