Diffusive transport of waves in a periodic waveguide

Details Diffusive transport of waves in a periodic waveguide Diffusive transport of waves in a periodic waveguide

2011-02-02

arxiv.org/abs/1102.0335v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 10 figures

Scientific paper

10.1103/PhysRevE.85.016209

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 $1\ll L \lesssim \sqrt{N}.$ After this regime, the average conductance saturates at a value of ${\mathcal O}(\sqrt{N})$ 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.

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