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.
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