We emphasize that Eq. (3.39) is bas

We emphasize that Eq. (3.39) is based on the assumption of complete equilibration of the current-carrying edge states in the region between the point contacts. In a quantizing magnetic field, local equilibrium is reached by inter-Landau level scattering. If the potential landscape (both in the point contacts themselves and in the 2DEG region in between) varies by less than the Landau level separation ¯hωc on the length scale of the magnetic length (¯h/eB)1/2, then inter-Landau level scattering is suppressed in the absence of other scattering mechanisms (see Section IV.A). This means that the transport from one point contact to the other is adiabatic. The series conductance is then simply Gseries = (2e2/h)N for two identical point contacts [N ≡ min(N1,N2) for two different point contacts in series]. This expression differs from Eq. (3.39) if a barrier is present in the point contacts, since that causes the number N of occupied Landau levels in the point contact to be less than the number Nwide of occupied levels in the wide 2DEG. [In a strong magnetic field, N ≈ (EF − Ec)/¯hωc, while Nwide ≈EF/¯hωc.] Adiabatic transport in a magnetic field through two point contacts in series has been studied experimentally by Kouwenhoven et al.373 and by Main et al.374