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

TL;DR

This paper investigates quantum transport of excitons on small-world networks using continuous-time quantum walks, revealing rapid transport without full network equipartition, especially at higher bond densities.

Contribution

It introduces a quantum walk model for exciton transport on small-world networks and numerically analyzes the dynamics, highlighting the speed and localization effects.

Findings

Transport is very fast for large B

Transition probability reaches equilibrium quickly

Exciton tends to remain near initial node

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.