一维非互惠准晶体中 Lyapunov 指数的非对称传递矩阵分析

Shan-Zhong Li, Enhong Cheng, Shi-Liang Zhu, Zhi Li
{"title":"一维非互惠准晶体中 Lyapunov 指数的非对称传递矩阵分析","authors":"Shan-Zhong Li, Enhong Cheng, Shi-Liang Zhu, Zhi Li","doi":"arxiv-2407.01372","DOIUrl":null,"url":null,"abstract":"The Lyapunov exponent, serving as an indicator of the localized state, is\ncommonly utilized to identify localization transitions in disordered systems.\nIn non-Hermitian quasicrystals, the non-Hermitian effect induced by\nnon-reciprocal hopping can lead to the manifestation of two distinct Lyapunov\nexponents on opposite sides of the localization center. Building on this\nobservation, we here introduce a comprehensive approach for examining the\nlocalization characteristics and mobility edges of non-reciprocal\nquasicrystals, referred to as asymmetric transfer matrix analysis. We\ndemonstrate the application of this method to three specific scenarios: the\nnon-reciprocal Aubry-Andr\\'e model, the non-reciprocal off-diagonal\nAubry-Andr\\'e model, and the non-reciprocal mosaic quasicrystals. This work may\ncontribute valuable insights to the investigation of non-Hermitian quasicrystal\nand disordered systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"57 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals\",\"authors\":\"Shan-Zhong Li, Enhong Cheng, Shi-Liang Zhu, Zhi Li\",\"doi\":\"arxiv-2407.01372\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Lyapunov exponent, serving as an indicator of the localized state, is\\ncommonly utilized to identify localization transitions in disordered systems.\\nIn non-Hermitian quasicrystals, the non-Hermitian effect induced by\\nnon-reciprocal hopping can lead to the manifestation of two distinct Lyapunov\\nexponents on opposite sides of the localization center. Building on this\\nobservation, we here introduce a comprehensive approach for examining the\\nlocalization characteristics and mobility edges of non-reciprocal\\nquasicrystals, referred to as asymmetric transfer matrix analysis. We\\ndemonstrate the application of this method to three specific scenarios: the\\nnon-reciprocal Aubry-Andr\\\\'e model, the non-reciprocal off-diagonal\\nAubry-Andr\\\\'e model, and the non-reciprocal mosaic quasicrystals. This work may\\ncontribute valuable insights to the investigation of non-Hermitian quasicrystal\\nand disordered systems.\",\"PeriodicalId\":501066,\"journal\":{\"name\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"volume\":\"57 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.01372\",\"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 - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.01372","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

在非对等准晶体中,非对等跳跃引起的非对等效应会导致在局部化中心的两侧出现两个不同的李亚普诺夫指数。基于这一观察结果,我们在此引入了一种全面的方法来研究非互易质子晶体的定位特性和迁移率边缘,即非对称传递矩阵分析。我们演示了这种方法在三种特定情况下的应用:对等奥布里-安德罗模型、非对等非对角奥布里-安德罗模型和非对等镶嵌准晶体。这项工作可能为研究非对角准晶和无序系统提供有价值的见解。
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
Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal hopping can lead to the manifestation of two distinct Lyapunov exponents on opposite sides of the localization center. Building on this observation, we here introduce a comprehensive approach for examining the localization characteristics and mobility edges of non-reciprocal quasicrystals, referred to as asymmetric transfer matrix analysis. We demonstrate the application of this method to three specific scenarios: the non-reciprocal Aubry-Andr\'e model, the non-reciprocal off-diagonal Aubry-Andr\'e model, and the non-reciprocal mosaic quasicrystals. This work may contribute valuable insights to the investigation of non-Hermitian quasicrystal and disordered systems.
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
Fast Analysis of the OpenAI O1-Preview Model in Solving Random K-SAT Problem: Does the LLM Solve the Problem Itself or Call an External SAT Solver? Trade-off relations between quantum coherence and measure of many-body localization Soft modes in vector spin glass models on sparse random graphs Boolean mean field spin glass model: rigorous results Generalized hetero-associative neural networks
×
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