Statistics of Wave Dynamics in Random Media

We measure the joint distribution of the energy transmission coefficient ${\varepsilon }_{\mathrm{ab}}$ and the single channel delay time ${\tau }_{\mathrm{ab}}$ for microwave radiation propagating through a random medium in the limit of zero pulse bandwidth. For fixed ${\varepsilon }_{\mathrm{ab}}$ the distribution of ${\tau }_{\mathrm{ab}}$ is Gaussian with variance inversely proportional to ${\varepsilon }_{\mathrm{ab}}$. In contradistinction to ${\tau }_{\mathrm{ab}}$, the dynamic matrix element ${\varepsilon }_{\mathrm{ab}}{\tau }_{\mathrm{ab}}$ has substantial long-range correlation with frequency shift. We present a new dynamic theory for a Gaussian process, which is in excellent agreement with experiment.