  We study the number of propagating Bloch modes N_B of an infinite periodic
billiard chain. The asymptotic semiclassical behavior of this quantity depends
on the phase-space dynamics of the unit cell, growing linearly with the
wavenumber k in systems with a non-null measure of ballistic trajectories and
going like ~ sqrt(k) in diffusive systems. We have calculated numerically N_B
for a waveguide with cosine-shaped walls exhibiting strongly diffusive
dynamics. The semiclassical prediction for diffusive systems is verified to
good accuracy and a connection between this result and the universality of the
parametric variation of energy levels is presented.
