Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot

We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage (eV=mu(L)-mu(R)) using a reduced density matrix (RDM). It is obtained in the Fock space by integrating out one of the two conduction channels, which can be separated from the dot. The remaining subspace is described by a single-channel Anderson model, and the statistical distribution is determined by the RDM. At zero temperature, the noninteracting RDM is constructed as the mixed states that show a close similarity to the high-temperature distribution in equilibrium. Specifically, when the system has an inversion symmetry, the one-particle states in an energy region between the two chemical potentials (mu(R)<epsilon <mu(L)) are occupied, or unoccupied, completely at random with an equal weight. The Coulomb interaction preserves these aspects, and the correlation functions can be expressed in a Lehmann-representation form with the mixed-state distribution. Furthermore, the statistical weight shows a broad distribution in the many-particle Hilbert space, spreading out in a wide energy region over the bias energy eV.