Electron-Phonon Dynamics in an Ensemble of Nearly Isolated Nanoparticles

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.