Efeito Parrondo em caminhadas quânticas em tempo contínuo

Abstract

The continuous-time quantum walks are dynamics of particles in networks, with various applications that involve transport. From the studies of physical phenomena, Juan M. R. Parrondo elaborated a mechanism that presents a paradoxical result: the alternation between two losing games might yield positive results. This mechanism has been widely applied in diverse areas of knowledge, including quantum walks. However, this effect had been documented in the literature only for discrete-time quantum walks. This work presents, for the first time, the detection of this paradox in continuous-time quantum walks, which, unlike other dynamics, do not use operators on coin states. Furthermore, the protocol aims to improve particle propagation, in contrast to recent developments that present a combination of unfavorable setups for achieving positive results or arrangements that manipulate probability distribution asymmetry. Therefore, this thesis presents an introduction to quantum walks; the consequences of the addition of defects, which were later used for the analysis of Parrondo's mechanism in this dynamic; Parrondo's paradox, and the historical context and application in which it was utilized; the mechanism of the Parrondo effect in the present dynamic, which transforms the scenario of impaired propagation by defects into one that surpasses the defect-free case; with an analysis for both the presence and absence of the effect. It turns out that the mechanism presented positive results regarding its proposal, clearly demonstrating the behavior presented in a probability distribution of dynamics with the effect. Once the discussions were presented related to periodic alternation cases were presented, the work was extended with studies of aperiodic alternations, thus expanding the possibility of new methods related to the control of propagations in continuous-time quantum walks.