Exact analytical results for quantum walks on star graph
Xinping Xu
TL;DR
This paper derives exact analytical expressions for quantum walks on star graphs, revealing perfect revivals and localization, and showing equivalence to complete graph transport when starting at the center.
Contribution
It provides the first exact solutions for quantum walks on star graphs, highlighting unique transport properties and their relation to complete graphs.
Findings
Quantum walks exhibit perfect revivals.
Strong localization occurs on the initial node.
Transport from the center mimics complete graph behavior.
Abstract
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.
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