Quantum transport on small-world networks: A continuous-time quantum walk approach
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.
Cite
@article{arxiv.0705.1608,
title = {Quantum transport on small-world networks: A continuous-time quantum walk approach},
author = {Oliver Muelken and Volker Pernice and Alexander Blumen},
journal= {arXiv preprint arXiv:0705.1608},
year = {2009}
}