Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Hernández-Sánchez, M. Tapia-Labra, G. Mendez-Bermudez, J. A. |
| author_facet | Hernández-Sánchez, M. Tapia-Labra, G. Mendez-Bermudez, J. A. |
| contents | 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 $|i-j|<b$ 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 non-vanishing 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 $γ,δ\sim 1$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties Hernández-Sánchez, M. Tapia-Labra, G. Mendez-Bermudez, J. A. Disordered Systems and Neural Networks 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 $|i-j|<b$ 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 non-vanishing 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 $γ,δ\sim 1$. 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. |
| title | Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2406.15426 |