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[pt] A GRAVE E GENERALIZADA VIOLAÇÃO DE DIREITOS HUMANOS: A PROTEÇÃO (INTER)NACIONAL DA PESSOA HUMANA E A CONSTRUÇÃO DA DEFINIÇÃO AMPLIADA DE REFUGIADA(O) NO BRASIL / [en] THE GROSS AND GENERALIZED VIOLATION OF HUMAN RIGHTS: THE (IN-TER)NATIONAL PROTECTION OF THE HUMAN PERSON AND THE CONSTRUCTION OF THE EXTENDED REFUGEE DEFINITION IN BRAZILADRIANA FERNANDES BASILIO 18 June 2021 (has links)
[pt] O presente trabalho realizou análise acerca do conceito de Grave e Genera-lizada Violação de Direitos Humanos (GGVDH), a fim de investigar quais são as fundações da definição ampliada de refugiado e como se deu a sua construção no Brasil. Através de pesquisa bibliográfica e documental, os dados usados nesta Dissertação de Mestrado foram coletados das seguintes fontes: teses, dissertações, livros e artigos; relatórios do governo, de organizações internacionais e não go-vernamentais; tratados, declarações e legislações. Esta dissertação buscou apre-sentar a arquitetura protetiva internacional da pessoa humana, investigando as conexões com os diversos mecanismos do Direito Internacional dos Direitos Hu-manos, suas complementaridades, seus regimes e aplicações regionais e nacionais para, então, explorar a trajetória do refúgio no Brasil não somente até a construção do conceito de GGVDH pelo governo, mas também no seu reconhecimento. Em um primeiro momento, deu-se a apresentação do arcabouço jurídico internacional, sua interdependência e relevância para a proteção humana, culminando na Decla-ração de Cartagena (1984) e seus processos revisionais. Posteriormente, desen-volveu-se o histórico brasileiro em matéria de refúgio, chegando ao período de redemocratização e incorporação do conceito de GGVDH pela Lei n° 9.474/1997. Por fim, passou-se à breve análise do reconhecimento de refúgio no Brasil por GGVDH, no intento de mapear o posicionamento do governo frente a essa defini-ção, sua aplicação e limitações, apontando algumas nuances e conclusões. / [en] The present study undertook an analysis about the concept of Gross and Generalized Violation of Human Rights (GGVDH), in an attempt to understand what the foundations of the extended definition of refugee are and how it has been constructed in Brazil. Through a bibliographic and documental research, the data used in this Master s Thesis was collected from the following sources: theses, dissertations, books and articles; reports from government, international and non-governmental organizations; treaties, declarations and legislation. This thesis sought to present the international protective architecture of the human person, investigating its connections with the various mechanisms of International Human Rights Law, their complementariness, regimes, regional and national applications to then, explore the refuge trajectory in Brazil, not only until the construction of the GGVDH concept by the government, but also its recognition. Initially, the international legal framework was presented, their interdependence and relevance to the human protection, culminating in the Cartagena Declaration (1984) and its revision processes. Subsequently, it demonstrated the Brazilian history in terms of refuge, up until the period of re-democratization and incorporation of the GGVDH concept by the Law n 9.474/1997. Finally, it presented a brief analysis of the refugee status recognition under GGVDH in Brazil, in an attempt to map the gov-ernment’s position in relation to this definition, its application and limitations, pointing out some nuances and conclusions.
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[pt] A PREVISIBILIDADE DAS TAXAS DE CRESCIMENTO DE EMPRESAS DE CAPITAL ABERTO LISTADAS NA BOVESPA NO PERÍODO 1994-2003 ATRAVÉS DE ÍNDICES DE VALOR / [en] THE PREDICABILITY OF GROWTH RATES OF COMPANIES LISTED AT BOVESPA IN THE PERIOD OF 1994-2003 USING VALUATION RATIOSPATRICIA HELENA GOES SEIZE 22 November 2005 (has links)
[pt] A busca por modelos de avaliação cada vez mais precisos
tem sido uma
preocupação permanente no âmbito das finanças
corporativas. No entanto, para
que estes modelos gerem bons resultados, é preciso que
estimativas do
comportamento futuro de contas como receitas, custos,
despesas e investimentos
estejam bem avaliadas. Dentro deste contexto se insere a
importância da previsão
das taxas de crescimento. Elas dependem de diversos
fatores, externos e internos à
empresa e que são, muitas vezes, de extrema complexidade.
