计算磁薛定谔算子特征对的典型量纲

Jeffrey S. Ovall, Li Zhu
{"title":"计算磁薛定谔算子特征对的典型量纲","authors":"Jeffrey S. Ovall, Li Zhu","doi":"arxiv-2409.06023","DOIUrl":null,"url":null,"abstract":"We consider the eigenvalue problem for the magnetic Schr\\\"odinger operator\nand take advantage of a property called gauge invariance to transform the given\nproblem into an equivalent problem that is more amenable to numerical\napproximation. More specifically, we propose a canonical magnetic gauge that\ncan be computed by solving a Poisson problem, that yields a new operator having\nthe same spectrum but eigenvectors that are less oscillatory. Extensive\nnumerical tests demonstrate that accurate computation of eigenpairs can be done\nmore efficiently and stably with the canonical magnetic gauge.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Canonical Gauge for Computing of Eigenpairs of the Magnetic Schrödinger Operator\",\"authors\":\"Jeffrey S. Ovall, Li Zhu\",\"doi\":\"arxiv-2409.06023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the eigenvalue problem for the magnetic Schr\\\\\\\"odinger operator\\nand take advantage of a property called gauge invariance to transform the given\\nproblem into an equivalent problem that is more amenable to numerical\\napproximation. More specifically, we propose a canonical magnetic gauge that\\ncan be computed by solving a Poisson problem, that yields a new operator having\\nthe same spectrum but eigenvectors that are less oscillatory. Extensive\\nnumerical tests demonstrate that accurate computation of eigenpairs can be done\\nmore efficiently and stably with the canonical magnetic gauge.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06023\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

我们考虑了磁性薛定谔算子的特征值问题,并利用一种称为量规不变性的性质,将给定的问题转化为一个更适于数值逼近的等效问题。更具体地说,我们提出了一个可以通过求解泊松问题来计算的典型磁规,它产生了一个具有相同频谱但特征向量振荡较小的新算子。广泛的数值测试表明,使用规范磁规可以更高效、更稳定地计算特征对。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
A Canonical Gauge for Computing of Eigenpairs of the Magnetic Schrödinger Operator
We consider the eigenvalue problem for the magnetic Schr\"odinger operator and take advantage of a property called gauge invariance to transform the given problem into an equivalent problem that is more amenable to numerical approximation. More specifically, we propose a canonical magnetic gauge that can be computed by solving a Poisson problem, that yields a new operator having the same spectrum but eigenvectors that are less oscillatory. Extensive numerical tests demonstrate that accurate computation of eigenpairs can be done more efficiently and stably with the canonical magnetic gauge.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
A Lightweight, Geometrically Flexible Fast Algorithm for the Evaluation of Layer and Volume Potentials Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations Conditions aux limites fortement non lin{é}aires pour les {é}quations d'Euler de la dynamique des gaz Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals A novel Mortar Method Integration using Radial Basis Functions
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1