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

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.