Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality

Entropy

C.T. Martínez-Martínez¹  J.A. Méndez-Bermúdez¹ 

[1] Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico;

关键词: information entropy;    Erdős–Rényi graphs;    random matrix theory;    scaling laws;   

DOI  :  10.3390/e21010086

来源: DOAJ

【 摘 要 】

We study the localization properties of the eigenvectors, characterized by their information entropy, of tight-binding random networks with balanced losses and gain. The random network model, which is based on Erdős–Rényi (ER) graphs, is defined by three parameters: the network size N, the network connectivityα , and the losses-and-gain strengthγ . Here, N andαare the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude iγ with random balanced signs, thus breaking the Hermiticity of the corresponding adjacency matrices and inducing complex spectra. By the use of extensive numerical simulations, we define a scaling parameter ξ ≡ ξ ( N , α , γ ) that fixes the localization properties of the eigenvectors of our random network model; such that, when ξ < 0.1 (10 < ξ), the eigenvectors are localized (extended), while the localization-to-delocalization transition occurs for 0.1 < ξ < 10. Moreover, to extend the applicability of our findings, we demonstrate that for fixedξ , the spectral properties (characterized by the position of the eigenvalues on the complex plane) of our network model are also universal; i.e., they do not depend on the specific values of the network parameters.

【 授权许可】

Unknown