Quantum transport and quantum measurement in mesoscopic systems: reduced density matrix approach

This thesis is dedicated to the study of quantum transport and quantum measurement in mesoscopic systems, and focuses on the following two important themes. One is the establishment of a general formalism for open quantum systems in terms of the density matrix of the reduced system. This theory is capable of describing not only the average output, but more importantly their fluctuation correlations. Another one is related to the applications of this theory to a variety of problems in mesoscopic systems. Main accomplishments of this thesis are summarized as follows. A general formalism is established for full counting statistics, which enables complete understanding of electronic transport. Electron charge transport through coupled quantum dot system have been investigated. Higher order cumulants of the current distribution are analyzed, and a number of remarkable results are obtained. In addition, real-time detection of single electron tunneling through a coupled quantum dot device is simulated, based on a Monte Carlo scheme. Particularly, in the context of full counting statistics, we investigate the essential difference between the dephasing mechanisms induced by the quantum point contact detection and the coupling to the external phonon bath. Quantum measurement is another important and interesting topic of this thesis. A mesoscopic quantum point contact is proposed as a charge qubit detector. Analysis was focused on an alternative backaction known as the energy renormalization, which becomes increasingly important as one lowers the measurement voltage, and can significantly affect the output power spectrum. Finally, a hierarchically coupled equation of motion approach is constructed on the basis of the auxiliary influence-generating functionals. In comparison with second-order master equation method, this approach is capable of handling systems involving strong coupling between the system and bath, and is valid at arbitrary temperature and voltages