A.C.-Transport Through a Two-Dimensional Quantum Point Contact
  We calculate the admittance of a two-dimensional quantum point contact (QPC) using a Boltzman-like kinetic equation derived for a partial Wigner distribution function in an effective potential. We show that this approach leads to the known stepwise behavior of the admittance as a function of the gate voltage. The emittance contains both a quantum inductance determined by the harmonic mean of the velocities for the propagating electron modes and a quantum capacitance determined by the reflected modes. 
I.E. Aronov, G.P. Berman, D.K. Campbell, and S.V. Dudiy