Full counting statistics in a propagating quantum front and random matrix spectra

TL;DR

This paper establishes an exact correspondence between the full counting statistics of particles in a quantum front of free fermions and the eigenvalue statistics of Gaussian unitary ensemble matrices, revealing insights into particle distribution and spreading.

Contribution

It introduces a novel connection between quantum particle counting statistics and random matrix eigenvalue distributions, providing exact results for the edge behavior of propagating fermionic fronts.

Findings

Full counting statistics matches GUE edge eigenvalue distribution.

Eigenvalue statistics determine particle position order statistics.

Particles exhibit subdiffusive spreading at the front edge.

Abstract

One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that the full counting statistics coincides with the eigenvalue statistics of the edge spectrum of matrices from the Gaussian unitary ensemble. The correspondence established between the random matrix eigenvalues and the particle positions yields the order statistics of the right-most particles in the front and, furthermore, it implies their subdiffusive spreading.