AI 中文总结
该研究基于非厄米随机矩阵理论，构建活性阻塞系统力学的理论框架，通过推导自洽方程揭示活性非互易性正则化软模发散，得到力学柔量标度律及活性阻塞点附近的标度形式。
AI 中文摘要
我们基于非厄米随机矩阵理论，构建了活性阻塞系统力学的理论框架。从具有非互易相互作用的活性粒子微观模型出发，我们将线性化动力学矩阵表述为描述被动接触网络的Wishart系综的非厄米微扰。利用Girko的厄米化方法结合自洽玻恩近似，我们基于完整的Marchenko–Pastur分布推导了低频预解式的自洽方程。我们表明，活性非互易性会正则化阻塞相变处的软模发散，得到力学柔量的标度律；还建立了微扰区与活性主导区之间的交叉，提出了活性阻塞点附近对应的标度形式。
英文摘要
We develop a theoretical framework for the mechanics of active jammed systems based on non-Hermitian random matrix theory. Starting from a microscopic model of active particles with non-reciprocal interactions, we formulate the linearized dynamical matrix as a non-Hermitian perturbation of a Wishart ensemble describing the passive contact network. Using Girko's Hermitization together with the self-consistent Born approximation, we derive a self-consistent equation for the low-frequency resolvent based on the full Marchenko--Pastur distribution. We show that active non-reciprocity regularizes the soft-mode divergence at the jamming transition, leading to a scaling law for the mechanical compliance. We further establish a crossover between perturbative and activity-dominated regimes and propose a corresponding scaling form near the active jamming point.
Comments24 pages, 4 figures
