Symmetry and Quantum Transport on Networks

TL;DR

This paper investigates how symmetry in finite networks affects classical and quantum transport processes, revealing that higher symmetry reduces quantum transport efficiency due to interference effects.

Contribution

It provides a comparative analysis of classical and quantum transport on symmetric networks, highlighting the impact of symmetry on quantum transport efficiency.

Findings

Quantum transport exhibits high return probability due to interference.

Symmetry in networks decreases quantum transport efficiency.

Classical transport is less affected by network symmetry.

Abstract

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.