  We study the coherent exciton transport on Apollonian networks generated by
simple iterative rules. The coherent exciton dynamics is modeled by
continuous-time quantum walks and we calculate the transition probabilities
between two nodes of the networks. We find that the transport depends on the
initial nodes of the excitation. For networks less than the second generation
the coherent transport shows perfect revivals when the initial excitation
starts at the central node. For networks of higher generation, the transport
only shows partial revivals. Moreover, we find that the excitation is most
likely to be found at the initial nodes while the coherent transport to other
nodes has a very low probability. In the long time limit, the transition
probabilities show characteristic patterns with identical values of limiting
probabilities. Finally, the dynamics of quantum transport are compared with the
classical transport modeled by continuous-time random walks.
