  It has been shown that solutions of a number of many-body problems out of
equilibrium can be expressed in terms of Toeplitz determinants with
Fisher-Hartwig (FH) singularities. In the present paper, such Toeplitz
determinants are studied numerically. Results of our numerical calculations
fully agree with the FH conjecture in an extended form that includes a
summation over all FH representations (corresponding to different branches of
the logarithms). As specific applications, we consider problems of Fermi edge
singularity and tunneling spectroscopy of Luttinger liquid with multiple-step
energy distribution functions, including the case of population inversion. In
the energy representation, a sum over FH branches produces power-law
singularities at multiple edges.
