Fermi-edge singularity in nonequilibrium systems

In this paper the problem of Fermi-edge singularity is studied in detail for a class of nonequilibrium systems with more than one Fermi seas with different chemical potentials coupling to each other. The problem is solved by generalizing the solution of Nozi\'eres and De Domincis for (equilibrium) single Fermi sea system to the nonequilibrium situation described in this paper. The concepts of nonequilibrium T matrices and phase shifts are introduced in this paper where a generalized Fumi theorem is being proved. We find that Fermi-edge singularities are found in all Fermi surfaces in the system. However the singularities are smeared out by a lifetime effect associated with finite potential differences between different Fermi seas. Some consequences of the result are pointed out. {} 1996 The American Physical Society.