  The topic of this review is the effects of electron-phonon interaction (EPI)
on the transport properties of molecular nano-conductors. A nano-conductor
connects to two electron leads and two phonon leads, possibly at different
temperatures or chemical potentials. The EPI appears only in the
nano-conductor. We focus on its effects on charge and energy transport. We
introduce three approaches. For weak EPI, we use the nonequilibrium Green's
function method to treat it perturbatively. We derive the expressions for the
charge and heat currents. For weak system-lead couplings, we use the quantum
master equation approach. In both cases, we use a simple single level model to
study the effects of EPI on the system's thermoelectric transport properties.
It is also interesting to look at the effect of currents on the dynamics of the
phonon system. For this, we derive a semi-classical generalized Langevin
equation to describe the nano-conductor's atomic dynamics, taking the
nonequilibrium electron system, as well as the rest of the atomic degrees of
freedom as effective baths. We show simple applications of this approach to the
problem of energy transfer between electrons and phonons.
