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

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 connectivity α , and the losses-and-gain strength γ . Here, N and α are the standard parameters of ER graphs, while we introduce losses and gain by including complex self-loops on all vertices with the imaginary amplitude i γ 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 fixed ξ , 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.

Statistical similarity between high energy charged particle fluxes in near-earth space and earthquakes

It has long been noticed that rapid short-term variations of high energy charged particle fluxes in near-Earth space occur more frequently several hours before the main shock of earthquakes. Physicists wish that this observation supply a possible precursor of strong earthquakes. Based on DEMETER data, we investigate statistical behaviors of flux fluctuations for high energy charged particles in near-Earth space. Long-term clustering, scaling, and universality in the temporal occurrence are found. There is high degree statistical similarity between high energy charged particle fluxes in near-Earth space and earthquakes. Thus, the observations of the high energy particle fluxes in near-Earth space may supply a useful tool in the study of earthquakes.