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We consider the phenomenon of weak localization of a short wave pulse in aquasi-1D disordered waveguide. We show that the long-time decay of the averagetransmission coefficient is not purely exponential, in contradiction withpredictions of the diffusion theory. The diffusion theory breaks downcompletely for times exceeding the Heisenberg time. We also study the survivalprobability of a quantum particle in a disordered waveguide and compare ourresults with previous calculations using the super-symmetric nonlinear sigmamodel.

Weak Localization of Short Pulses in Disordered Waveguides