 Antidot resonance conductance bounds

A spin-resolved resonant path adds at most $e^2/h$ to the electrical conductance of directly transmitted spectator channels. Conversely, resonant transfer into a returning edge removes at most $e^2/h$ from an otherwise open channel. For an isolated level, $T(E)={\Gamma }_L{\Gamma }_R/[(E-{ϵ}_d{)}^2+({\Gamma }_L+{\Gamma }_R{)}^2/4]$ reaches one only for equal couplings. Integer offsets follow the channel connectivity and do not follow from a local filling factor alone. temperature, asymmetry, coherent background paths and inelastic processes can change the apparent resonance height and shape.