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arXiv · 0705.1608

Quantum transport on small-world networks: A continuous-time quantum walk approach

Oliver Muelken·Volker Pernice·Alexander Blumen
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Abstract

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks and we evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that the limiting value of the transition probability is reached very quickly; second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.

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Oliver Muelken, Volker Pernice, Alexander Blumen. 2007-11-30. Quantum transport on small-world networks: A continuous-time quantum walk approach. https://doi.org/10.1103/physreve.76.051125

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