Diffusive transport of waves in a periodic waveguide.

We study the propagation of waves in quasi-one-dimensional finite periodic systems whose classical (ray) dynamics is diffusive. By considering a random matrix model for a chain of L identical chaotic cavities, we show that its average conductance as a function of L displays an ohmic behavior even though the system has no disorder. This behavior, with an average conductance decay N/L, where N is the number of propagating modes in the leads that connect the cavities, holds for 1≪L≲√N. After this regime, the average conductance saturates at a value of O(√N) given by the average number of propagating Bloch modes of the infinite chain. We also study the weak localization correction and conductance distribution, and characterize its behavior as the system undergoes the transition from diffusive to Bloch ballistic. These predictions are tested in a periodic cosine waveguide.