Coherent transport on Apollonian networks and continuous-time quantum walks

TL;DR

This paper investigates how quantum exciton transport behaves on Apollonian networks using continuous-time quantum walks, revealing dependence on initial nodes, partial revivals in larger networks, and differences from classical transport.

Contribution

It provides a detailed analysis of quantum transport dynamics on Apollonian networks, highlighting the effects of network size and initial conditions on transport efficiency and revival phenomena.

Findings

Perfect revivals in small networks with central initial excitation

Partial revivals in larger networks

Quantum transport favors initial nodes with low transition probabilities elsewhere

Abstract

We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks less than the second generation the coherent transport shows perfect revivals when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.