离散周期薛定谔算子零势的 Floquet 等谱性

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-07-01 DOI:10.1063/5.0201744

Matthew Faust, Wencai Liu, Rodrigo Matos, Jenna Plute, Jonah Robinson, Yichen Tao, Ethan Tran, Cindy Zhuang

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引用次数: 0

摘要

设Γ=q1Z⊕q2Z⊕⋯⊕qdZ，其中 qj∈Z+ 表示每个 j∈ {1, ..., d}，并用 Δ 表示 ℓ2Zd 上的离散拉普拉斯函数。利用 Macaulay2，我们首先从数值上找到复值Γ周期势 V:Zd→C，使得算子 Δ + V 和 Δ 是 Floquet 等谱的。然后，我们使用组合方法来验证这些数值解。

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Floquet isospectrality of the zero potential for discrete periodic Schrödinger operators

Let Γ=q1Z⊕q2Z⊕⋯⊕qdZ, with qj∈Z+ for each j ∈ {1, …, d}, and denote by Δ the discrete Laplacian on ℓ2Zd. Using Macaulay2, we first numerically find complex-valued Γ-periodic potentials V:Zd→C such that the operators Δ + V and Δ are Floquet isospectral. We then use combinatorial methods to validate these numerical solutions.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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