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 {\em 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 step-like manner in synchronism with the conductance steps. For vanishing reflection, the capacitance vanishes and the emittance is negative.