The injection distribution (3.31) c

The injection distribution (3.31) can be used to obtain (in the semiclassical limit) the direct transmission probability Td between two opposite identical point contacts separated by a large distance L. To this end, first note that Td/N is the fraction of the injected current that reaches the opposite point contact (since the transmission probability through the first point contact is N, for N occupied subbands in the point contact). Electrons injected within a cone of opening angle Wmax/L centered at α = 0 reach the opposite point contact and are transmitted. If this opening angle is much smaller than the total opening angle 2αmax of the beam, then the distribution function P(α) can be approximated by P(0) within this cone. This approximation requires Wmax/L ≪ 1/f, which is satisfied experimentally in devices with a sufficiently large point contact separation. We thus obtain Td/N = P(0)Wmax/L, which, using Eq. (3.31), can be written as329