Electron transport through a circular constriction

We calculate the conductance of a circular constriction of radius a in an insulating diaphragm which separates two conducting half spaces characterized by the mean free path l. Using the Boltzmann equation we obtain an answer for all values of the ratio $l/a.\mathrm{}$ Our exact result interpolates between the Maxwell conductance in diffusive $(l\ll a)$ and the Sharvin conductance in ballistic $\left(l\gg a\right)$ transport regimes. Following Wexler’s work, our main advance is to find the explicit form of the Green’s function for the linearized Boltzmann operator. The formula for the conductance deviates by less than $11\%$ from the naive interpolation formula obtained by adding resistances in the diffusive and the ballistic regime.