Impact of Weak Localization in the Time Domain

We find a renormalized “time-dependent diffusion coefficient,” $D(t)$, for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. 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, $L$, of the cylindrical sample with reflecting side walls and open ends. 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 only upon $k{\ell }_0$ for $R/L\gg 1$, where $k$ is the wave vector and ${\ell }_0$ is the bare mean free path.