Theory of Quantum Conduction through a Constriction

A theory of ballistic conduction through a constriction is developed which predicts a steplike structure with amplitude $\frac{e^2}{h}$ in the conductance as a function of Fermi energy or width. For a sharp (abrupt) constriction the steps are only quantized to 1 part in ${10}^3$ at $T=0\mathrm{}$. Disorder destroys the steps and they are modulated by novel resonant structure in certain regimes of shape and temperature.