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

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.

5 pages, 3 figures

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• Front dynamics and entanglement in the XXZ chain with a gradient
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• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
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• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"