  Non-equilibrium bosonization technique facilitates the solution of a number
of important many-body problems out of equilibrium, including the Fermi-edge
singularity, the tunneling spectroscopy and full counting statistics of
interacting fermions forming a Luttinger liquid. We generalize the method to
non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish
interrelations between all these problems. The results can be expressed in
terms of Fredholm determinants of Toeplitz type. We analyze the long time
asymptotics of such determinants, using Szeg\H{o} and Fisher-Hartwig theorems.
Our analysis yields dephasing rates as well as power-law scaling behavior, with
exponents depending not only on the interaction strength but also on the
non-equilibrium state of the system.
