Floquet isospectrality of the zero potential for discrete periodic Schrödinger operators-Reference-Cited by-同舟云学术

Floquet isospectrality of the zero potential for discrete periodic Schrödinger operators

Published:2024-07-01 Issue:7 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Faust Matthew¹^ORCID,Liu Wencai¹^ORCID,Matos Rodrigo²^ORCID,Plute Jenna¹^ORCID,Robinson Jonah¹^ORCID,Tao Yichen¹^ORCID,Tran Ethan¹^ORCID,Zhuang Cindy¹^ORCID

Affiliation:

1. Department of Mathematics, Texas A&M University 1 , College Station, Texas 77843-3368, USA

2. Department of Mathematics, PUC-Rio 2 , 22451-900 Rio de Janeiro, Brazil

Abstract

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.

Funder

National Science Foundation

Ciência sem Fronteiras

College of Arts and Sciences, Texas A and M University

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0201744/20020755/073501_1_5.0201744.pdf

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