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We present a theoretical analysis of low frequency dynamics of asingle-channel mesoscopic capacitor, which is composed by a quantum dotconnected to an electron reservoir via a single quantum channel. At lowfrequencies, it is known that the Wigner-Smith delay time $\tau_W$ plays adominant role and it can be interpreted as the time delay between the currentleaving the dot and the current entering the dot. At higher frequencies, wefind that another characteristic time $\tau_S$ can also be important. Itdescribes the deformation of the leaving current to the entering one and hencecan be referred as the deformation time. At sufficient low temperatures, thedeformation time $\tau_S$ can be approximated from the second-order derivativeof $\tau_W$ via a simple relation $\tau"_W/\tau^3_S=24/\hbar^2$. As thetemperature increases, this relation breaks down and one has instead$\tau"_W/\tau^3_S \to 0$ in the high temperature limit. We further show thatthe deformation time $\tau_S$ can have a pronounced influence on the quantuminductance $L_q$ of the mesoscopic capacitor, leading to features differentfrom the ones of the quantum capacitance. The most striking one is that $L_q$can change its sign as the temperature increases: It can go from positivevalues at low temperatures to large negative values at high temperatures. Theabove results demonstrate the importance of the deformation time $\tau_S$ onthe ac conductance of the mesoscopic capacitor.

Current deformation and quantum inductance in mesoscopic capacitors