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The ensemble averaged power scattered in and out of lossless chaotic cavitiesdecays as a power law in time for large times. In the case of a pulse with afinite duration, the power scattered from a single realization of a cavityclosely tracks the power law ensemble decay initially, but eventuallytransitions to an exponential decay. In this paper, we explore the nature ofthis transition in the case of coupling to a single port. We find that for agiven pulse shape, the properties of the transition are universal if time isproperly normalized. We define the crossover time to be the time at which thedeviations from the mean of the reflected power in individual realizationsbecome comparable to the mean reflected power. We demonstrate numerically that,for randomly chosen cavity realizations and given pulse shapes, the probabilitydistribution function of reflected power depends only on time, normalized tothis crossover time.

Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay