Mode-count balance in a ballistic junction
= Mode-count balance in a ballistic junction
Let $T_{ij}$ count transmitted <modes> from injector $j$ to collector $i$, excluding reflection $R_{ii}$. Scattering conservation gives $\sum_{i\ne j}T_{ij}=N_j-R_{jj}$; <unitarity> also gives the corresponding row balance. The conductance matrix has zero row sum, making equal lead potentials carry no current, and zero column sum, conserving total current.