  Employing the nonequilibrium Green's function method, we develop a fully
quantum mechanical model to study the coupled electron-phonon transport in
one-dimensional atomic junctions in the presence of a weak electron-phonon
interaction. This model enables us to study the electronic and phononic
transport on an equal footing. We derive the electrical and energy currents of
the coupled electron-phonon system and the energy exchange between them. As an
application, we study the heat dissipation in current carrying atomic junctions
within the self-consistent Born approximation, which guarantees energy current
conservation. We find that the inclusion of phonon transport is important in
determining the heat dissipation and temperature change of the atomic
junctions.
