Universal distributions from non-Hermitian Perturbation of Zero-Modes

TL;DR

This paper studies how zero modes of Hermitian operators are affected by non-Hermitian perturbations, revealing a universal elliptic Gaussian distribution governed by symmetry class and robust to deformations.

Contribution

It introduces a universal distribution model for zero-mode broadening under non-Hermitian perturbations, based on a central limit theorem for matrices.

Findings

Zero modes follow an elliptic Gaussian distribution.

Distribution depends on the symmetry class of perturbation.

Distribution is robust to deformations of the average.

Abstract

Hermitian operators with exact zero modes subject to non-Hermitian perturbations are considered. Specific focus is on the average distribution of the initial zero modes of the Hermitian operators. The broadening of these zero modes is found to follow an elliptic Gaussian random matrix ensemble of fixed size, where the symmetry class of the perturbation determines the behaviour of the modes. This distribution follows from a central limit theorem of matrices, and is shown to be robust to deformations of the average.