Dinâmica da condensação de Bose-Einstein em gases fracamente interagentes

A presente dissertação estuda com detalhes a evolução temporal fora do equilíbrio de um condensado de Bose-Einstein homogêneo diluído imerso em um reservatório térmico. Nós modelamos o sistema através de um campo de Bose escalar complexo. É apropriado descrever o comportamento microscópico desse sistema por meio da teoria quântica de campos através do formalismo de Schwinger-Keldysh. Usando esse formalismo, de tempo real a dinâmica do condensado é solucionada por um grupo de equações integro-diferencial auto consistente, essas são solucionadas numericamente. Estudamos também o cenário quench, e como a densidade do gás e as interações entre as flutuações tem o efeito de provocar as instabilidades nesse sistema. Aplicamos esse desenvolvimento para estudar o comportamento de duas espécies homogêneas de um gás de Bose diluído imerso em um reservatório térmico.

Inflação em sistemas com fluidos de radiação com viscosidade e dissipação e análise de estabilidade

Este trabalho apresenta um estudo da estabilidade das equações da inflação morna com um fluido de radiação viscoso. A viscosidade do fluido é proveniente do constante decaimento de partículas neste, devido à dissipação do campo escalar da inflação, o ínflaton.Esta viscosidade, que pode ser volumar ou laminar, é tratada em termos de teorias termodinâmicas fora do equilíbrio. Este estudo se limita às equações de fundo da inflação morna, de modo que somente a viscosidade volumar tem um efeito significativo, sendo a viscosidade laminar importante somente no contexto de perturbações cosmológicas. A descrição da viscosidade em termos de uma termodinâmica fora do equilíbrio, porém, não pode ser realizada univocamente, pois a única informação que temos sobre processos irreversíveis é a segunda lei da termodinâmica. Portanto, parte-se em busca de teorias que estejam de acordo com esta lei e que, por argumentos plausíveis, sejam capazes de descrever o comportamento dos fluxos dissipativos próximo ao equilíbrio. O objetivo deste trabalho é estudar a estabilidade da inflação morna viscosa para teorias causais e não causais para o fluido de radiação com viscosidade, de forma que se possa observar o impacto da viscosidade no regime inflacionário e a relevância de se passar a considerar a causalidade. Para o fluido de radiação, as teorias consideradas são a teoria não causal de Eckart e as teorias causais de Israel-Stewart e de Denicol et al (hidrodinâmica dissipativa causal não linear). Obtém-se que as teorias causais, como era de se esperar, além de serem, por definição, consistentes no tocante à finitude da velocidade de propagação dos fluxos dissipativos, tornam o sistema dinâmico estável para valores de viscosidade mais distantes do equilíbrio. Observa-se também, nitidamente, que a teoria de Denicol et al é a mais robusta nesse sentido. Este trabalho, portanto, visa dar continuidade ao estudo dos efeitos não-isentrópicos na inflação, já que, além da dissipação do ínflaton na inflação morna, o impacto da viscosidade tem despertado bastante interesse.

Effective masses of pentaquark Theta(+) in nuclear matter

The properties of baryons in nuclear matter are analysed in the relativistic mean-field theory(RMF). It is found that the scalar field sigma meson affects the properties of baryon at high density. A density dependent scalar coupling g(sigma)(N) is determined according to the idea of quark-meson coupling model and extended to RMF. It is shown that g(sigma)(N), affects the property of nuclear matter weakly at low density, but strongly at high density. The relation between the scalar density rho(S) and the nuclear density rho and the effective mass of the pentaquark circle minus(+) are studied with the density dependent coupling constant. The density dependent scalar coupling obviously affects the effective masses of baryons in nuclear matter, especially at high density.

Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SLL(2, R) x SLR(2, R) Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.

Entropy of Kaluza-Klein black hole from Kerr/CFT correspondence

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four-dimensional Kaluza-Klein black hole in Einstein-Maxwell-Dilaton theory. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza-Klein black hole, and find the left and right temperatures of the dual conformal field theory. Furthermore, we find that the entropy of non-extremal Kaluza-Klein black hole is reproduced by Cardy formula. (C) 2010 Elsevier B.V. All rights reserved.

