In this thesis, we investigate the coherent scattering of light propagating in a random medium. We are interested in phenomena like the super- and subradiance and Anderson localization that are related to waves interferences and spatial disorder. However, the fundamental difference between subradiance and Anderson localization still needs to be clarified. This thesis gives new elements for the understanding of these phenomena and we present a new method to observe Anderson localization. A mean-field model that does not contain disorder is developed, and we show that super- and subradiance do not require disorder whereas Anderson localization does. In this theoretical work, the coupling between the light and many atoms is reduced to a coupling matrix between the atoms by tracing over the degrees of freedom of the light, which results in a linear problem for the atomic dipoles. The study of the eigenvalues and eigenmodes of this matrix then allows to determine the super- and subradiant modes, and to probe the Anderson localization phase transition with a scaling analysis. Furthermore, the link to the experiment is realized by showing that the intensity fluctuations present an increase at the localization transition. The system is studied in the steady-state regime when the medium is continuously charged by a laser until reaches a stationary regime, and the decay dynamics, when the laser is switched off, so the cloud releases the energy stored. Finally, we present a preliminary work that shows that the diagonal disorder might be a good strategy to reach Anderson localization. / Nesta tese, investigamos o espalhamento coerente de luz propagando em um meio aleatório. Estamos interessados em fenômenos como superradiância, subradiância e localização de Anderson, os quais estão relacionados com interferências de ondas e desordem espacial. No entanto, as diferenças fundamentais entre subradiância e localização de Anderson ainda precisam ser esclarecidas. Esta tese traz novos elementos na compreensão destes fenômenos e apresentamos um novo método para observar a localização de Anderson. Neste trabalho teórico, estudamos os autovalores e os automodos de uma matriz de acoplamento que permite extrair modos super- e subradiantes, e exibem uma transição de fase de localização de Anderson através de uma análise de escalamento. Além disso, a conexão com o experimento é feita através da intensidade irradiada pela nuvem em todas as direções. Distinguimos dois casos: o regime de estado estacionário, quando o meio é continuamente excitado por um laser e alcança um regime estacionário; e o caso dinâmico, onde o laser é desligado e a nuvem libera a energia armazenada. Desenvolvemos um modelo de campo médio que não inclui desordem, e mostramos que super- e subradiância não precisam da desordem para existir, ao contrário da localização de Anderson. Mostramos também que podemos observar uma transição de fase de localização de Anderson na estatística da intensidade. Finalmente, apresentamos um trabalho preliminar que mostra que a desordem diagonal pode ser uma boa estratégia para alcançar a localização de Anderson.

