A presente dissertação tem como objeto de estudo sistemas da física da matéria condensada que sejam capazes de simular sistemas gravitacionais, tais como buracos negros e universos em expansão, onde processos quânticos tomam parte. Neste estudo nos debruçamos principalmente sobre o modelo do fluido e condensados de Bose-Einstein. No modelo do fluido exploramos a geometria efetiva que surge e os problemas de back-reaction e dos modos trans-planckianos de campos quânticos. No modelo baseado em condensados exploramos sua faceta cosmológica e a possibilidade de campos maciços. Além destes dois modelos de grande relevância na literatura, ainda expomos os análogos em cordas elásticas e os baseados em ondas na superfícies de fluidos e uma análise geral baseada no formalismo lagrangeano para campos. / This dissertation has as object of study systems of condensate-matter physics which can simulate gravitational systems like black holes and expanding universes where quantum processes take place. In this study we lay attention mainly on the fluid model and on Bose-Einstein-condensate-based models. In the fluid model we explore the features of the emergent geometry and other problems like the back-reaction and the trans-planckian modes of quantum fields. In the condensate-based models we explore their cosmological aspects and the possibility for massive fields. Moreover, we shall present two other models, the elastic string and the surface-wave-based models in fluids, and a very general analysis based on the Lagrangean formalism for fields.

The vacuum, as described by Quantum Field Theory, is not as empty as classical physics once led us to believe. In fact, it is characterised by an infinite energy stored in the ground state of its constituent fields. This infinite energy has real, tangible effects on the macroscopic clusters of matter that make up our universe. Moreover, the configuration of these clusters of matter within the vacuum in turn influences the form of the vacuum itself and so forth. In this work, we shall consider the changes to the quantum vacuum brought about by the presence of time-dependent dielectrics. Such changes are thought to be responsible for phenomena such as the simple and dynamical Casimir effects and Quantum Friction. After introducing the physical and mathematical descriptions of the electromagnetic quantum vacuum, we will begin by discussing some of the basic quasi-static effects that stem directly from the existence of an electromagnetic ground state energy, known as the \textit{zero-point energy}. These effects include the famous Hawking radiation and Unruh effect amongst others. We will then use a scenario similar to that which exhibits Cherenkov radiation in order to de-mystify the 'negative frequency' modes of light that often occur due to a Doppler shift in the presence of media moving at a constant velocity by showing that they are an artefact of the approximation of the degrees of freedom of matter to a macroscopic permittivity function. Here, absorption and dissipation of electromagnetic energy will be ignored for simplicity. The dynamics of an oscillator placed within this moving medium will then be considered and we will show that when the motion exceeds the speed of light in the dielectric, the oscillator will begin to absorb energy from the medium. It will be shown that this is due to the reversal of the 'radiation damping' present for lower velocity of stationary cases. We will then consider how the infinite vacuum energy changes in the vicinity, but outside, of this medium moving with a constant velocity and show that the presence of matter removes certain symmetries present in empty space leading to transfers of energy between moving bodies mediated by the electromagnetic field. Following on from this, we will then extend our considerations by including the dissipation and dispersion of electromagnetic energy within magneto-dielectrics by using a canonically quantised model referred to as 'Macroscopic QED'. We will analyse the change to the vacuum state of the electromagnetic field brought about by the presence of media with an arbitrary time dependence. It will be shown that this leads to the creation of particles tantamount to exciting the degrees of freedom of both the medium and the electromagnetic field. We will also consider the effect these time-dependencies have on the two point functions of the field amplitudes using the example of the electric field. Finally, we will begin the application of the macroscopic QED model to the path integral methods of quantum field theory with the purpose of making use of the full range of perturbative techniques that this entails, leaving the remainder of this adaptation for future work.

Po zhrnutí potrebných teoretických základov a predošlého výskumu v ob- lasti, prezentujeme semi-klasickú kvantovaciu schému pre uzavretú Nambuovu- Gotovu strunu. Týmto zovšeobecňujeme predošlú prácu, ktorá bola vykonaná pre otvorenú strunu a uzavretú strunu kruhového tvaru. Pomocou metód kvan- tovej teórie po©a v zakrivených priestoročasoch počítame strednú hodnotu vo©- ného Hamiltoniánu struny rotujúcej v dvoch na seba kolmých priestorových rovinách v priestoročase všeobecnej dimenzie. Táto hodnota je priamo úmerná kvantovej korekcii k celkovej energii struny, ktorá má formu tzv. Reggeovho interceptu. Výslednú hodnotu Reggeovho interceptu porovnávame s predošlým výskumom. Taktiež uvádzame porovnanie získaného spektra fyzikálnych stavov struny kvantovanej našou metódou so spektrom odvodeným pomocou kovariant- ného kvantovania. 1

This thesis is an investigation of the subject of extra dimensions in particle physics. In recent years, there has been a large interest in this subject. In particular, a number of models have been suggested that provide solutions to some of the problem with the current Standard Model of particle physics. These models typically give rise to experimental signatures around the TeV energy scale, which means that they could be tested in the next generation of high-energy experiments, such as the LHC. Among the most important of these models are the universal extra dimensions model, the large extra dimensions model by Arkani-Hamed, Dimopolous, and Dvali, and models where right-handed neutrinos propagate in the extra dimensions. In the thesis, we study phenomenological aspects of these models, or simple modifications of them. In particular, we focus on Kaluza–Klein dark matter in universal extra dimensions models, different aspects of neutrino physics in higher dimensions, and collider phenomenology of extra dimensions. In addition, we consider consequences of the enhanced renormalization group running of physical parameters in higher-dimensional models. / QC 20120427

No description available.