Design Optimization and Security For Communication Networks

In this work we introduce a new mathematical tool for optimization of routes, topology design, and energy efficiency in wireless sensor networks. We introduce a vector field formulation that models communication in the network, and routing is performed in the direction of this vector field at every location of the network. The magnitude of the vector field at every location represents the density of amount of data that is being transited through that location. We define the total communication cost in the network as the integral of a quadratic form of the vector field over the network area. With the above formulation, we introduce a mathematical machinery based on partial differential equations very similar to the Maxwell's equations in electrostatic theory. We show that in order to minimize the cost, the routes should be found based on the solution of these partial differential equations. In our formulation, the sensors are sources of information, and they are similar to the positive charges in electrostatics, the destinations are sinks of information and they are similar to negative charges, and the network is similar to a non-homogeneous dielectric media with variable dielectric constant (or permittivity coefficient). In one of the applications of our mathematical model based on the vector fields, we offer a scheme for energy efficient routing. Our routing scheme is based on changing the permittivity coefficient to a higher value in the places of the network where nodes have high residual energy, and setting it to a low value in the places of the network where the nodes do not have much energy left. Our simulations show that our method gives a significant increase in the network life compared to the shortest path and weighted shortest path schemes. Our initial focus is on the case where there is only one destination in the network, and later we extend our approach to the case where there are multiple destinations in the network. In the case of having multiple destinations, we need to partition the network into several areas known as regions of attraction of the destinations. Each destination is responsible for collecting all messages being generated in its region of attraction. The complexity of the optimization problem in this case is how to define regions of attraction for the destinations and how much communication load to assign to each destination to optimize the performance of the network. We use our vector field model to solve the optimization problem for this case. We define a vector field, which is conservative, and hence it can be written as the gradient of a scalar field (also known as a potential field). Then we show that in the optimal assignment of the communication load of the network to the destinations, the value of that potential field should be equal at the locations of all the destinations. Another application of our vector field model is to find the optimal locations of the destinations in the network. We show that the vector field gives the gradient of the cost function with respect to the locations of the destinations. Based on this fact, we suggest an algorithm to be applied during the design phase of a network to relocate the destinations for reducing the communication cost function. The performance of our proposed schemes is confirmed by several examples and simulation experiments. In another part of this work we focus on the notions of responsiveness and conformance of TCP traffic in communication networks. We introduce the notion of responsiveness for TCP aggregates and define it as the degree to which a TCP aggregate reduces its sending rate to the network as a response to packet drops. We define metrics that describe the responsiveness of TCP aggregates, and suggest two methods for determining the values of these quantities. The first method is based on a test in which we drop a few packets from the aggregate intentionally and measure the resulting rate decrease of that aggregate. This kind of test is not robust to multiple simultaneous tests performed at different routers. We make the test robust to multiple simultaneous tests by using ideas from the CDMA approach to multiple access channels in communication theory. Based on this approach, we introduce tests of responsiveness for aggregates, and call it CDMA based Aggregate Perturbation Method (CAPM). We use CAPM to perform congestion control. A distinguishing feature of our congestion control scheme is that it maintains a degree of fairness among different aggregates. In the next step we modify CAPM to offer methods for estimating the proportion of an aggregate of TCP traffic that does not conform to protocol specifications, and hence may belong to a DDoS attack. Our methods work by intentionally perturbing the aggregate by dropping a very small number of packets from it and observing the response of the aggregate. We offer two methods for conformance testing. In the first method, we apply the perturbation tests to SYN packets being sent at the start of the TCP 3-way handshake, and we use the fact that the rate of ACK packets being exchanged in the handshake should follow the rate of perturbations. In the second method, we apply the perturbation tests to the TCP data packets and use the fact that the rate of retransmitted data packets should follow the rate of perturbations. In both methods, we use signature based perturbations, which means packet drops are performed with a rate given by a function of time. We use analogy of our problem with multiple access communication to find signatures. Specifically, we assign orthogonal CDMA based signatures to different routers in a distributed implementation of our methods. As a result of orthogonality, the performance does not degrade because of cross interference made by simultaneously testing routers. We have shown efficacy of our methods through mathematical analysis and extensive simulation experiments.

Les bulles de masse négative dans un espace de de Sitter.

Nous étudions différentes situations de distribution de la matière d’une bulle de masse négative. En effet, pour les bulles statiques et à symétrie sphérique, nous commençons par l’hypothèse qui dit que cette bulle, étant une solution des équations d’Einstein, est une déformation au niveau d’un champ scalaire. Nous montrons que cette idée est à rejeter et à remplacer par celle qui dit que la bulle est formée d’un fluide parfait. Nous réussissons à démontrer que ceci est la bonne distribution de matière dans une géométrie Schwarzschild-de Sitter, qu’elle satisfait toutes les conditions et que nous sommes capables de résoudre numériquement ses paramètres de pression et de densité.

