Riemann-Hilbert approach to the Full Counting Statistics in Mesoscopic Devices

We use the Riemann-Hilbert (RH) approach to investigate the Full Counting Statistics (FCS) of charge transfer across a quantum tunnel junction driven by a time dependent periodic Lorentzian potential V(t) at zero temperature. We find that the FCS for a quantised Lorentzian time-dependent potential can be described by two statistically independent binomial processes resulting from the DC and AC component of the potential. These AC and DC processes are shown to have relatively simple physical interpretations. vVe derive the expressions which describes the probability distribution underlying these DC and AC events. Moreover, we demonstrate that our formalism is equally valid for an arbitrary time dependent potential. To illustrate our method, we evaluate the results for the FCS for some important and non-trivial examples of periodic quantised Lorentzian potentials. vVe discuss how the relative overlap between the Lorentzian pulses in the potential affects the probability distributions. vVe describe the non-zero temperature generalisation of the RH method in chapter 5. We investigate the analytical properties of the non-zero tempera~ure RH solution and discuss their consequence on the evaluation of finite temperature FCS for devices driven out of equilibrium. As a consistency check we apply our formalism to calculate the FCS for a quantum point contact in the absence of any external potential and rederive the result from Levitov et al [51] for the equilibrium FCS.EThOS - Electronic Theses Online ServiceGBUnited Kingdo