  Inelastic effects in electron transport through nano-sized devices are
addressed with a method based on nonequilibrium Green's functions (NEGF) and
perturbation theory to infinite order in the electron-vibration coupling. We
discuss the numerical implementation which involves an iterative scheme to
solve a set of coupled non-linear equations for the electronic Green's
functions and the self-energies due to vibrations. To illustrate our method, we
apply it to a one-dimensional single-orbital tight-binding description of the
conducting electrons in atomic gold wires, and show that this simple model is
able to capture most of the essential physics.
