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Department of Physics, Queens College of the City University of New York, Flushing, New York 11367, USA(Dated: February 2, 2008)We study the dynamics of wave propagation in nominally diusive samples by solving the Bethe-Salpeter equation with recurrent scattering included in a frequency-dependentvertex function, whichrenormalizes the mean free path of the system. We calculate the renormalized time-dependentdiusion coecient, D(t), following pulsed excitation of the system. For cylindrical samples withreecting side walls and open ends, we observe a crossover in dynamics in the transformation froma 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 slopethat approaches an asymptotic value for R/L ≫ 1. The value of D(t) extrapolated to t = 0, dependsonly upon the dimensionless conductance g for R/L ≪ 1 and upon kl

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