Counting statistics for non-additive molecular nanojunctions at strong electron-phonon coupling

Moore's law predicts that the number of transistors on a computer microchip doubles every two years. As a society we focus on decreasing the size of our computers. As a result the transistors present on computers have been rapidly reduced in size over the past decade. We have now begun to infringe on the quantum regime, resulting in the need for the theoretical development and manufacture of quantum technologies. Current evidence suggests that the length of transistors on microchips will soon be as small as approximately fifteen atoms placed side by side, as such it is important that we are able to model molecular nanojunctions. A molecular nanojunction is a circuit which makes use of molecules as its building blocks, the molecule itself is attached to two electronic leads as a means of completing a circuit. The theoretical model for such devices must be able to accurately predict the behaviours of systems which couple to several environments. The central transport mechanism of the molecule is treated as a quantum system while the remainder of the molecule is modelled as a phonon bath. As such the electron-phonon coupling considered when electrons move through the molecule must be evaluated beyond the perturbative approach. Throughout this body of work we shall discuss and develop the reaction coordinate formalism, allowing for the incorporation of strong phonon contributions in our models. The strong vibrational coupling invalidates the additive treatment of our model and so we shall develop a non-additive master equation. Our non-additive master equation will properly account for the influence of strong and non-Markovian coupling. We shall extend our analysis to consider regimes where our molecular nanojunctions act as thermoelectrics. A thermoelectric device makes use of temperature gradients between the system and surrounding environments in order to overcome chemical potential or energetic barriers. Using a reaction coordinate formalism we will consider the impact of strong electron-phonon coupling on the properties of several thermoelectric regimes for multiple models. We shall finish our analysis by designing quantum refrigeration models and comparing their operations with classical emulators. Component cooling is a problem of considerable importance in the development of quantum technologies and through our work we aim to discover thermodynamic properties for quantum fridges while comparing and contrasting with their classical counterparts. Using counting statistics throughout our analysis we shall track particle and energy exchange to calculate current, noise, heat flow, power, efficiency and Fano factor as required. As a result we will be able to identify the importance of non-additive and strong coupling effects within molecular nanojunctions as well as determining the overlap between quantum fridges and their classical emulators.