Na tentativa de tornar
esta estimativa mais objetiva, o presente trabalho procura
avaliar a hipótese de que
índices de mercado bastante utilizados pelos analistas
financeiros, como preço de
mercado da ação-lucro, preço de mercado da ação-valor
patrimonial por ação e
preço de mercado da ação - vendas, são capazes de fornecer
indícios sobre o
comportamento futuro das contas receita bruta, EBITDA e
lucro operacional de
empresas listadas na Bolsa de Valores de São Paulo
(BOVESPA) durante o
período 1994-2003. Através do teste estatístico não-
paramétrico de Wilcoxon, o
estudo fornece indícios de que a variável preço de mercado
da ação - valor
patrimonial por ação possui valores maiores para empresas
de baixo crescimento e
menores para empresas de médio e alto crescimento. Para as
variáveis preço-lucro
e preço-vendas não se observam diferenças significativas
de valor entre os grupos
de baixo, médio ou alto crescimento. / [en] The search for more accurate evaluation models has been a
permanent activity
within the field of corporative finances. A successful
model must forecast, with a
high degree of confidence and accuracy, the future
behavior of incomes, costs,
expenditures and investments. Companies´ growth rates are
also important; they
depend on several internal and external factors and their
evaluation can be a very
complex task. Our work evaluates critically some valuation
ratios used by
financial analysts like: price-to-earnings, market-to-book
and price-to-sales ratios,
in order to obtain useful information about the following
itens future behavior:
Gross Revenue, EBITDA and Operating Profit of companies
listed at São Paulo
Stock Exchange (BOVESPA) during the period 1994-2003. The
Wilcoxon´s nonparametric
test suggests: an inverse relationship between the market-
to-book
index to the registered companies growth rate and no
noticeable relationship
between price-to-earnings ratios and price-to-sales ratios
to the same companies´
growth rate.
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Exact solutions for Schrodinger and Gross-Pitaevskii equations and their experimental applications.Bhalgamiya, Bhavika 12 May 2023 (has links) (PDF)
A prescription is given to obtain some exact results for certain external potentials �� (r) of the time-independent Gross-Pitaevskii and Schrodinger equations. The study motivation is the ability to program �� (r) experimentally in cold atom Bose-Einstein condensates. Rather than derive wavefunctions that are solutions for a given �� (r), we ask which �� (r) will have a given pdf (probability density function) �� (r). Several examples in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) are presented for well-known pdfs in the position space. Exact potentials with zero, one and two walls are obtained and explained in detail. Apart from position space, the method is also applicable to obtain exact solutions for the Time-independent Schr¨odinger equation (TISE) and Gross-Pitaevskii equation (GPeq) for pdfs in momentum space. For this, we derived the potentials which are generated from the pdfs of the hydrogen atom in the real space as well as in the momentum space.
However, the method was also extended for the time-dependent case. The prescription is also applicable to solve time-dependent pdfs. The aim is to find the ��(r, ��) which generates the pdf ��(r, ��). As a special case, we tested our method by studying the well known case for the Gaussian wave packet in 1D with zero potential ��(��, ��) = 0.
