Case for nonadiabatic quantized conductance in smooth ballistic constrictions

We present quantum-mechanical calculations of the conductance (G) of smooth, but not adiabatic, ballistic constrictions (BC’s). Although the BC width varies smoothly with position, the effective potential for each transverse mode exhibits a pair of peaks that cause multiple reflections. If mode is neglected, G is dominated by transmission resonances. However, the exact (nonadabatic) G is a smooth function of ${\mathit{E}}_{\mathit{F}}$ with quantized plateaus. This is an explicit example of the breakdown of adiabaticity being the source of conductance quantization in a smooth BC.