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September 2004 Impact of Weak Localization on Wave Dynamics: Crossover from Quasi-1D to Slab Geometry
Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack
Methods Appl. Anal. 11(3): 465-474 (September 2004).

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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Z. Q. Zhang. S. K. Cheung. X. Zhang. A. A. Chabanov. A. Z. Genack. "Impact of Weak Localization on Wave Dynamics: Crossover from Quasi-1D to Slab Geometry." Methods Appl. Anal. 11 (3) 465 - 474, September 2004.

Information

Published: September 2004
First available in Project Euclid: 11 May 2006

zbMATH: 1092.81028
MathSciNet: MR2214688

Rights: Copyright © 2004 International Press of Boston

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Vol.11 • No. 3 • September 2004
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