Conductance of a molecule with a center of mass motion

We calculate the zero temperature conductance and characteristic correlation functions of a molecule with a center of mass (CM) motion which modulates couplings to the leads. In the first model studied, the CM vibrational mode is simultaneously coupled to the electron density on the molecule. The conductance is suppressed in regimes corresponding to non-integer occupancy of the molecule. In the second model, where the CM mode is not directly coupled to the electron density, the suppression of conductance is related to the dynamic breaking of the inversion symmetry.