M Hernández-Sánchez, G Tapia-Labra, J A Méndez-Bermúdez
{"title":"Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties.","authors":"M Hernández-Sánchez, G Tapia-Labra, J A Méndez-Bermúdez","doi":"10.1103/PhysRevE.110.044124","DOIUrl":null,"url":null,"abstract":"<p><p>Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of N×N real nonsymmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if |i-j|<b and zero otherwise, moreover off-diagonal matrix elements within the bandwidth b are randomly set to zero such that the sparsity α is defined as the fraction of the N(b-1)/2 independent nonvanishing off-diagonal matrix elements. By means of a detailed numerical study we demonstrate that the eigenfunction and spectral properties of the nHdBRM ensemble scale with the parameter x=γ[(bα)^{2}/N]^{δ}, where γ,δ∼1. Moreover, the normalized localization length β of the eigenfunctions follows a simple scaling law: β=x/(1+x). For comparison purposes, we also report eigenfunction and spectral properties of the Hermitian diluted banded random matrix ensemble.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"110 4-1","pages":"044124"},"PeriodicalIF":2.2000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.044124","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","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×N real nonsymmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if |i-j|
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.