A mechanism involving diffusion-controlled electron transfer processes in Debye and non-Debye dielectric media is proposed to elucidate the power-law distribution for the lifetime of a blinking quantum dot. This model leads to two complementary regimes of power law with a sum of the exponents equal to 2, and to a specific value for the exponent in terms of a distribution of the diffusion correlation times. It also links the exponential bending tail with energetic and kinetic parameters. DOI: 10.1103/PhysRevLett.95.107401 PACS numbers: 78.67.Bf, 73.21.La, 73.63.Kv, 78.67.Hc Recent advances in nanoscience and nanotechnology and their potential applications have generated wide interest. The development of techniques in probing single molecules has provided a tool to study its intrinsic properties and its interaction with the surroundings. One of the unusual phenomena observed in nanoparticles is fluorescence intermittency of quantum dots and the power-law statistics for the duration time for the ''on'' an ''off'' events [1][2][3][4][5][6][7][8][9][10]. Supplementing previous theoretical studies [6,7,[11][12][13][14][15][16]], a mechanism is provided in this Letter to elucidate these phenomena. This model involves diffusioncontrolled charge transfer processes in energy or configuration space [17,18]. For fast diffusion, the model yields the well-known simple exponential decay. However, in the regime of slow diffusion, the model leads naturally to a power-law behavior. To be more general, we consider anomalous diffusion in a non-Debye dielectric medium with a distribution of diffusion correlation times. There exists in the literature two approaches, partial ordering prescription (POP) with a time-dependent but nonretarded diffusion coefficient, and chronological ordering prescription (COP) with convolution of a time-retarded diffusion kernel [19]. POP is more commonly used in treating electron transfer reactions [20], These diffusion-controlled reaction models provide physical insight into the specific value of the exponent, a reason for the bending tail at longer times, and the connection of the bending factor to the activation energy of the electron transfer rate constant.In this work, one models stochastic processes in the energy or configuration space that represent the fluctuating interactions of a probe (a single molecule or a quantum dot) with its surrounding heat bath (supporting substrate or anchored organic molecules). We consider a POP type 1D non-Markovian equation, with a population sink at the potential energy crossing (Q Q c ) between U 1 Q for the ''light'' state j1i and U 2 Q for the ''dark'' state j2i. One hasOne can obtain the Green function for sink-free diffusion in a harmonic potential q 2 =2 as [20]where the diffusion constant D k t is related to the dielectric response function s and the dielectric permittivity " s by [20]For a Debye medium CD . At times t much longer than the diffusion correlation time, however, 2 t becomes a constant as the system approaches thermal equilibrium. The asym...