Impurity problems for steady-state nonequilibrium dynamical mean-field theory

The mapping of steady-state nonequilibrium dynamical mean-field theory from the lattice to the impurity is described in detail. Our focus is on the case with current flow under a constant dc electric field of arbitrary magnitude. In addition to formulating the problem via path integrals and functional derivatives, we also describe the distribution-function dependence of the retarded and advanced Greenʹs functions. Our formal developments are exact for the Falicov–Kimball model. We also show how these formal developments are modified for more complicated models (like the Hubbard model).