Unified description of charge transfer mechanisms and vibronic dynamics in nanoscale junctions.

We propose a general framework that unifies the description of counting statistics of transmitted (fermionic) charges as it is commonly used in the quantum transport community with the description of counting statistics of phonons (bosons). As a particular example, we study on the same footing the counting statistics of electrons transferred through a molecular junction and the corresponding population dynamics of the associated molecular vibrational mode. In the tunnel limit, non-perturbative results in the electron-phonon interaction are derived that unify complementary approaches based on rate equations or on the use of non-equilibrium Green functions.