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The science
Electrons in the constriction are confined across a width W, so the transverse energy is quantised: eps_n = (hbar^2/2m*)(n pi / W)^2. At the Fermi energy E_F = hbar^2 kF^2 / 2m* a mode n is open when eps_n < E_F, i.e. N = floor(kF W / pi) (the same rule as the 3D page).
Landauer: G = (2e^2/h) sum_n T_n, with G0 = 2e^2/h = 77.48 uS. For a smooth saddle potential (Buettiker) T_n(E) = 1/(1 + exp(-2 pi (E - eps_n)/(hbar wx))), and at finite temperature the conductance averages T_n over the thermal window -df/dE. Cold and sharp gives exact plateaus; heating or a soft saddle rounds the steps.
Simplifications: spin-degenerate non-interacting electrons, no 0.7 anomaly, no impurity scattering, and the linear gate-to-width law taken from the 3D page.
What to try
- Choose Ideal staircase and sweep Vg: G jumps by exactly 1 G0.
- Raise the temperature: the steps round off and vanish near kT/E_F of 0.07.
- Watch the dots: closed modes bounce back, and the counted conductance converges to the Landauer sum.