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

Understand

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.