title: Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit.
abstract: 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 wave number k in systems with a non-null measure of ballistic trajectories and going like ∼square root of 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.
authors.affiliation: Departamento de Física y CIMAT, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile.
authors.forename: Felipe
authors.initials: F
authors.lastname: Barra
authors.forename: Agnes
authors.initials: A
authors.lastname: Maurel
authors.forename: Vincent
authors.initials: V
authors.lastname: Pagneux
authors.forename: Jaime
authors.initials: J
authors.lastname: Zuñiga