Caminhadas Quânticas de Tempo Contínuo: um tratamento na Rede Dendrímero Modificado

Abstract

Quantum Random Walks find, in various areas of science, a range of problems in which they can be applied. They establish the basis for modeling difierent random phenomena that occur in the real world. In 1993, Aharonov et al. propose a model for these quantum walks, the so-called Discrete Quantum Random Walks, or Coin Model, due to the fact that the dynamics in this framework requires the introduction of an internal degree of freedom (coin), which serves as orientation parameter for the walk. Another way of dealing with the problem was proposed by Farhi and Gutmann in 1998, the socalled Continuous-time Quantum Walks (CTQW, in English). In this model the time is considered as a continuous varriable, although thw walk occurs in the discrete position space. In our work we focus on the continuous-time model (CTQW), applied to dendrimers (or Cayley tree), with some modifications; more precise, by using a probability parameter p, we add new links between nodes from the same generation. The newly created networks will be called by Modified Dendrimers or Modified Spiderweb Networks (Spidernets). Our main interest is to study the quantum transport on these new networks. To do this, we will calculate the eficiency of quantum transport on these networks using the exact quantum probabilities to return and their averages. By doing this, we notice an increase of the quantum eficiency and we observe that for almost all the generation numbers the maximum value is encountered for p ~0:9.