Exact analytical results for quantum walks on star graph

In this paper, we study coherent exciton transport of continuous-time quantum walks on star graph. Exact analytical results of the transition probabilities are obtained by means of the Gram-Schmidt orthonormalization of the eigenstates. Our results show that the coherent exciton transport displays perfect revivals and strong localization on the initial node. When the initial excitation starts at the central node, the transport on star graph is equivalent to the transport on a complete graph of the same size.