Énergie des vortex dans un modèle abélien de Higgs en 2+1 dimensions avec un potentiel d’ordre six

Dans ce travail, j’étudierai principalement un modèle abélien de Higgs en 2+1 dimensions, dans lequel un champ scalaire interagit avec un champ de jauge. Des défauts topologiques, nommés vortex, sont créés lorsque le potentiel possède un minimum brisant spontanément la symétrie U(1). En 3+1 dimensions, ces vortex deviennent des défauts à une dimension. Ils ap- paraissent par exemple en matière condensée dans les supraconducteurs de type II comme des lignes de flux magnétique. J’analyserai comment l’énergie des solutions statiques dépend des paramètres du modèle et en particulier du nombre d’enroulement du vortex. Pour le choix habituel de potentiel (un poly- nôme quartique dit « BPS »), la relation entre les masses des deux champs mène à deux types de comportements : type I si la masse du champ de jauge est plus grande que celle du champ sca- laire et type II inversement. Selon le cas, la dépendance de l’énergie au nombre d’enroulement, n, indiquera si les vortex auront tendance à s’attirer ou à se repousser, respectivement. Lorsque le flux emprisonné est grand, les vortex présentent un profil où la paroi est mince, permettant certaines simplifications dans l’analyse. Le potentiel, un polynôme d’ordre six (« non-BPS »), est choisi tel que le centre du vortex se trouve dans le vrai vide (minimum absolu du potentiel) alors qu’à l’infini le champ scalaire se retrouve dans le faux vide (minimum relatif du potentiel). Le taux de désintégration a déjà été estimé par une approximation semi-classique pour montrer l’impact des défauts topologiques sur la stabilité du faux vide. Le projet consiste d’abord à établir l’existence de vortex classi- quement stables de façon numérique. Puis, ma contribution fut une analyse des paramètres du modèle révélant le comportement énergétique de ceux-ci en fonction du nombre d’enroulement. Ce comportement s’avèrera être différent du cas « BPS » : le ratio des masses ne réussit pas à décrire le comportement observé numériquement.

An analytical study of the power distribution pattterns of silica waveguides with high paraboloic cylindrical deformation

An attempt is made to determine the relative power distribution in a step-index parabolic cylindrical waveguide (PCW) with high deformation across the direction of propagation. The guide is assumed to be made of silica. The scalar field approximation is employed for the analysis under which a vanishing refractive-index (RI) difference in the waveguide materials is considered. Further, no approximation for folds- is used in the analytical treatment. Due to the geometry of such waceguides, PCWs lose the well-defined modal discreteness, and a kind of mode bunching is observed instead, which becomes much more prominent in PCWs with high bends. However, with the increase in cross-sectional size, the mode-bunching tendency is slightly reduced. The general expressions for power in the guiding and nonguiding sections are obtained, and the fractional power patterns in all of the sections are presented for PCWs of various cross-sectional dimensions. It is observed that the confinement of power in the core section is increased for PCWs of larger cross-sectional size. Moreover, a fairly uniform distribution of power is seen over the modes having intermediate values of propagation constants

Studies on Quasinormal Modes and Late-time Tails in Black Hole Spacetimes

This thesis Entitled Studies on Quasinormal modes and Late-time tails black hole spacetimes. In this thesis, the signature of these new theories are probed on the evolution of field perturbations on the black hole spacetimes in the theory. Chapter 1 gives a general introduction to black holes and its perturbation formalism. Various concepts in the area covered by the thesis are also elucidated in this chapter. Chapter 2 describes the evolution of massive, charged scalar field perturbations around a Reissner-Nordstrom black hole surrounded by a static and spherically symmetric quintessence. Chapter 3 comprises the evolution of massless scalar, electromagnetic and gravitational fields around spherically symmetric black hole whose asymptotes are defined by the quintessence, with special interest on the late-time behavior. Chapter 4 examines the evolution of Dirac field around a Schwarzschild black hole surrounded by quintessence. Detailed numerical simulations are done to analyze the nature of field on different surfaces of constant radius . Chapter 5is dedicated to the study of the evolution of massless fields around the black hole geometry in the HL gravity.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Quantized fields and gravitational particle creation in f (R) expanding universes

The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic universes is discussed in the context of f (R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the universe. (C) 2010 Elsevier B.V. All rights reserved.

Simplified quartessence cosmology

We propose a new class of accelerating world models unifying the cosmological dark sector (dark matter and dark energy). All the models are described by a simplified version of the Chaplygin gas quartessence cosmology. It is found that even for Omega(k) not equal 0, this quartessence scenario depends only on a pair of parameters which can severely be constrained by the cosmological tests. As an example we perform a joint analysis involving the latest SNe type la data and the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations. In our analysis we have considered the SNe type la Union sample compiled by Kowalski et al. [M. Kowalski et al., Astrophys. J. 686 (2008) 749, arXiv:0804.4142]. At 95.4% (c.l.), we find for BAD + Union sample, alpha = 0.81(-0.04)(+0.04) and Omega(Q4) = 1.15(-0.17)(+0.16) The best-fit for this simplified quartessence scenario is a spatially closed Universe and its reduced chi(2) is exactly the same of the flat concordance model (Lambda CDM). (C) 2009 Elsevier B.V. All rights reserved.