Implementação numérica da teoria quântica de circuitos - Silva, José Jaédson Barros da (2019)
During the decade 1980s, advances in nanoscience became possible the construction of nanodevices that allowed the discovery of phenomena related to quantum mechanics such as weak localization, universal conductance fluctuations and the quantization of conductance. Since then, coherent electronic transport in mesoscopic systems has attracted the interest of various experimental and theoretical physicists. In this thesis we developed a numerical method, based on Newton’s iterative method, to calculate pseudocurrent of quantum circuit theory. From the pseudoccurent we determine the observables of transport, as conductance and shot noise power, in a linear network and in a ring of quantum dots. In order to show the effectiveness of the numerical method, when possible we compare our results with analytical predictions from the literature and with simulations of random matrices theory. In all cases the numerical results showed excellent agreement with the analytical predictions and with the simulation. We also determine the transport observables for situations in which the analytical method can not approach such as a linear network of quantum dots with the transparencies of the barriers random and a ring of quantum dots with all the transparencies of the barriers independent. We calculate the average processing time of the algorithm for a linear network of L quantum dots and we show that it scales with L. Therefore, the algorithm has excellent efficiency. We also apply the numerical method to calculate the density of Fabry-Perot resonant modes in quantum dots networks which, according to the literature, can be identified as a kind of order parameter in a second-order quantum phase transition theory. When comparing these numerical results with analytical predictions and simulation of random matrices theory, again the numerical method showed excellent agreement. For certain barrier transparency values, Fabry-Perot resonant modes are suppressed. We calculate the critical properties of this suppression in a linear network and a ring of quantum dots. In all cases the critical exponent obtained was 1/2, therefore it is a universal behavior. We show that for certain values of barrier transparency, in a linear network with L ≥ 2 quantum dots and in a ring of quantum dots, arises a new transition line delimiting the region of the Fabry-Perot resonant modes and the region in which these modes are suppressed. For the quantum dots ring, we also show that the transition lines become asymmetric for certain barrier transparency values.