Spectral diffusion in a one-dimensional percolation model

Spectral diffusion on a one-dimensional chain with a random distribution of interruptions is considered. An exact solution for the time decay of the initial excitation is computed. The solution exhibits an exponential behavior initially, diffusion ($t^{\frac{-1\mathrm{}}{2}}$) behavior at intermediate times, and a long time decay $\sim \exp [-{\left(\lambda t\right)}^{\frac{1}{3}}]$. The relationship of this problem to the vibrating chain with some infinite masses, and to a related band-structure problem, is discussed. The possibility of observing the predicted behavior in fluorescent-line-narrowing experiments is also discussed, and some limits on the relevant parameters are given.