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Basinward Trends in Fluvial Architecture, Connectivity, and Reservoir Characterization of the Trail Member, Ericson Sandstone, Mesaverde Group in Wyoming, Utah, and Colorado, USAJolley, Chelsea Anne 01 June 2019 (has links)
The Late Cretaceous Trail Member of the Ericson Sandstone represents a regionally extensive fluvial system that transported sediments from the Sevier fold and thrust belt and Uinta Mountain uplift to the Western Interior Seaway. The Trail Member is a petroleum reservoir target that has unpredictable production rates due to the unknown behavior and connectivity of channel sandstones. The abundant outcrop, wellbore, and core data available allows for a comprehensive analysis of how the fluvial architecture, connectivity, and reservoir quality change along 65 km of depositional dip. Observations made at Flaming Gorge and Clay Basin (most landward field locations) suggest a highly mobile fluvial system that was influenced by both autogenic channel clustering and allogenic forcing. Evidence is seen for movement along the Sevier fold and thrust belt and early Laramide uplift of the Uinta Mountains. Specifically, three zones identify temporal tectonic changes throughout deposition of the Trail Member. The Upper and Lower Trail zones represent times of low accommodation as the fluvial system must avulse and move laterally to find available space. The Middle Trail zone represents a higher accommodation setting with internal autogenic channel clustering. This shows that on a finer timescale, autogenic processes control sediment distribution, while on a longer timescale, external drivers, specifically tectonics, control the distribution of sediment in the Trail fluvial system. Significant changes were observed within the Trail Member towards the basin. At Northern Colorado, lenticular, fluvial-dominated sands are still common, preserved organic and woody material, mud cracks, and increased bioturbation are observed that are not present elsewhere. The sandstone channels are slightly wider, have more common occurrences of low flow-regime sedimentary structures such as ripples and mud cracks, and appear to be more individually isolated with thin fine-grained material surrounding the channels. On a larger scale, photogrammetric analysis shows a rapid lateral change (0.3 km) from a sand-rich, channel-dominated expression to a mud-rich, channel-poor character. These observations suggest a lower energy fluvial system focused within a possible incised valley showing that the fluvial system is being influenced primarily by eustatic forces, rather than tectonics. Subsurface data from twelve wells located north of the Northern Colorado locality show a rapid (15 km) increase in thickness (97 m to 182 m) and decrease in net-to-gross (89.3% to 65.3%). Early subsidence of the Washakie sub-basin just east of the wells could account for the rapid increase in accommodation. Another possible explanation for the rapid thickness increase to the northeast could be the presence of an incised valley. These possibilities show the complexity of the environment within which the Trail Member fluvial system deposited sediments.
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The Impact of Emission Trading System on Economic Growth and Gross Fixed Capital Formation / Utsläppshandelns påverkan på ekonomisk tillväxt och investeringarWall, Hanna January 2022 (has links)
Policymakers' action of mitigating and slowing down the continued increase of carbon emission is a significant global priority. One way to internalise the negative externality of pollution is to put a price on greenhouse gases and use the market-based approach of emission trading systems. On the other hand, according to economic reasoning, pollution is an essential tool for economic development. This paper aims to investigate the economic effects of introducing the first international emission trading system of greenhouse gases, the EU emission trading system, by observing the economic growth and gross fixed capital formation. Mankiw, Romer, and Wiel's (1992) theory is utilised in this study and based on cross-country and cross-state panel data between 1999-2012, an empirical analysis using the fixed effects model was followed. The finding shows that the EU emission trading system has a negative effect on the growth of real gross domestic product per capita compared to states and countries not participating in an emission trading system. In addition, the first phase results having a positive effect and the second phase has a negative effect on the economic growth compared to states and countries not participating in an emission trading system. There is no statistical evidence of the effect on gross fixed capital formation as a percentage share of GDP. Organisations can use the findings to decide whether developing countries can afford the consequence of an implemented emission trading system since it tends to slow down growth. However, further research needs to consider the effect of the financial crisis of 2008 and the interpretation of the EU emission trading scheme.
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Geometric Integrators for Schrödinger EquationsBader, Philipp Karl-Heinz 11 July 2014 (has links)
The celebrated Schrödinger equation is the key to understanding the dynamics of
quantum mechanical particles and comes in a variety of forms. Its numerical solution
poses numerous challenges, some of which are addressed in this work.
Arguably the most important problem in quantum mechanics is the so-called harmonic
oscillator due to its good approximation properties for trapping potentials. In
Chapter 2, an algebraic correspondence-technique is introduced and applied to construct
efficient splitting algorithms, based solely on fast Fourier transforms, which
solve quadratic potentials in any number of dimensions exactly - including the important
case of rotating particles and non-autonomous trappings after averaging by Magnus
expansions. The results are shown to transfer smoothly to the Gross-Pitaevskii
equation in Chapter 3. Additionally, the notion of modified nonlinear potentials is
introduced and it is shown how to efficiently compute them using Fourier transforms.
It is shown how to apply complex coefficient splittings to this nonlinear equation and
numerical results corroborate the findings.
