非ermitian稀释带状随机矩阵：特征函数的缩放和频谱特性

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-05-21 DOI:arxiv-2406.15426

M. Hernández-Sánchez, G. Tapia-Labra, J. A. Mendez-Bermudez

{"title":"非ermitian稀释带状随机矩阵：特征函数的缩放和频谱特性","authors":"M. Hernández-Sánchez, G. Tapia-Labra, J. A. Mendez-Bermudez","doi":"arxiv-2406.15426","DOIUrl":null,"url":null,"abstract":"Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM)\nensemble as the set of $N\\times N$ real non-symmetric matrices whose entries\nare independent Gaussian random variables with zero mean and variance one if\n$|i-j|<b$ and zero otherwise, moreover off-diagonal matrix elements within the\nbandwidth $b$ are randomly set to zero such that the sparsity $\\alpha$ is\ndefined as the fraction of the $N(b-1)/2$ independent non-vanishing\noff-diagonal matrix elements. By means of a detailed numerical study we\ndemonstrate that the eigenfunction and spectral properties of the nHdBRM\nensemble scale with the parameter $x=\\gamma[(b\\alpha)^2/N]^\\delta$, where\n$\\gamma,\\delta\\sim 1$. Moreover, the normalized localization length $\\beta$ of\nthe eigenfunctions follows a simple scaling law: $\\beta = x/(1 + x)$. For\ncomparison purposes, we also report eigenfunction and spectral properties of\nthe Hermitian diluted banded random matrix ensemble.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties\",\"authors\":\"M. Hernández-Sánchez, G. Tapia-Labra, J. A. Mendez-Bermudez\",\"doi\":\"arxiv-2406.15426\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM)\\nensemble as the set of $N\\\\times N$ real non-symmetric matrices whose entries\\nare independent Gaussian random variables with zero mean and variance one if\\n$|i-j|<b$ and zero otherwise, moreover off-diagonal matrix elements within the\\nbandwidth $b$ are randomly set to zero such that the sparsity $\\\\alpha$ is\\ndefined as the fraction of the $N(b-1)/2$ independent non-vanishing\\noff-diagonal matrix elements. By means of a detailed numerical study we\\ndemonstrate that the eigenfunction and spectral properties of the nHdBRM\\nensemble scale with the parameter $x=\\\\gamma[(b\\\\alpha)^2/N]^\\\\delta$, where\\n$\\\\gamma,\\\\delta\\\\sim 1$. Moreover, the normalized localization length $\\\\beta$ of\\nthe eigenfunctions follows a simple scaling law: $\\\\beta = x/(1 + x)$. For\\ncomparison purposes, we also report eigenfunction and spectral properties of\\nthe Hermitian diluted banded random matrix ensemble.\",\"PeriodicalId\":501066,\"journal\":{\"name\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-21\",\"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-2406.15426\",\"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-2406.15426","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

在此，我们将非ermitian稀释带状随机矩阵（nHdBRM）集合定义为：如果$|i-j|本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties

Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of $N\times N$ real non-symmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if $|i-j|

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

arXiv - PHYS - Disordered Systems and Neural Networks

自引率

0.00%

发文量