Orientador: Antonio Vidiella Barranco / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T14:05:56Z (GMT). No. of bitstreams: 1 Roque_ThalesFigueiredo_D.pdf: 3246905 bytes, checksum: 13e2147eea29b73345cec6df9138b5a1 (MD5) Previous issue date: 2017 / Resumo: Os sistemas optomecânicos são sistemas físicos onde a radiação interage com graus de liberdade mecânicos por meio da pressão de radiação. Estes sistemas destacam-se pela flexibilidade e pelo alto grau de controle sobre a interação optomecânica. Nesta tese, nós apresentamos um estudo teórico acerca dos sistemas optomecânicos, o qual pode ser dividido em duas partes: a primeira parte se dedica ao uso de sistemas optomecânicos na geração de estados não clássicos, e a segunda parte se dedica ao estudo da localização de Anderson em redes optomecânicas. Na primeira parte, nós estudamos, primeiramente, a geração de estados da radiação com estatística sub-Poissoniana no regime quântico não linear. Este tópico já havia sido estudado anteriormente em um sistema convencional composto por uma cavidade ótica acoplada a um oscilador mecânico. Neste trabalho, consideramos um sistema onde duas cavidades óticas interagem com um único oscilador mecânico. Nós mostramos que o sistema estudado permite a geração de estados com estatística sub-Poissoniana significativamente mais acentuada do que o sistema convencional. Além disso, os estados gerados são mais robustos com respeito ao ruído térmico do ambiente. Em seguida, estudamos a geração de estados estacionários comprimidos do oscilador mecânico em sistemas optomecânicos quadráticos operando no regime quântico linear. Nós mostramos que, bombeando a cavidade ótica com \textit{lasers} com frequências e amplitudes específicas, é possível gerar estados estacionários comprimidos do oscilador mecânico. Na segunda parte, nós estudamos a localização de Anderson em redes optomecânicas desordenadas. Redes optomecânicas são arranjos espacialmente ordenados de inúmeros modos óticos e mecânicos que interagem entre si por meio do acoplamento optomecânico. Em um cenário realista, devido a imprecisões na fabricação deste sistema, os parâmetros seriam desordenados. Nossos resultados mostram que os autoestados deste sistema são exponencialmente localizados. Além disso, observamos a existência de dois regimes de operação em redes optomecânicas desordenadas: o regime de acoplamento fraco e o regime de acoplamento forte. A transição entre estes dois regimes apresenta características não triviais que poderiam ser utilizadas para detectar experimentalmente a localização nestas estruturas. Nós estudamos também a dinâmica clássica de redes optomecânicas desordenadas no regime instável. Este é um tópico bastante desafiador, uma vez que a dinâmica é essencialmente não linear neste regime. Nós mostramos que, em um regime de parâmetros específico, é possível utilizar a aproximação linear para tempos curtos, e os resultados desta aproximação fornecem importantes informações sobre a dinâmica não linear. Nós ainda analisamos brevemente a emergência de comportamento caótico neste regime / Abstract: Optomechanical systems are systems in which radiation interacts with mechanical degrees of freedom via radiation pressure. These systems are well known for allowing great flexibility and high control over the optomechanical interaction. In this thesis, we present a theoretical investigation about optomechanical systems. This investigation can be divided in two parts: the first part is devoted to the generation of nonclassical states in optomechanical systems, and the second part is devoted to the study of Anderson localization in optomechanical arrays. In the first part, we study, firstly, the generation of optical sub-Poissonian states in the quantum nonlinear regime. This topic has been previously investigated in a conventional optomechanical system with one optical cavity coupled to one mechanical oscillator. Here, we investigate a system with two optical cavities coupled to one mechanical oscillator. We show that our system allows the generation of stronger sub-Poissonian states in comparison with the conventional system. In addition, the states generated in our system are more robust against thermal noise. Next, we investigate the generation of squeezed steady states of the mechanical oscillator in a quadratic optomechanical system operating in the quantum linear regime. We show that, if the optical cavity is pumped by lasers with specific frequencies and amplitudes, it is possible to generate such states. In the second part, we investigate Anderson localization in disordered optomechanical arrays. Optomechanical arrays are periodic arrays of optical and mechanical modes, which interact with each other via optomechanical coupling. In a realistic scenario, due to imprecisions in the fabrication of such a structure, the parameters of the system will be disordered. We show that the eigenstates in this system are exponentially localized. Furthermore, we show the existence of two regimes in disordered optomechanical arrays: the weak coupling regime and the strong coupling regime. The transition between these regimes displays nontrivial features that could be used to detect localization experimentally. We study also the classical dynamics of disordered optomechanical arrays in the unstable regime. This is a very challenging topic, since the unstable regime is essentially nonlinear. We show that, for a specific regime of parameters, it is possible to use the linear approximation for small times, and the linear results give us important informations about the nonlinear dynamics. We analyze briefly the emergence of chaotic behavior in the regime / Doutorado / Física / Doutor em Ciências / 2012/10476-0 / FAPESP