In the semiclassical limit, the evolution operator becomes highly oscillatory and standard
splitting methods suffer from exponentially increasing complexity when raising
the order of the method. Algorithms with only quadratic order-dependence of the
computational cost are found using the Zassenhaus algorithm. In contrast to classical
splittings, special commutators are allowed to appear in the exponents. By construction,
they are rapidly decreasing in size with the semiclassical parameter and can be
exponentiated using only a few Lanczos iterations. For completeness, an alternative
technique based on Hagedorn wavepackets is revisited and interpreted in the light of
Magnus expansions and minor improvements are suggested. In the presence of explicit
time-dependencies in the semiclassical Hamiltonian, the Zassenhaus algorithm
requires a special initiation step. Distinguishing the case of smooth and fast frequencies,
it is shown how to adapt the mechanism to obtain an efficiently computable
decomposition of an effective Hamiltonian that has been obtained after Magnus expansion,
without having to resolve the oscillations by taking a prohibitively small
time-step.
Chapter 5 considers the Schrödinger eigenvalue problem which can be formulated as
an initial value problem after a Wick-rotating the Schrödinger equation to imaginary
time. The elliptic nature of the evolution operator restricts standard splittings to
low order, ¿ < 3, because of the unavoidable appearance of negative fractional timesteps
that correspond to the ill-posed integration backwards in time. The inclusion
of modified potentials lifts the order barrier up to ¿ < 5. Both restrictions can be
circumvented using complex fractional time-steps with positive real part and sixthorder
methods optimized for near-integrable Hamiltonians are presented.
Conclusions and pointers to further research are detailed in Chapter 6, with a special
focus on optimal quantum control. / Bader, PK. (2014). Geometric Integrators for Schrödinger Equations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/38716 / Premios Extraordinarios de tesis doctorales
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The Impact of Corporate Social Responsibility Expenditure on Financial Performance : A Quantitative Study of Financial Institutions in Sri LankaBodiyabaduge, Dilusha Madushani Perera, Rajakaruna Mudalige, Himesha Kushani Thibbotuwawa January 2024 (has links)
This research examines at the effect of corporate social responsibility (CSR) expenditure in two state commercial banks and few other financial institutions that are listed on the CSE in Sri Lanka. The independent variable in this analysis is CSR expenditure, whereas the dependent variable is financial performance. Market- and accounting-based performance metrics (ROA, ROE and EPS) are used to assess the financial performance of the financial institutions. The study's control variables were firm age, firm size, and GDP growth rate. For a duration of Eight years, the researchers gathered secondary data on the financial institutions from 2015 to 2022 by using audited annual reports, which included 13 financial institutions as a sample. The study findings reveal that CSR has a statistically significant impact on financial performance. The correlation analysis demonstrated a statistically significant relationship between CSR expenditure and ROA, ROE, and EPS. The correlation coefficient showed that all of the suggested hypotheses were significant and acceptable. The findings from the regression analysis revealed that CSR expenditure has an impact on the financial institution's ROA, ROE, and EPS. The results and implications can assist Sri Lankan financial institutions in designing their CSR projects to maximize value for the organization, resulting in a win-win situation. In addition, investing in CSR as a non-profit endeavor might help financial institutions meet their social responsibility obligations while also enhancing future intangible revenues and preparing them for market competitiveness. In contrast, CSR investments may improve community development, diversity promotion, and quality of life while treating social challenges including poverty, healthcare, education, and environmental sustainability.
