Abstract: The quantum transport theory of mesoscopic system provides the physical model and basis for the design and implementation of quantum devices with excellent performance。It is presented that a transfer matrix method to calculate various transmission coefficients for two-terminal systems based on tight-banding models with fluctuating on-site energies in the scattering region, then, a two-dimension T-shaped three-terminal quantum dot array model is presented，and then it is reformulated and treated as a standard two-terminal model to study the electron transport of T-shaped quantum dot arrays with asymmetric and symmetric electrodes relative to the middle original point. It is shown that for asymmetric T-shaped quantum dot array, the number of transmission peaks is equal to the number of quantum dots at the input terminal, while for symmetric T-shaped quantum dot array, the number of transmission peaks is equal to the number of quantum dots at the left and right terminal. It is also found that the transmission coefficients is related to the transition integral and the number of quantum dots, but not to the width of quantum dots.

Key words: quantum mechanics, quantum transport, transfer matrix, T-shape, three-terminal system, quantum dot array