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We propose a general framework that unifies the point of view of countingstatistics of transmitted (fermionic) charges as it is commonly used in thequantum transport community to the point of view of counting statics of phonons(bosons) as it is known from the field of quantum optics. As a particularexample, we study on the same footing the counting statistics of electronstransfered through a molecular junction and the corresponding populationdynamics of the associated molecular vibrational mode. In the tunnel limit,non-perturbative results in the electron-phonon interaction are derived thatunify complementary approaches based on rate equations or on the use ofnon-equilibrium Green functions.

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