Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2018-05-03T12:34:24Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Danilo Cius.pdf: 2128036 bytes, checksum: 5b2c47a2a56fc484a69be66ca861ff21 (MD5) / Made available in DSpace on 2018-05-03T12:34:24Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Danilo Cius.pdf: 2128036 bytes, checksum: 5b2c47a2a56fc484a69be66ca861ff21 (MD5) Previous issue date: 2018-02-27 / Este trabalho tem como principal objetivo investigar a dinâmica de spin-1=2 no contexto de sistemas quânticos não-hermitianos. Propõe-se um modelo fenomenológico heurístico que inclui simetria dinâmica SL(2;C), cujo operador Hamiltoniano não-hermitiano efetivo de uma única partícula de dois níveis é empregado para simular a dinâmica coletiva de um ensemble de spin- 1=2. O modelo teórico é elaborado a partir da análise do decaimento da magnetização líquida em um experimento constituído de um ensemble de núcleos de 31P (com spin nuclear I = 1=2) de uma amostra de H3PO4, via técnica de Ressonância Magnética Nuclear. Verifica-se que as magnetizações experimentais evidenciam a validade do modelo teórico. / This work aims to investigating the dynamics of spin-1=2 in the context of non-Hermitian quantum systems. It is proposed a heuristic phenomenological model embedding SL(2;C) dynamical symmetry, whose the effective non-Hermitian Hamiltonian operator of a single particle is employed to mimic the damped dynamics of an ensemble of spin-1=2. The theorical model is built by the decay on net magnetization analysis in an experiment made up of an ensemble of 31P nuclei (spin I = 1=2) of H3PO4 sample by applying Nuclear Magnetic Resonance technique. It is verified that the experimental magnetizations emphasize the validity of the theoretical model.

Over the last decades, both band topology and Anderson transitions, as well as their interplay, have been well understood in the context of time-independent energy-conserved systems. This switches the research focus in this field from theoretical descriptions to experimental designs, realizations, and engineering. In such a background, time-dependent perturbations and coupling between quantum systems and environments become the main concern. Along this route, this dissertation first studies the properties of a Chern insulator, one of the simplest topological systems, under time-periodic disorder. We reveal that in certain cases disorder fully localizes the bulk, but surprisingly has a positive effect on the edge, propagating edge states exist throughout the full spectrum. Along this direction, we further explore disorder effects in a network model constructed by arrays of unitary scattering matrices. Here, we go beyond previous works and show that also the shape of network (lattice symmetries) is important. It will result in a new type of topological phase, known as a higher-order topological phase, in which the topological states of a d-dimensional system have a dimension less than (d − 1). Afterwards, we focus on a network model with gain and loss, which breaks energy conservation. Here, we find the system now exhibits a 'supermetal' behavior that surpasses the conventional ballistic transport for perfect metals. At the end of this dissertation, we perform a study on the non-Hermitian defect in time-periodic systems. Our study shows that a boundary defect, due to its non-Hermiticity, can stop the propagation of chiral edge states, which should otherwise be the most robust manifestations of topology in quantum systems.