  The ensemble averaged power scattered in and out of lossless chaotic cavities
decays as a power law in time for large times. In the case of a pulse with a
finite duration, the power scattered from a single realization of a cavity
closely tracks the power law ensemble decay initially, but eventually
transitions to an exponential decay. In this paper, we explore the nature of
this transition in the case of coupling to a single port. We find that for a
given pulse shape, the properties of the transition are universal if time is
properly normalized. We define the crossover time to be the time at which the
deviations from the mean of the reflected power in individual realizations
become comparable to the mean reflected power. We demonstrate numerically that,
for randomly chosen cavity realizations and given pulse shapes, the probability
distribution function of reflected power depends only on time, normalized to
this crossover time.