In this work the extension of the criterion for local thermal equilibrium by Buchholz, Ojima and Roos to curved spacetime as introduced by Schlemmer is investigated. Several problems are identified and especially the instability under time evolution which was already observed by Schlemmer is inspected. An alternative approach to local thermal equilibrium in quantum field theories on curved spacetimes is presented and discussed. In the following the dynamic system of the linear field and matter perturbations in the generic model of inflation is studied in the view of ambiguity of quantisation. In the last part the compatibility of the temperature fluctuations of the cosmic microwave background radiation with local thermal equilibrium is investigated. / In dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft.

The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula. Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed. It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.

A presente dissertação tem como objeto de estudo sistemas da física da matéria condensada que sejam capazes de simular sistemas gravitacionais, tais como buracos negros e universos em expansão, onde processos quânticos tomam parte. Neste estudo nos debruçamos principalmente sobre o modelo do fluido e condensados de Bose-Einstein. No modelo do fluido exploramos a geometria efetiva que surge e os problemas de back-reaction e dos modos trans-planckianos de campos quânticos. No modelo baseado em condensados exploramos sua faceta cosmológica e a possibilidade de campos maciços. Além destes dois modelos de grande relevância na literatura, ainda expomos os análogos em cordas elásticas e os baseados em ondas na superfícies de fluidos e uma análise geral baseada no formalismo lagrangeano para campos. / This dissertation has as object of study systems of condensate-matter physics which can simulate gravitational systems like black holes and expanding universes where quantum processes take place. In this study we lay attention mainly on the fluid model and on Bose-Einstein-condensate-based models. In the fluid model we explore the features of the emergent geometry and other problems like the back-reaction and the trans-planckian modes of quantum fields. In the condensate-based models we explore their cosmological aspects and the possibility for massive fields. Moreover, we shall present two other models, the elastic string and the surface-wave-based models in fluids, and a very general analysis based on the Lagrangean formalism for fields.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-22T13:25:11Z No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:20:21Z (GMT) No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) / Made available in DSpace on 2017-01-31T10:20:21Z (GMT). No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) Previous issue date: 2015-06-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese é composta por assuntos distintos entre si de teorias quânticas de campos onde alguns deles são descritos em espaços não-comutativos (NC). Em primeiro lugar, analisamos a dinâmica de uma partícula livre sobre uma 2-esfera e através da dinâmica das suas equações de movimento, obtivemos as perturbações NCs neste espaço de fase. Este modelo sugere uma origem para o Zitterbewegung do elétron. Depois disso, consideramos umaversãoNCdasegundaleideNewtonparaestemodelo, quefoiobtidocomestecenário geométrico aplicado a este modelo. Em seguida, discutimos um formalismo alternativo relacionado à não-comutatividade chamado DFR onde o parâmetro NC é considerado uma coordenada e demonstramos exatamente que ela tem obrigatoriamente um momento conjugado neste espaço de fase DFR, diferentemente do que alguns autores da atual literatura sobre DFR afirmam. No próximo assunto, usando o formalismo de solda que, em poucaspalavras,colocapartículascomquiralidadesopostasnomesmomultipleto,soldamos algumas versões NCs de modelos bem conhecidos como modelos de Schwinger quirais e modelos (anti) auto duais no espaço-tempo de Minkowski estendido. Em outro assunto estudado aqui, também construímos a versão NC do modelo de Jackiw-Pi com um grupo de calibre arbitrário e usamos o mapeamento bem conhecido de Seiberg-Witten para obter este modelo NC em termos de variáveis comutativos. Finalmente, utilizamos o formalismo de campos e anticampos (ou método BV) para construir a ação de Batalin-Vilkovisky (BV) do modelo Jackiw-Pi estendido e após o prEntendiocedimento de fixação de calibre chegamos a uma ação completa, pronta para quantização. / This thesis is composed of distinct aspects of quantum field theories where some of them are described in noncommutative (NC) spaces. Firstly, we have analyzed the dynamics of a free particle over a 2-sphere and through the dynamics of the equations of motion we have derived its NC perturbations in the phase-space. This model suggests an origin for Zitterbewegung feature of the electron. After that we have considered the NC version of Newton’s second law for this model, which was obtained with the geometricalscenarioappliedtothismodel. Thenwehavediscussedtheso-calledDoplicher– Fredenhagen–Roberts (DFR) alternative formalism concerning noncommutativity where the NC parameter has a coordinate role and we showed exactly that it has a conjugated momentum in the DFR phase-space, differently of what some authors of the current DFR-literature claims. In the next issue, using the soldering formalism which, in few words, put opposite chiral particles in the same multiplet, we have soldered some NC versions of well known models like the chiral Schwinger model and (anti)self dual models in the extended Minkowski spacetime. Changing the subject, we have constructed the NC spacetime version of Jackiw-Pi model with an arbitrary gauge group and we used the well known Seiberg-Witten map to obtain the NC model expressed in terms of commutative variables. Finally, we have used the field-antifield (or BV method) formalism to construct the Batalin-Vilkovisky (BV) action of the extended Jackiw-Pi model and after the gauge fixing procedure we have arrived at a quantized-ready action for this model.

