  We present a theoretical analysis of low frequency dynamics of a
single-channel mesoscopic capacitor, which is composed by a quantum dot
connected to an electron reservoir via a single quantum channel. At low
frequencies, it is known that the Wigner-Smith delay time $\tau_W$ plays a
dominant role and it can be interpreted as the time delay between the current
leaving the dot and the current entering the dot. At higher frequencies, we
find that another characteristic time $\tau_S$ can also be important. It
describes the deformation of the leaving current to the entering one and hence
can be referred as the deformation time. At sufficient low temperatures, the
deformation time $\tau_S$ can be approximated from the second-order derivative
of $\tau_W$ via a simple relation $\tau"_W/\tau^3_S=24/\hbar^2$. As the
temperature increases, this relation breaks down and one has instead
$\tau"_W/\tau^3_S \to 0$ in the high temperature limit. We further show that
the deformation time $\tau_S$ can have a pronounced influence on the quantum
inductance $L_q$ of the mesoscopic capacitor, leading to features different
from 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 positive
values at low temperatures to large negative values at high temperatures. The
above results demonstrate the importance of the deformation time $\tau_S$ on
the ac conductance of the mesoscopic capacitor.

Mesoscale and Nanoscale Physics