We investigate the electron population dynamics in an ensemble of nearly
isolated insulating nanoparticles, each nanoparticle modeled as an electronic
two-level system coupled to a single vibrational mode. We find that at short
times the ensemble-averaged excited-state population oscillates but has a
decaying envelope. At long times, the oscillations become purely sinusoidal
about a ``plateau'' population, with a frequency determined by the
electron-phonon interaction strength, and with an envelope that decays
algebraically as t^-{1/2} We use this theory to predict electron-phonon
dynamics in an ensemble of Y_2 O_3 nanoparticles.Comment: 11 pages, 3 figure