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>>1. The value of D(t) extrapolated to t=0 depends only upon the dimensionless conductance g for R/L<<1 and only upon kl(0) for R/L>>1, where k is the wave vector and l(0) is the bare mean free path.