Criticality in Brownian ensembles

TL;DR

This paper investigates the critical statistical fluctuations in Brownian ensembles, revealing their invariance properties and spectral sensitivity, which are key for understanding intermediate states in spectral perturbations.

Contribution

It introduces the concept of scale-invariant local fluctuations in Brownian ensembles and analyzes their non-stationary behavior along the spectrum.

Findings

Local fluctuations are system-size invariant under specific perturbation scaling.

Critical statistics measures are non-stationary along the spectrum.

Spectral density influences the sensitivity of local fluctuations.

Abstract

The local statistical fluctuations in Brownian ensembles, the intermediate state of perturbation of one classical ensemble by another one, are system-size invariant if the perturbation parameter has the same size-dependence as that of the ensemble averaged local level density. The sensitivity to local spectral density however makes the measures for the critical statistics non-stationary along the spectrum.