| This dissertation addresses the delicate problem of aging in complex systems characterized by non-Poissonian statistics.; With reference to a generic two-states system interacting with a bath it is shown that, to properly describe the evolution of such a system within the formalism of the continuous time random walk (CTRW), it has to be taken into account that, if the system is prepared at time t = 0 and the observation of the system starts at a later time t a > 0, the distribution of the first sojourn times in each of the two states depends on ta, the age of the system.; It is shown that this aging property in the fractional derivative formalism forces to introduce a fractional index depending on time. It is shown also that, when a stationary condition exists, the Onsager regression principle is fulfilled only if the system is aged and consequently if an infinitely aged distribution for the first sojourn times is adopted in the CTRW formalism used to describe the system itself.; This dissertation, as final result, shows how to extend to the non-Poisson case the Kubo Anderson (KA) lineshape theory, so as to turn it into a theoretical tool adequate to describe the time evolution of the absorption and emission spectra of CdSe quantum dots. The fluorescence emission of these single nanocrystals exhibits interesting intermittent behavior, namely, a sequence of "light on" and "light off" states, departing from Poisson statistics. Taking aging into account an exact analytical treatment is derived to calculate the spectrum. In the regime fitting experimental data this final result implies that the spectrum of the "blinking" quantum dots must age forever. |