Nesta dissertação, apresentamos uma aplicação simples de RMN de 1H no domínio do tempo (TD-NMR) de baixo campo para caracterização de dinâmica molecular variando do regime intermediário ao rápido. O método se baseia no filtro dipolar seguido da aplicação do Mixed Magic Sandwich Echo(MSE), o qual denominamos DF-MSE. O filtro dipolar suprime os sinais oriundo de segmentos com mobilidade abaixo de kHz, de modo que somente segmentos móveis sejam detectados. Assim, a dependência com a temperatura da intensidade do sinal mostra diretamente a temperatura em que movimentos moleculares ocorrem ao atingirem taxas maiores que kHz. Para que não ocorra variação da intensidade com a temperatura, mas somente pelos movimentos moleculares, os sinais são normalizados por uma intensidade de referência obtida pela aquisição de DF-MSE sem aplicação do filtro dipolar. A intensidade normalizada DF-MSE pode ser descrita adequadamente por uma expressão analítica baseada na aproximação de Anderson-Weiss, de forma a permitir que parâmetros de ativação de movimentos sejam avaliados. Ademais, também propomos um método baseado na diferença entre sinais DF-MSE normalizados adquiridos com tempos de filtro distintos, permitindo assim quantificar a largura da ditribuição de tempos de correlação de uma forma independente. A aplicação geral foi testada de forma bem sucedida em polímeros monofásicos e multifásicos. De fato, o método apresentado é um prosseguimento da análise feita pelo MSE já presente na literatura, porém sondando movimentos mais rápidos e com uma forma aprimorada para avaliação de heterogeneidades de movimento. / In this dissertation, we present a simple NMR approach for characterizing intermediate to fast regime molecular dynamics using 1H time-domain NMR (TD-NMR) at low magnetic field. The method is based on a dipolar filter followed by a Mixed Magic Sandwich Echo and FID acquisition, which is symbolized DF-MSE. The dipolar filter suppresses the signals of segments presenting sub kHz mobility, so only signals from mobile segments are detected. Thus, the temperature dependence of the signal intensities directly evidences the onset of molecular motions with rates higher than kHz. In order to avoid temperature variation of the signal intensities other than that due to motions, the signals are normalized by a reference intensity obtained in a DF-MSE acquisition without the dipolar filter. The normalized DF-MSE intensity can be well described by an analytical function based on the Anderson-Weiss approach, so the activation parameters of the motion can be evaluated. Furthermore, we also propose a method based on the difference between normalized DF-MSE signals acquired with different dipolar filter times, which provide evaluation of the width of the distribution of correlation times in an independent fashion. The general approach was successfully tested in single and multiphase polymer systems. Indeed, the presented method is a follow up of the MSE analysis previously reported, but probing faster motions and with an improved way of evaluating the motion heterogeneities.

Neste trabalho, realizamos o estudo da transição metal-isolante e da localização de Anderson na liga de Pb1-xEuxTe do tipo p para x variando de 0 até 0.1. As propriedades de transporte nessa liga (mobilidade, concentração de portadores e resistividade elétrica) foram obtidas utilizando o método de caracterização elétrica por efeito Hall entre as temperaturas de 300 K e 10 K. Nessa região de temperatura, foi possível observar uma transição metal-isolante para x > 0.05. Verificamos que a transição é do tipo Anderson e ocorre devido à desordem presente na liga. Para baixas temperaturas (T < 10 K) e em amostras com x > 0.01, verificamos a presença de magnetorresistência positiva e negativa aplicando campos magnéticos de até 11T. Nas amostras metálicas, a presença de magnetorresistência negativa é causada pelo efeito conhecido como localização de Anderson (efeito de interferência quântica construtiva entre as funções de onda) e a presença de magnetorresistência positiva é causada, principalmente, pelo acoplamento spin-órbita, e é chamada de antilocalização. Nas amostras isolantes, a magnetorresistência negativa é originada pelo efeito Zeeman enquanto que a magnetoresistência positiva é causada pela redução do comprimento de localização. Assim, os valores positivos e negativos da magnetoresistência têm origens diferentes dependendo do regime de condução (metálicoou isolante). Por esse motivo, o estudo dos resultados experimentais apresentados nesse trabalho foi dividido em duas partes: uma parte que trata as amostras metálicas (região de desordem fraca) e outra parte para as amostras isolantes (região de desordem forte). A partir dessa divisão, e utilizando os modelos teóricos disponíveis na literatura, foi possível fazer uma análise das medidas experimentais de magnetotransporte. Como resultado, identificamos os principais mecanismos de interação (espalhamento inelástico, efeito Zeeman, acoplamento spin-órbita, etc.) que interferem no transporte e nos efeitos de localização e antilocalização. / In this work, we investigated Anderson localization and the metal-insulator transition in p-type films of Pb1-xEuxTe for x varying from 0 up to 0.1. The transport properties of this alloy (mobility, carrier concentration and electrical resistivity) were obtained using the Hall method of electrical caracterization for temperatures ranging from 300 K down to 10 K. In this temperature range, it was possible to observe a metal-insulator transition for x > 0:05. The transition is of the Anderson type and is due to the disorder present in the alloy. For low temperatures (T < 10 K) and for samples with x > 0.01, we observed positive and negative magnetoresistance for magnetic fields up to 11 T. For metallic samples, the negative magnetoresistance originates from Anderson’s localization (constructive quantum interference effect between the wave functions) while positive magnetoresistence is caused, mainly, by the spin-orbit scattering, and it is called antilocalization. For insulating samples, negative magnetoresistance is originated from the Zeeman effect while positive magnetoresistance is caused by the localization length reduction. Therefore, positive and negative magnetoresistance values have different origins depending on the conduction regime (metallic or insulating). For this reason, our experimental investigation, presented in this work, was separated into two parts: the first one treats the metallic samples (weak-disorder regime) and the other treats the insulating samples (strong-disorder regime). From this division, and using available theoretical models, it was possible to analyze the magnetotransport experimental measurements. As a result, we identify the main interaction mechanisms (inelastic scattering, Zeeman effect, spin-orbit coupling, etc.) that interfere on the transport and localization and antilocalization effects.

