Low frequency admittance of a quantum point contact

We present a current and charge conserving theory for the low frequency admittance of a quantum point contact. We derive expressions for the electrochemical capacitance and the displacement current. The latter is determined by the emittance which equals the capacitance only in the limit of vanishing transmission. With the opening of channels the capacitance and the emittance decrease in a steplike manner in synchronism with the conductance steps. For vanishing reflection, the capacitance vanishes and the emittance is negative.