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 succinctly summarize parts of our past work related to 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). In addition, we provide a novel account of the response to an ac field exerted on the junction (on top of the dc bias voltage); in particular, we study the nonequilibrium distribution and the displacement fluctuations of the vibrational modes. Remarkably, we find a behavior pattern that cannot be accounted for by classical forced oscillations. 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.
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