The phase interference between two distinct electron (or hole) waves was treated in the Introduction to this book. Whereas the past few chapters dealt largely with the quasi-ballistic transport of these waves through mesoscopic systems, in this chapter we want to begin to treat systems in which the transport is more diffusive than quasi-ballistic. How do we distinguish between these two regimes? Certainly the existence of scattering is possible in both regimes, but we distinguish the diffusive regime from the quasi-ballistic regime by the level of the scattering processes. In the diffusive regime, we assume that scattering dominates the transport to a level such that there are no “ballistic” trajectories that extend for any significant length within the sample. That is, we assert that l = εF τ ≪ L, where L is any characteristic dimension of the sample. Typically, this means that the material under investigation is characterized by a relatively low mobility, certainly not the mobility of several million that can be obtained in good modulation-doped heterostructures. In a sense, the transport is now considered to be composed of short paths between a relatively large number of impurity scattering centers. Thus, we deal with the smooth diffusion of particles through the mesoscopic system. To be sure, the Landauer formula does not distinguish ballistic from diffusive transport, but its treatment in multimode waveguides is more appropriately considered a ballistic transport. To illustrate the difference, consider the Aharonov-Bohm effect and the presence of weak localization. In the former, the wavefunction (particles) splits into two parts that propagate around opposite sides of a ring “interferometer,” as illustrated in Fig. 1.4.