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A.c. transport and collective excitations in a quantum point contact

We study the a.c. transport through a two-dimensional quantum point contact (QPC) using a Boltzmann-like kinetic equation derived for the partial Wigner distribution function. An integral equation for a potential inside a QPC is solved numerically. It is shown that the electric field inside a QPC is an inhomogeneous function of the spatial coordinate, with a characteristic scale equal to the distance between the electron's turning points. A dependence of the admittance on the frequency of the a.c. field is found in the frequency range, -50 GHz. The contribution to the imaginary part of the admittance due to the open and closed channels is numerically calculated. It is shown that the crossover of quantum capacitance and quantum inductance from localized behaviour to distributed behaviour takes place at GHz. A transition from 2D plasmons to quasi-1D plasmons is analysed as a function of two dimensionless parameters: (where is the longitudinal wavevector and is the width of the QPC) and the number of open electron channels, N.