Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties

Abstract

We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta =x^{\ast }/(1+x^{\ast })$. The scaling parameter of the model is defined as $x^{\ast }\propto (b_{eff}^2/N{)}^{\delta }$, where $b_{eff}$ is the average number of non-zero elements per matrix row, $N$ is the matrix size, and $\delta \sim 1$. Additionally, we show that $x^{\ast }$ also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues.

6 pages, 3 figures. arXiv admin note: text overlap with arXiv:1611.06695

References in corpus (4)

• Anderson Transitions
• Universality in the spectral and eigenfunction properties of random networks
• Scaling Properties of Multilayer Random Networks
• Genuine localisation transition in a long-range hopping model

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