In this thesis, the properties of nonlinear disordered one dimensional lattices is investigated. Part I gives an introduction to the phenomenon of Anderson Localization, the Discrete Nonlinear Schroedinger Equation and its properties as well as the generalization of this model by introducing the nonlinear index α. In Part II, the spreading behavior of initially localized states in large, disordered chains due to nonlinearity is studied. Therefore, different methods to measure localization are discussed and the structural entropy as a measure for the peak structure of probability distributions is introduced. Finally, the spreading exponent for several nonlinear indices is determined numerically and compared with analytical approximations. Part III deals with the thermalization in short disordered chains. First, the term thermalization and its application to the system in use is explained. Then, results of numerical simulations on this topic are presented where the focus lies especially on the energy dependence of the thermalization properties. A connection with so-called breathers is drawn. / In dieser Arbeit wird das Verhalten nichtlinearer Ketten mit Zufallspotential untersucht. Teil I enthaelt eine Einfuehrung in das Phaenomen der Anderson Lokalisierung, die Diskrete Nichtlineare Schroedinger Gleichung und ihren Eigenschaften sowie die verwendete Verallgemeinerung des Modells durch Einfuehrung eines Nichtlinearitaets-Indizes α. In Teil II wird das Ausbreitungsverhalten von lokalisierten Zustaenden in langen, ungeordneten Ketten durch die Nichtlinearitaet untersucht. Dazu werden zuerst verschiedene Lokalisierungsmaße besprochen und außerdem die strukturelle Entropie als Messgroeße der Peakstruktur eingefuehrt. Im Anschluss wird der Ausbreitungskoeffzient fuer verschiedene Nichtlinearitaets-Indizes bestimmt und mit analytischen Absch¨tzungen verglichen. Teil III behandelt schließlich die Thermalisierung in kurzen, ungeordneten Ketten. Dabei wird zuerst der Begriff Thermalisierung in dem verwendeten Zusammenhang erklaert. Danach erfolgt eine numerische Analyse von Thermalisierungseigenschaften lokalisierter Anfangszustaende, wobei die Energieabhaengigkeit besondere Beachtung genießt. Eine Verbindung mit sogenannten Breathers wird dargelegt.

The work in this thesis is motivated by the problem of localization of interacting particles. The qualitative investigation of Thouless-type arguments in Chap.~\ref{ch:interacting-particles} lead us to consider the question of competition between alternative propagation channels, a question which we studied in great detail in the form of a single particle problem with two parallel, coupled channels. The theory also naturally applies for the Anderson localization of hybrid particles such as polaritons. These systems have a common feature: Two or more propagating channels with parametrically different transport properties are coupled and compete with each other. The principal question is: What happens to the localization properties when a less localized lattice is coupled to a more localized one? Will the less localized lattice dominate the localization of the system or the more localized? The qualitative answer to this question depends on the dimensionality of the system. Correspondingly, we exactly solved the Anderson models on a two-leg ladder ($D=1$) and on a two-layer Bethe lattice (formally $D=\infty$). In one dimension, weak disorder has a strong localization effect. In the \emph{weak disorder limit} we have found that under \emph{resonance} conditions the localization lengths of two coupled chains are of the order of the localization length of the more localized, uncoupled leg. We may interpret this phenomenon as a manifestation of the fact that in one dimension the mean free path is the relevant length scale that sets the localization length. It is not surprising that the backscattering rate, and thus the ''worst'' leg of the chains determines the localization properties of a coupled system. If away from resonance the two legs are hardly affected by each other. However, the close relation (proportionality) between mean free path and localization length is special for one-dimensional systems. On coupled Bethe lattices, weak disorder is irrelevant to localization. The localization effect is significant only if the disorder is intermediate or strong. Therefore, resonance conditions, which require weak disorder as compared to the hopping, can not be achieved. In general, we found that the less disordered lattice is not affected much by the more disordered lattice in the presence of coupling, except in the case where the less disordered (delocalized) lattice is very close to the transition and the more disordered lattice is strongly localized, in which case the more disordered lattice can push the less disordered lattice to a localized phase. We believe that these trends persist in high dimensions ($D>2$) where the metal-insulator transition takes places at strong disorder. In two dimensions, the localization length becomes parametrically larger than the mean free path at weak disorder. However, since the proliferation of weak-localization and backscattering leads to complete localization (in the absence of special symmetries), we expect that a well propagating channel becomes more strongly localized upon resonant coupling to a more disordered channel, similarly as in one dimension. It might be interesting to investigate this numerically. Investigating the localization properties of few- or many-particle systems is more complicated. First, we should map an interacting Hamiltonian to the Anderson model in the few- many-particle Fock space [cf. Eq.~\ref{ipfham}]. Thereby, the interaction provides effective hopping among the Fock states. This hopping in Fock space can be organized into channels with rather different propagation characteristics [e.g. Fig.~\ref{four-par} for four particles], namely, faster channels and slower channels. According to our analysis, the slow channel dominates only if it is \emph{resonantly} coupled to the fast channel. If the two channels are away from resonance, the fast channel essentially dominates the localization properties. For the few-particle problems discussed in Chap.~\ref{ch:interacting-particles} we expect that the fast channel, that is, the hierarchical structure we predicted, dominates the delocalization of the interacting particles, since the resonance between the fast and slow channels should be an exception rather than a rule. At this stage, this remains a conjecture which needs to be tested further.

