Dynamic responses of series parallel-plate mesoscopic capacitors to time-dependent external voltage

We investigate the dynamic responses of the series parallel-plate mesoscopic capacitors to a time-dependent external voltage. The results indicate that the quantum coherence between two capacitors strongly depends on the frequency of the external voltage and the distance between the two capacitors （c-c distance）. The behaviors of the series capacitance incompletely follow the Kirchhoff＇s laws; only in the low frequency case or the limit of the c-c distance, the capacitance approaches to the classical series capacitance. In addition, the real part of the frequency-dependent capacitance shows a maximum and a minimum, which appear around the peak of the imaginary part. These phenomena may be associated with the plasmon excitation in the mesoscopic capacitors.