M. Hernández-Sánchez, G. Tapia-Labra, J. A. Mendez-Bermudez
{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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|
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