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Dynamics and stability of a Bose-Fermi mixture : counterflow of superfluids and inelastic decay in a strongly interacting gas / Dynamique et stabilité d'un mélange de Bose-Fermi : contre-courant de superfluides et pertes inélastiques dans un gaz fortement corréléLaurent, Sébastien 09 October 2017 (has links)
La compréhension des effets des interactions dans un ensemble de particules quantiques représente un enjeu majeur de la physique moderne. Les atomes ultra-froids sont rapidement devenus un outil incomparable pour étudier ces systèmes quantiques fortement corrélés. Dans cette thèse, nous présentons plusieurs travaux portant sur les propriétés d’un mélange de superfluides de Bose et de Fermi créé à l’aide de vapeurs ultra-froides de ⁷Li et de ⁶Li. Nous étudions tout d'abord les propriétés hydrodynamiques du mélange en créant un contre-courant entre les superfluides. L'écoulement est dissipatif uniquement au dessus d'une vitesse critique que nous mesurons dans le crossover BEC-BCS. Une simulation numérique d’un contre-courant de deux condensats permet de mieux comprendre les mécanismes sous-jacents mis en jeu dans la dynamique. En particulier, l'étude numérique fournit des preuves supplémentaires que l'origine de la dissipation dans nos expériences est liée à l'émission d'excitation élémentaires dans chaque superfluide. Finalement, nous nous intéressons aux pertes inélastiques par recombinaison à trois corps qui peuvent limiter la stabilité de nos nuages. Ces pertes sont intimement liées aux corrélations à courte distance présentes dans le système et sont ainsi connectées aux propriétés universelles du gaz quantique. Cela se manifeste notamment par l’apparition de dépendances en densité ou en température inusuelles du taux de perte lorsque le système devient fortement corrélé. Nous démontrons cet effet dans deux exemples où les interactions sont résonantes, le cas du gaz de Bose unitaire et celui de notre mélange de superfluides Bose-Fermi. Plus généralement, nos travaux montrent que ces pertes inélastiques peuvent être utilisées pour sonder les corrélations quantiques dans un système en fortes interactions. / Understanding the effect of interactions in quantum many-body systems presents some of the most compelling challenges in modern physics. Ultracold atoms have emerged as a versatile platform to engineer and investigate these strongly correlated systems. In this thesis, we study the properties of a mixture of Bose and Fermi superfluids with tunable interactions produced using ultracold vapors of ⁷Li and ⁶Li. We first study the hydrodynamic properties of the mixture by creating a counterflow between the superfluids. The relative motion only exhibit dissipation above a critical velocity that we measure in the BEC-BCS crossover. A numerical simulation of counterflowing condensates allows for a better understanding of the underlying mechanisms at play in the dynamics. In particular, this numerical study provides additional evidence that the onset of friction in our experiment is due to the simultaneous generation of elementary excitations in both superfluids. Finally, we consider the inelastic losses that occur via three-body recombination in our cold gases. This few-body process is intimately related to short-distance correlations and is thereby connected to the universal properties of the many-body system. This manifests as the apparition of an unusual dependence on density or temperature in the loss rate when increasing the interactions. We demonstrate this effect in two examples where interactions are resonant: the case of a dilute unitary Bose gas and the one of impurities weakly coupled to a unitary Fermi gas. More generally, our work shows that inelastic losses can be used to probe quantum correlations in a many-body system.
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Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein / Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein CondensatesVergez, Guillaume 06 June 2017 (has links)
Le phénomène de condensation d’un gaz de bosons lorsqu’il est refroidi à zéro degrés Kelvin futdécrit par Einstein en 1925 en s’appuyant sur des travaux de Bose. Depuis lors, de nombreux physiciens,mathématiciens et numériciens se sont intéressés au condensat de Bose-Einstein et à son caractère superfluide. Nous proposons dans cette étude des méthodes numériques ainsi qu’un code informatique pour la simulation d’un condensat de Bose-Einstein en rotation. Le principal modèle mathématique décrivant ce phénomène physique est une équation de Schrödinger présentant une non-linéarité cubique,découverte en 1961 : l’équation de Gross-Pitaevskii (GP). En nous appuyant sur le logiciel FreeFem++,nous nous servons d’une discrétisation spatiale en éléments-finis pour résoudre numériquement cette équation. Une méthode d’adaptation du maillage à la solution et l’utilisation d’éléments-finis d’ordre deux nous permet de résoudre finement le problème et d’explorer des configurations complexes en deux ou trois dimensions d’espace. Pour sa version stationnaire, nous avons développé une méthode de gradient de Sobolev ou une méthode de point intérieur implémentée dans la librairie Ipopt. Pour sa version instationnaire, nous utilisons une méthode de Time-Splitting combinée à un schéma de Crank-Nicolson ou une méthode de relaxation. Afin d’étudier la stabilité dynamique et thermodynamique d’un état stationnaire, le modèle de Bogoliubov-de Gennes propose une linéarisation de l’équation de Gross-Pitaevskii autour de cet état. Nous avons élaboré une méthode permettant de résoudre ce système aux valeurs et vecteurs propres, basée sur un algorithme de Newton ainsi que sur la méthode d’Arnoldi implémentée dans la librairie Arpack. / The phenomenon of condensation of a boson gas when cooled to zero degrees Kelvin was described by Einstein in 1925 based on work by Bose. Since then, many physicists, mathematicians and digitizers have been interested in the Bose-Einstein condensate and its superfluidity. We propose in this study numerical methods as well as a computer code for the simulation of a rotating Bose-Einstein condensate.The main mathematical model describing this phenomenon is a Schrödinger equation with a cubic nonlinearity, discovered in 1961: the Gross-Pitaevskii (GP) equation. By using the software FreeFem++ and a finite elements spatial discretization we solve this equation numerically. The mesh adaptation to the solution and the use of finite elements of order two allow us to solve the problem finely and to explore complex configurations in two or three dimensions of space. For its stationary version, we have developed a Sobolev gradient method or an internal point method implemented in the Ipopt library. .For its unsteady version, we use a Time-Splitting method combined with a Crank-Nicolson scheme ora relaxation method. In order to study the dynamic and thermodynamic stability of a stationary state,the Bogoliubov-de Gennes model proposes a linearization of the Gross-Pitaevskii equation around this state. We have developed a method to solve this eigenvalues and eigenvector system, based on a Newton algorithm as well as the Arnoldi method implemented in the Arpack library.
