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arXiv · 1102.0345

Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit

Felipe Barra·Agnes Maurel·Vincent Pagneux·Jaime Zuñiga
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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 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.

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Felipe Barra, Agnes Maurel, Vincent Pagneux, Jaime Zuñiga. 2011-02-02. Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit. https://doi.org/10.1103/physreve.81.066210

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