The mesoscopic quantum interference phenomenon （QIP） can be observed and behaves as the oscillation of conductance in nano-devices when the external magnetic field changes. Excluding the factor of impurities or defects, specific QIP is determined by the sample geometry. We have improved a first-principles method based on the matrix Green＇s function and the density functional theory to simulate the transport behaviour of such systems under a magnetic field. We have studied two kinds of QIP： universal conductance fluctuation （UCF） and Aharonov Bohm effect （A-B effect）. We find that the amplitude of UCF is much smaller than the previous theoretical prediction. We have discussed the origin of difference and concluded that due to the failure of ergodic hypothesis, the ensemble statistics is not applicable, and the conductance fluctuation is determined by the flux-dependent density of states （DOSs）. We have also studied the relation between the UCF and the structure of sample. For a specific structure, an atomic circle, the A-B effect is observed and the origin of the oscillation is also discussed.
