  We report on theoretical investigations of frequency dependent quantum
capacitance. It is found that at finite frequency a quantum capacitor can be
characterized by a classical RLC circuit with three parameters: a static
electrochemical capacitance, a charge relaxation resistance, and a quantum
inductance. The quantum inductance is proportional to the characteristic time
scale of electron dynamics and due to its existence, the time dependent current
can accumulate a phase delay and becomes lagging behind the applied ac voltage,
leading to a negative effective capacitance.
