Voltage partition in a ballistic constriction

A channel supporting ballistic electron transport carries incident populations set by different source and drain chemical potentials, rather than an everywhere-equilibrated local distribution with an Ohmic voltage gradient. Its electrostatic barrier responds self-consistently to contacts, gates and electrostatic screening. A symmetric rigid-barrier model places reservoir energies at $E_F\pm eV/2$ relative to the barrier. Asymmetric partition or bias-dependent transmission changes the weights in the differential electrical conductance, and must be included when extracting an energy scale.