The effects of anomalous diffusion on power-law blinking statistics of CdSe nanorods

In this study of fluorescence blinking statistics for nanorods, we present a diffusion-controlled reaction model that leads to a more general formula: t(-m) exp[-(Gammat)(n)]. This formula describes a short-time power law with a crossover to a stretched exponential decay at later times. Based on quantum Brownian motion for a coupled central harmonic oscillator coupled to heat bath oscillators, we show that the position distribution follows anomalous diffusion with time-dependent diffusion coefficient and drift coefficient. The first and the second moments of the energy fluctuations are shown to be related to the exponent m and n for the blinking statistics.