  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.
