Scattering approach to counting statistics in quantum pumps

We consider the Fermi gas in a nonequilibrium state obtained by applying an arbitrary time-dependent potential to the Fermi gas in the ground state. We present a general method that gives the quantum statistics of any single-particle quantity, such as the charge, total energy, or momentum, in this nonequilibrium state. We show that the quantum statistics may be found from the solution of a matrix Riemann-Hilbert problem. We use the method to study how the finite measuring time modifies the distribution of charge transferred through a biased quantum point contact.