Methods and Applications of Analysis

Volume 11 (2004)

Number 3

Impact of Weak Localization on Wave Dynamics: Crossover from Quasi-1D to Slab Geometry

Pages: 465 – 474

DOI: http://dx.doi.org/10.4310/MAA.2004.v11.n3.a15

Authors

A. A. Chabanov

S. K. Cheung

A. Z. Genack

X. Zhang

Z. Q. Zhang

Abstract

We study the dynamics of wave propagation in nominally diffusive samples by solving the Bethe-Salpeter equation with recurrent scattering included in a frequency-dependent vertex function, which renormalizes the mean free path of the system. We calculate the renormalized time-dependent diffusion coefficient, $D(t)$, following pulsed excitation of the system. For cylindrical samples with reflecting side walls and open ends, we observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, $R$, to the length, L. Immediately after the peak of the transmitted pulse, $D(t)$ falls linearly with a nonuniversal slope that approaches an asymptotic value for $R/L\gg 1$. The value of $D(t)$ extrapolated to $t=0$, depends only upon the dimensionless conductance $g$ for $R/L \ll 1$ and upon $kl_0$ and $L$ for $R/L \gg 1$, where $k$ is the wave vector and $l_0$ is the bare mean free path.

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