  Compressibility measurements, sensitive to charge rearrangements, are
performed on a quantum point contact (QPC). Screening due to mobile charges in
the QPC is quantitatively measured, using a second point contact to detect the
screened electrical potential. These measurements are performed from pinch-off
through the opening of the first few modes in the QPC. While the measured
signal closely matches a Thomas-Fermi-Poisson prediction, deviations from the
classical behavior, in the form of additional dips, are apparent near the
openings of the different modes, with the largest dip at the opening of the
first mode. Density functional calculations attribute the first dip to exchange
interactions. The other dips reflect the diverging density of states at the
opening of each one-dimensional mode, which affects both kinetic and exchange
contributions to the energy.