Esta tese trata a existência de Princpios de Grandes Desvios (PGD), no âmbito de sistemas fermiônicos em equilbrio. A motivação fsica detrás de nossos estudos são medidas experimentais de resistência elétrica de nanofios de silcio dopados com átomos de fósforo. Estas medidas mostram que efeitos quânticos no transporte de carga elétrica quase desaparecem para nanofios de comprimentos maiores que alguns nanômetros, mesmo para temperaturas muito baixas (4.2°K). A fim de provar matematicamente tal efeito, dividimos nosso trabalho em diversos passos: 1. No primeiro passo, para férmions não interagentes numa rede com desordem, mostramos que a incerteza quântica da densidade da corrente elétrica microscópica, em torno de seus valores macroscópicos(clássicos), é suprimida exponencialmente rápido em relação ao volume da região da rede onde um campo elétrico externo é aplicado. A desordem é modelada como um potencial elétrico aleatório juntamente com amplitudes aleatórias de saltos com valores complexos. O célebre modelo de Anderson de tight-binding é um exemplo particular do caso geral considerado aqui. Nossa análise matemática é baseada em estimativas de Combes-Thomas, o Teorema Ergódico de Akcoglu-Krengel e no formalismo de Grandes Desvios, em particular o Teorema de Gärtner-Ellis. 2. Em segundo lugar, provamos que, para férmions interagindo fracamente na rede, as funções geradoras J(s), s R de cumulantes de distribuições de probabilidades associadas com estados KMS pode ser escrito como o limite de logartmos de integrais gaussianas de Berezin. Mostramos que os determinantes das covariáncias associadas às integrais gaussianas são majorados uniformemente (via desigualdades de Hölder para normas Schatten). Tais covariâncias são também somáveis, em casos gerais de interesse, incluindo assim, sistemas que não são invariantes por translação. 3. No terceiro passo, analisamos expansões de logartmos de integrais gaussianas de Berezin, e assim combinando com métodos construtivos de teoria quântica de campos, mostramos a analiticidade de J(s) para s nas vizinhanças de 0. Finalmente, discutimos como combinar os passos 2-3, a fim de provar (matematicamente falando) os resultados experimentais mencionados acima para férmions interagindo em equilbrio. De fato, os resultados encontrados nesta tese, generalizam trabalhos prévios no âmbito do PGD usado para o estudo de sistemas quânticos. / This Thesis deals with the existence of Large Deviation Principles (LDP) in the scope of fermionic systems at equilibrium. The physical motivation beyond our studies are experimental measures of electric resistance of nanowires in silicon doped with phosphorus atoms. The latter demonstrate that quantum effects on charge transport almost disappear for nanowires of lengths larger than a few nanometers, even at very low temperature (4.2°K). In order to mathematically prove the latter, we divide our work in several steps: 1. In the first step, for noninteracting lattice fermions with disorder, we show that quantum uncertainty of microscopic electric current density around their (classical) macroscopic values is suppressed, exponentially fast with respect to the volume of the region of the lattice where an external electric field is applied. Disorder is modeled by a random external potential along with random, complex-valued, hopping amplitudes. The celebrated tight-binding Anderson model is one particular example of the general case considered here. Our mathematical analysis is based on Combes-Thomas estimates, the Akcoglu-Krengel ergodic theorem, and the large deviation formalism, in particular the Gärtner-Ellis theorem. 2. Secondly, we prove that for weakly interacting fermions on the lattice, the logarithm moment generating function J(s), s R of probability distributions associated with KMS states can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform determinant bound (via Hölder inequalities for Schatten norms) and to be summable in general cases of interest, including systems that are not translation invariant. 3. In the third step we analyze expansions of logarithms of Gaussian Berezin integrals, which combined with constructive methods of quantum field theory is useful to show the analyticity of J(s) for s in a neighborhood of 0. We finally discuss how to combine steps 2-3 in order to prove (mathematically speaking) for interacting fermions in equilibrium the experimental results above mentioned. In fact, the found results in this Thesis generalize previous works in the scope of LDP used to study quantum systems.