Transporte quântico sobre redes do tipo dendrímero e redes livres de escala

Abstract

We study quantum transport on different complex networks by using continuous-time quantum walks (CTQWs). In this model the quantum transport is completely solved by determining all eigenvalues and eigenvectors of the connectivity matrix. For comparison reasons we have also investigated the classical transport through continuous-time random walks (CTRWs) model. The quantum walks (QWs) technique is a powerful tool in the analysis of transport phenomena. One method to monitor the efficiency of quantum transport is through the exact and the average return probabilities. First, we have implemented the CTQW model to transport on multilayer dendrimer networks (RMTDs). In order to overcome the localization effects, we have chosen to stack many dendrimer networks on top of each and connecting them by links between nodes from the neighboring layers. We have added new links (intraconnections) between vertices from the same generation with the probability parameter p. We have removed links (interconnections) between vertices from the neighboring layers with probability 1 − q. The quantum transport is investigated by numerical combinations of these two parameters. For these networks a proper choice of these parameters provides a greater efficiency by several orders of magnitude. We have found something peculiar: the highest efficiency is reached for the following values: q ≈ 0.9 and p ≈ 0.9. Thus, the best transport is obtained when is missing a single intra- and interconnection. Then, we have used the CTQW model on generalized scale-free networks (GSFNs). Such networks are a non-trivial mixture between linear segments and starlike networks. Regarding the quantum transport on GSFNs, we have noticed a interplay between strong localization effects, due to the the starlike segments, and a good spreading, due to the linear segments. We have shown that the quantum transport on GSFNs can be improved by varying two modularity parameters: the maximum and the minimum degree allowed for all nodes of the network. We have identified the same quantum efficiency for different combinations of the network’s construction parameters, which correspond to different topologies.