Where is the potential drop in a quantum point contact?

A scattering theory calculation is presented for the potential distribution and the associated current-voltage characteristic in a ballistic quantum point contact. Following Landauer's idea, the electric field is calculated as the response to a given incoming current. The field is finite only near the entrance to or exit from the constriction, while no potential drop occurs in the device itself, where the motion is adiabatic. As a result dissipation is restricted to the reservoirs, whose detailed description, however, requires inelastic scattering.