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.
@article{arxiv.cond-mat/9609239,
title = {A.C.-Transport Through a Two-Dimensional Quantum Point Contact},
author = {I. E. Aronov and G. P. Berman and D. K. Campbell and S. V. Dudiy},
journal= {arXiv preprint arXiv:cond-mat/9609239},
year = {2008}
}