  The coupling of the charge carriers passing through a molecule bridging two
bulky conductors with local vibrational modes of the molecule, gives rise to
distinct features in the electronic transport properties on one hand, and to
nonequilibrium features in the vibrations' properties, e.g., their population,
on the other. Here we explore theoretically a generic model for a molecular
junction biased by an arbitrary dc voltage in the weak-coupling regime. We
analyze the signature of the electron-vibration interaction on the
full-counting statistics of the current fluctuations (i.e., the cumulant
generating-function of the current correlations), we give a detailed account of
the response to an ac field exerted on the junction (on top of the dc bias
voltage), we study the nonequilibrium distribution of the vibrational modes and
the fluctuations they cause in the displacement of the molecule center of mass.
The calculations use the technique of nonequilibrium Green's functions, and
treat the electron-vibration coupling in perturbation theory, within the
random-phase approximation when required.
