Symmetry and Quantum Transport on Networks

Details Symmetry and Quantum Transport on Networks Symmetry and Quantum Transport on Networks

2011-04-04

arxiv.org/abs/1104.0596v1

International Journal of Quantum Information Vol. 8, No. 8 (2010) 1323-1335

Physics

Quantum Physics

18 pages, 20 figures

Scientific paper

We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition probabilities between two nodes of the network. We numerically show that there is a high probability to find the walker at the initial node for CTQWs on the underlying networks due to the interference phenomenon, even for long times. To get global information (independent of the starting node) about the transport efficiency, we average the return probability over all nodes of the network. We apply the decay rate and the asymptotic value of the average of the return probability to evaluate the transport efficiency. Our numerical results prove that the existence of the symmetry in the underlying networks makes quantum transport less efficient than the classical one. In addition, we find that the increasing of the symmetry of these networks decreases the efficiency of quantum transport on them.

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