  A novel route to the exponential trapping-time distribution within a
solidlike state in water clusters is described. We propose a simple homogeneous
network (SHN) model to investigate dynamics on the potential energy networks of
water clusters. In this model, it is shown that the trapping-time distribution
in a solidlike state follows the exponential distribution, whereas the
trapping-time distribution in local potential minima within the solidlike state
is not exponential. To confirm the exponential trapping-time distribution in a
solidlike state, we investigate water clusters, $($H${}_2$O$)_6$ and
$($H${}_2$O$)_{12}$, by molecular dynamics simulations. These clusters change
dynamically from solidlike to liquidlike state and vice versa. We find that the
probability density functions of trapping times in a solidlike state are
described by the exponential distribution whereas those of interevent times of
large fluctuations in potential energy within the solidlike state follow the
Weibull distributions. The results provide a clear evidence that transition
dynamics between solidlike and liquidlike states in water clusters are well
described by the SHN model, suggesting that the exponential trapping-time
distribution within a solidlike state originates from the homogeneous
connectivity in the potential energy network.
