Transmission-phase of an electron in a quantum point contact

For the first time we calculate the electron transmission phase through a quantum point contact (QPC). The QPC is considered in the saddle point approximation in the single-electron picture. We show that when the electron energy is close to the height of the potential barrier the transmission-phase depends linearly on the energy. The coefficient in the linear dependence is logarithmically enhanced by the ratio of the height over the curvature of the barrier potential. We compare the calculated transmission phase with the first experimental measurements of the phase.