Non-Hermitian Random Matrix Theory of Jamming in Active Disordered Media
arXiv:2607.26406
The paper develops a theoretical framework for the mechanics of active jammed systems using non‑Hermitian random matrix theory, deriving scaling laws for mechanical compliance and identifying crossover regimes between perturbative and activity‑dominated behavior.
Abstract
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.
24 pages, 4 figures