  We develop a nonperturbative dynamical theory (NDT) to calculate the retarded
Green's function under nonequilibrium conditions. The NDT is particularly
useful for treating nonequilibrium transport problems in systems with strong
correlation. We apply our NDT to the well-known single-impurity Anderson model
at equilibrium to determine its feasibility. We then apply it to a
nonequilibrium transport problem in a system with Kondo coupling. An Anderson
model with two metallic reservoirs is studied to understand the phenomenon of
Kondo-peak splitting in a single-electron transistor of mesoscopic size. We
calculate the nonequilibrium retarded Green's function by using the NDT and
analyze it in the atomic limit, where the novel coherent phenomenon manifested
only under nonequilibrium conditions can be described in an analytical manner.
We finally construct a self-consistent loop to calculate the retarded Green's
function and present the results for spectral density and differential
conductance obtained by the self-consistent method. Our results explain all the
features of Kondo-peak splitting observed in experiments. One remarkable
conclusion is that Kondo-peak splitting is not the splitting of a conventional
Kondo peak, but the splitting of a novel coherent peak created under
nonequilibrium steady-state conditions.
