Transporte quântico em redes hexagonais

Abstract

The quantum walk is the quantum analog of the random walk, and is divided into two models: the discrete-time and the continuous-time models. In this work, the continuous-time model was used to analyze the average return probability and its average value over time in graphene and fullerene networks. These quantities are determined from the eigenvalues and eigenvectors of the Laplacian matrix. For the graphene structures, as we reduce the number of hexagons along the x direction, the transport efficiency decreases. Moreover, this loss also occurs when we have a smaller number of vertices. Therefore, the most efficient network was the graphene with 17 hexagonal faces along x and 1 hexagonal face along y, and the most inefficient was fullerene C60.