We study the statistics of single electron transfers through quantum dot and single molecule junctions. For that purpose, we derive a path-integral formalism where the effects of the electrodes on the system are characterized by a Feynman-Vernon influence functional. This approach is more general than previous master equation formalisms based on perturbation theory or semiclassical stochastic path integrals. The path-integral is solved utilizing the hierarchical equations of motions approach. From the path-integral, quantum master- and rate equations are recovered. Based on the derived set of transport formalisms, we obtain generating functions that provide the full counting statistics of single electron transfers. From a trajectory approach, we derive transfer operators which are emplo...[ Read more ]

We study the statistics of single electron transfers through quantum dot and single molecule junctions. For that purpose, we derive a path-integral formalism where the effects of the electrodes on the system are characterized by a Feynman-Vernon influence functional. This approach is more general than previous master equation formalisms based on perturbation theory or semiclassical stochastic path integrals. The path-integral is solved utilizing the hierarchical equations of motions approach. From the path-integral, quantum master- and rate equations are recovered. Based on the derived set of transport formalisms, we obtain generating functions that provide the full counting statistics of single electron transfers. From a trajectory approach, we derive transfer operators which are employed to calculate joint-probabilities of consecutive electron transfers. As a consequence, we introduce waiting time distributions to the field of electron transport. The derived theories are then applied to examine electron transfer statistics experiments utilizing quantum dots, single molecules and quantum dot Aharonov-Bohm interferometers. We find that the statistics is sensitive to the presence of quantum mechanical interference and the Aharonov-Bohm phase, when two parallel transport legs are present. It is observed that the fluctuation theorem is not violated by this form of interference. The transfer statistics provides detailed information on the electronic states of the system and transfer rates. This can be used for novel applications such as single electron counting spectroscopy, as we show in a model simulation of a single porphyrin molecule. We are able to investigate non-Markovian and cotunneling effects, since the path-integral allows to go beyond previous second-order system-electrode perturbation approaches.