Nonergodicity of blinking nanocrystals and other Lévy-walk processes

We investigate the nonergodic properties of blinking nanocrystals modeled by a Lévy-walk stochastic process. Using a nonergodic mean field approach we calculate the distribution functions of the time averaged intensity correlation function. We show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe ergodicity breaking in systems modeled by Lévy walks, for example, certain types of chaotic maps and spin dynamics to name a few.