  We describe some exact high-energy properties of a single Anderson impurity
connected to two noninteracting leads in a nonequilibrium steady state. In the
limit of high bias voltages, and also in the high-temperature limit at thermal
equilibrium, the model can be mapped on to an effective non-Hermitian
Hamiltonian consisting of two sites, which correspond to the original impurity
and its image that is defined in a doubled Hilbert space referred to as
Liouville-Fock space. For this, we provide a heuristic derivation using a
path-integral representation of the Keldysh contour and the thermal field
theory, in which the time evolution along the backward contour is replicated by
extra degrees of freedom corresponding to the image. We find that the effective
Hamiltonian can also be expressed in terms of charges and currents. From this,
it can be deduced that the dynamic susceptibilities for the charges and the
current fluctuations become independent of the Coulomb repulsion U in the high
bias limit. Furthermore, the equation of motions for the Green's function and
two other higher-order correlation functions constitute a closed system. The
exact solution obtained from the three coupled equations extends the
atomic-limit solution such that the self-energy correctly captures the
imaginary part caused by the relaxation processes at high energies. The
spectral weights of the upper and lower Hubbard levels depend sensitively on
the asymmetry in the tunneling couplings to the left and right leads.