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Conductivité pour des fermions de Dirac près d’un point critique quantiqueMartin, Simon 08 1900 (has links)
Les matériaux de Dirac constituent une classe intéressante de systèmes pouvant subir une transition de phase quantique à température nulle, lorsqu’un paramètre non-thermique atteint un point critique quantique. À l’approche d’un tel point, les observables physiques sont affectées par les importantes fluctuations thermiques et quantiques. Dans ce mémoire, on utilise des techniques de théorie conforme des champs afin d’étudier le tenseur de conductivité électrique dans des théories en 2 + 1 dimensions contenant des fermions de Dirac près d’un point critique quantique. À basse énergie, ces dernières décrivent de façon adéquate de nombreux matériaux de Dirac ainsi que leur transition de phase quantique. La conductivité est étudiée dans le régime des hautes fréquences, à température non-nulle et lorsque le paramètre non-thermique est près de sa valeur critique. Dans ce projet, l’emphase est mise sur les points critiques quantiques invariants sous la parité et le renversement du temps. Dans ce cas, l’expansion de produit d’opérateurs (Operator product expansion en anglais) ainsi que la théorie des perturbations conforme permettent d’obtenir une expression générale pour l’expansion à grandes fréquences des conductivités longitudinales et transverses (de Hall) lorsque le point critique quantique est déformé par un opérateur scalaire relevant. Grâce à ces dernières, nous sommes en mesure de déduire des règles de somme exactes pour ces deux quantités. À titre d’exemple, nos résultats généraux sont appliqués dans le cadre du modèle interagissant de Gross-Neveu, où nous obtenons l’expansion des deux conductivités ainsi que les règles de somme pour un nombre de saveurs de fermions de Dirac N arbitraire. Ces mêmes expressions sont ensuite obtenues par un calcul explicite à N = infini, permettant la comparaison avec les résultats pour un N quelconque. Par la suite, des résultats généraux similaires sont obtenus dans le cas où le point critique quantique est déformé par un opérateur pseudoscalaire relevant. Ces derniers sont finalement appliqués à une théorie de fermions de Dirac libres perturbée par un terme de masse. / Dirac materials constitute an interesting class of systems that can undergo a quantum phase transition at zero temperature, when a non-thermal parameter reaches a quantum critical point. As we approach such a point, physical observables are altered by the important thermal and quantum fluctuations. In this thesis, conformal field theory techniques are used to study the electrical conductivity tensor in theories with Dirac fermions in 2+1 dimensions close to a quantum critical point. At low energies, these adequately describe various Dirac materials as well as their quantum phase transition. In this project, we focus on theories that have a quantum critical point invariant under parity and time-reversal. In this case, the operator product expansion and conformal perturbation theory allow to obtain a general expression for the large frequency expansion of the longitudinal and transverse (Hall) conductivities when the quantum critical point is deformed by a relevant scalar operator. Using these, we are able to deduce exact sum rules for both quantities. As an example, our general results are applied to the Gross-Neveu model, where we obtain the large frequency expansion for both conductivities and the associated sum rules for an arbitrary number of Dirac fermion flavors N. The same expressions are then obtained by an explicit calculation at N = infinity, allowing to compare with our results for any N. Afterwards, analogous general results are obtained for theories where the quantum critical point is deformed by a relevant pseudoscalar. These are finally applied to a theory of massless free Dirac fermions perturbed by a mass term.
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