Abstract: In the paper, It is presented that a general 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 H-shaped quantum dot array of four-terminal system based on real-space lattice models is presented，a problem of the quantum transport in a four-terminal system can be reformulated into a problem of the quantum transport in an effective two-terminal system and then be treated using a standard two-terminal method. By exploiting real-space Green’s functions, the transmission coefficients of four-terminal quantum dot array is calculated ,and its problem of quantum transport is treated.

Key words: mesoscopic physics；quantum transport；transfer matrix； quantum dot array；H-shape；four-terminal system；