  Following recent experiments on power law blinking behavior of single
nano-crystals, we calculate two-time intensity correlation functions
<I(t)I(t+t')> for these systems. We use a simple two state (on and off)
stochastic model to describe the dynamics. We classify possible behaviors of
the correlation function and show that aging, e.g., dependence of the
correlation function on age of process t, is obtained for classes of the on
time and off time distributions relevant to experimental situation. Analytical
asymptotic scaling behaviors of the intensity correlation in the double time t
and t' domain are obtained. In the scaling limit <I(t)I(t+t')> --> h(x), where
four classes of behaviors are found: (i) finite averaged on and off times x=t'
(standard behavior) (ii) on and off times with identical power law behaviors
x=t/t' (case relevant for capped nano-crystals). (iii) exponential on times and
power law off times x=tt' (case relevant for uncapped nano-crystals). (iv) For
defected off time distribution we also find x=t+t' . Origin of aging behavior
is explained based on simple diffusion model. We argue that the diffusion
controlled reaction A+B <--> AB, when followed on a single particle level
exhibits aging behavior.
