Accelerated diffusion by chaotic fluctuation in probability in photoexcitation transfer system

Abstract: We report a new accelerated diffusion phenomenon that is produced by a one-dimensional ran- dom walk in which the flight probability to one of the two directions (i.e., bias) oscillates dynam- ically in periodic, quasiperiodic, and chaotic manners. The probability oscillation dynamics can be physically observed in nanoscale photoexcitation transfer in a quantum-dot network, where the existence probability of an exciton at the bottom energy level of a quantum dot fluctuates dif- ferently with a parameter setting. We evaluate the ensemble average of the time-averaged mean square displacement (ETMSD) of the time series obtained from the quantum-dot network model that generates various oscillatory behaviors because the ETMSD exhibits characteristic changes depending on the fluctuating bias; in the case of normal diffusion, the asymptotic behavior of the ETMSD is proportional to the time (i.e., a linear growth function), whereas it grows nonlinearly with an exponent greater than 1 in the case of superdiffusion. We find that the diffusion can be accelerated significantly when the fluctuating bias is characterized as weak chaos owing to the transient nonstationarity of its biases, in which the spectrum contains high power at low frequen- cies. By introducing a simplified model of our random walk, which exhibits superdiffusion as well as normal diffusion, we explain the mechanism of the accelerated diffusion by analyzing the mean square displacement.