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We describe some exact high-energy properties of a single Anderson impurityconnected to two noninteracting leads in a nonequilibrium steady state. In thelimit of high bias voltages, and also in the high-temperature limit at thermalequilibrium, the model can be mapped on to an effective non-HermitianHamiltonian consisting of two sites, which correspond to the original impurityand its image that is defined in a doubled Hilbert space referred to asLiouville-Fock space. For this, we provide a heuristic derivation using apath-integral representation of the Keldysh contour and the thermal fieldtheory, in which the time evolution along the backward contour is replicated byextra degrees of freedom corresponding to the image. We find that the effectiveHamiltonian can also be expressed in terms of charges and currents. From this,it can be deduced that the dynamic susceptibilities for the charges and thecurrent fluctuations become independent of the Coulomb repulsion U in the highbias limit. Furthermore, the equation of motions for the Green's function andtwo other higher-order correlation functions constitute a closed system. Theexact solution obtained from the three coupled equations extends theatomic-limit solution such that the self-energy correctly captures theimaginary part caused by the relaxation processes at high energies. Thespectral weights of the upper and lower Hubbard levels depend sensitively onthe asymmetry in the tunneling couplings to the left and right leads.

Exact interacting Green's function for the Anderson impurity at high bias voltages