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Motivated by recent experimental observations of power-law statistics both in spectral diffusion process and fluorescence intermittency of individual semiconductor nanocrystals (quantum dots), we consider two different but related problems: (a) a stochastic lineshape theory for the Kubo–Anderson oscillator whose frequency modulation follows power-law statistics and (b) photon counting statistics of quantum dots whose intensity fluctuation is characterized by power-law kinetics. In the first problem, we derive an analytical expression for the lineshape formula and find rich type of behaviors when compared with the standard theory. For example, new type of resonances and narrowing behavior have been found. We show that the lineshape is extremely sensitive to the way the system is prepared at time t=0 and discuss the problem of stationarity. In the second problem, we use semiclassical photon counting statistics to characterize the fluctuation of the photon counts emitted from quantum dots. We show that the photon counting statistics problem can be mapped onto a Le´vy walk process. We find unusually large fluctuations in the photon counts that have not been encountered previously. In particular, we show that Mandel’s Q parameter may increase in time even in the long time limit. [Copyright &y& Elsevier]

Fo¨rster–Dexter theory for excitation energy transfer (EET) is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation–bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed. [Copyright &y& Elsevier]