| Summary: | 碩士 === 國立臺灣大學 === 物理研究所 === 101 === In this thesis, we investigate the non-Markovian dynamics of a quantum dot system between two electrodes. Going beyond the wideband limit (WBL) and the Markovian approximation usually employed in the theoretical study for the electron transport in the nanostructure devices, we use the exact reduced master equation derived from the non-Markovian quantum state diffusion (NMQSD) approach. We start from the Heisenberg equation and further derive the reduced master equation and the current equation for the quantum dot system by NMQSD. Then, we show that the time-dependent coefficients in both of the reduced master equation and the current equation can be exactly expressed in terms of the time-dependent coefficients calculated by the non-equilibrium theory based on Feynman-Vernon influence functional approach. Furthermore, we generalize NMQSD formalism to treat the transport problem of a single quantum dot with time-dependent bias voltage and time-dependent gate voltage. Taking the spectral densities of the two electrodes as Lorentzian-type shapes, we study the quantum transport dynamics through the quantum dot system. We set the bias voltage and gate voltage to be time-independent or/and time-dependent. The dependence of the width and center of the Lorentzian-type electrode spectral density and the behavior of the gate voltage and bias voltage on the effectively tunneling rates and average current are investigated.
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