We discuss the capacitance of a coherent mesoscopic parallel-plate capacitor based on the self-consistent theory of dynamic response for mesoscopic systems. The results show that the capacitance is a complex function of frequency which is strongly dependent on the frequency of the external field. The capacitance-frequency curve shows a significant characteristic that a peak in the imaginary part of the capacitance corresponds to the minimum in the real part, and further study shows that they are related to a plasmon-like excitation. In addition,we discuss the size effect of the capacitor, and find that the capacitance approaches geometric capacitance when the distance between two plates of the capacitor is very large.

In order to study the role of contacts in the coherent transport of mesoscopic structure systems, a 2D-1D-2D model of nano-sized single-barrier system is considered, which includes a single-barrier structure conductor with two reservoirs. Basing on the scattering-matrix method and the Thomas-Fermi approximation, we have calculated the transmission probability and the distribution of internal potential when a dc voltage is applied to the system. The results show that: (1) the contacts can produce significant effects on the transmission probability; (2) the behaviors of conductance and the distribution of internal potential differ from the usual transport conductance give by the Kirchhoff's laws. Therefore we conclude that since contacts and the mesocopic systems are quantum coherent, the role of contacts is important for in-depth investigation of the transport in mesoscopic systems.