This project examines the effectiveness of a citizens' advisory committee initiated by the author to assist in the development of a bicycle facilities plan for Madison County, Indiana. A "ladder of citizen participation" was used to rank the level of citizen participation achieved. The MCCOG Bicycle Facility Plan was authored as part of the creative project is also studied in this project. Two components of the plan that were analyzed were the plan's success in meeting performance criteria, and the plan's approach in dealing with the question of separating bicycle traffic from auto traffic or integrating bicycles with auto traffic.This study finds that the participatory process is dynamic and that the level of citizen participation is variable and perhaps progressive. The plan was measured for meeting benchmarks of accessibility and continuity in its proposed routes. Local systems were found to have an integrated approach, while regional systems tend to have a nearly even mix of separated and integrated route systems. / Department of Urban Planning

This thesis has traced the development and demise of Allen Chapel Terrace Estates. Its purpose has been to identify why the project failed and presented alternative proposals for the reuse of the complex. This was done within the framework of actual funding possibilities which exist at the present time.The thesis was developed by presenting the project history, program characteristics, demographic information, demand and supply, project financing, and the reuse alternative suggestions. / Department of Urban Planning

Buildings can be built that use no energy from external power grids. They can be essentially carbon neutral in their environmental load, and they can be built and operated at fair market values. Although this may sound like a dream of the future, the World Business Council for Sustainable Development (WBCSD) is working toward making that dream a reality today. The Council announced on March 26, 2006 (Environment News Service) that it is forming an alliance of global companies to ensure that by 2050 all new buildings meet these standards.1The profession of architecture, at the beginning of the 21st century, finds itself in a position where architectural philosophies and methodologies must respond to the world changing events that are impacting our planet. This creative project outlines some of the methodologies used to create a carbon-neutral public library. Within a public library, architects respond to two of the primary concerns of this young century; the global need for a clean, livable planet and the proliferation of digital media and methods that are driving globalization as we are beginning to know it.The proposed new Union Township Branch of the Anderson Public Library seemed a logical subject for this Creative Project because much of the past work of our firm and much of my personal experience involved the design of public libraries. The carbon neutral concepts evolved gradually, after much study, and the goal of this creative project is that this particular library and many other sustainable libraries in the future will benefit from the concepts and methodologies outlined here, as those new buildings approach carbon neutrality. / Department of Architecture

This creative project has been initiated and researched out of the need for development of historic district guidelines for Anderson, Indiana's wonderous West Eighth Street and West Central Historic Districts. This study included the consultation, involvement and approval of the Anderson City Planning Department, the Anderson Historic Preservation Commission and district residents.In addition, this guideline document has intended to be used as a reference and resource tool in the legal development of district control of regulations and enforcement procedures. The purpose of this project has been to protect the integrity and maintain the character of Anderson's districts while providing education as to the importance and value of preserving our historical treasures. / Department of Urban Planning