Electrochemical capacitance and charge relaxation resistance of mesoscopic capacitors

We investigate numerically the transport properties of a mesoscopic capacitor which consists of a quantum dot connected via a single lead to an electron reservoir. The fluctuations and distributions of electrochemical capacitance $C_\mu$ and charge relaxation resistance $R_q$ have been studied. It shows that the distribution of electrochemical capacitance $C_\mu$ at one conducting channel case in our numerical calculation is different from the former theoretical prediction obtained from the scattering matrix theory. The difference is due to the existence of necklace states which has been observed in a recent optical experiment.