Programa de Pós-graduação em Física

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Navegando Programa de Pós-graduação em Física por Por Orientador "Avelar, Ardiley Torres"

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    Relativistic symmetry in quantum information theory
    (Universidade Federal de Goiás, 2022-04-04) Bidinotto, Alexandre Borges; Taillebois, Emile Raymond Ferreira; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Avelar, Ardiley Torres; Santana, Ademir Eugênio de; Cardoso, Wesley Bueno
    This dissertation begins with a succinct introduction to group theory to enable the understanding of special relativity theory from a symmetrical point of view. From this perspective, the notion of hierarchy of dynamical variables, which is present in relativity, is introduced to quantum mechanical formalism in order to construct the irreducible unitary representations of the Poincaré group for secondary variables. Given this discussion, the questions regarding the existence of a subset of transformations in which the Wigner rotations associated do not depend on the momenta. In sequence, the relativistic Stern-Gerlach observable is presented. This observable also depends on the momenta, so the initial problem on the density matrices for spin remains unsolved. The open question on the Stern-Gerlach observable is what is the minimum number of measurements in order to fully determine a relativistic density matrix. Both questionings on this dissertation can lead to the determination of the quantum state tomography of relativistic particles, which is the further goal of this document.
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    Incerteza quântica local em transições de fase quânticas e uma generalização para sistemas multipartidos
    (Universidade Federal de Goiás, 2018-05-02) Carrijo, Thiago Mureebe; Céleri, Lucas Chibebe; http://lattes.cnpq.br/6630683190018665; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Almeida, Agnaldo Rosa de; Avelar, Ardiley Torres; Valverde, Clodoaldo; Oliveira, Guilherme Colherinhas de; Cardoso, Wesley Bueno
    In this work, we have studied how local quantum uncertainty (LQU) and linear entropy behave in critical systems. Two models of spin 1/2 systems were investigated: XY and XY with triple interaction (XYT), both unidimensional. It was concluded that these measures and their derivatives locate the phase transitions of these systems and a justification was given for the difference of behavior between the LQU and the linear entropy in the region near the transition in the XY model. A measure of multipartite quantum correlations was also created according to a set of axiomatic criteria, which was tested in the family of Werner-GHZ quantum states, producing results in accordance with the expected result, according to the literature.
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    Correlações quânticas e generalização da entropia de von Neumann
    (Universidade Federal de Goiás, 2012-04-10) Carrijo, Thiago Mureebe; Almeida, Norton Gomes de; Avelar, Ardiley Torres; http://lattes.cnpq.br/573228661137637; Avelar, Ardiley Torres; Almeida, Norton Gomes de; Cardoso, Wesley Bueno; Serra, Roberto Menezes
    This work has the goal to treat the concept of correlation on both classical and quantum, addressing what already exists about the matter and giving a new perspective about it. Beyond this, we propose a new manner to calculate the amount of information of a quantum system. For this, the EPR paradox, Bell theorem, entanglement concept, Shannon and von Neumann entropies, code theory and the quantum correlation measure so-called quantum discord will be discussed. From those subjects, two generalizations will be proposed: of the von Neumann entropy and the quantum correlation concept. Some features e properties will be discussed about these new definitions, however there is still much to be investigated about its implications.
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    On the controversies of the Unruh effect
    (Universidade Federal de Goiás, 2021-08-16) Diniz, João Vítor Barnez Pignata Leal; Taillebois, Emile Raymond Ferreira; http://lattes.cnpq.br/1212175267808857; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Avelar, Ardiley Torres; Céleri, Lucas Chibebe; Matsas, George Emanuel Avraam
    In the 50 years since it was first proposed, the Unruh effect has been discussed extensively in literature, with many theoretical results supporting its existence and some questioning whether it is actually observed. The Unruh effect states that observers with constant proper acceleration in Minkowski spacetime will respond as if interacting with a thermal bath at a temperature proportional to the acceleration. For common accelerations this temperature is very low, so experimental confirmation has been challenging. To understand the effect and the discussion around it, we review some important results from quantum field theory and work out a detailed derivation of the Unruh effect for massless and massive fields, including the calculation of the Bogoliubov coefficients for these problems. Furthermore, we follow a discussion on the role that the boundary conditions play in this effect, showing that they may lead to an incomplete description of the field in Minkowski spacetime when written in terms of the modes in Rindler spacetime.
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    Emaranhamento genuínos nas variáveis espaciais de sistemas tripartidos e quadripartido de fótons
    (Universidade Federal de Goiás, 2020-04-27) Gonçalves Netto, Victor; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Avelar, Ardiley Torres; Taillebois, Emile Raymond Ferreira; Gomes, Rafael De Morais
    This dissertation deals with the genuine entanglement in the spatial variables of a tripartite photon system and of a quadripartite photon system. Each term used in the previous sentence was investigated during the course of this work and the first chapters of this dissertation are reserved to discuss the meaning of these terms. The photon states are reached with the use of an experimental scheme that uses the spontaneous parametric down-conversion, SPDC. We dedicate a few pages to deal with SPDC, but with one goal in mind: to obtain the tripartite state of photons. These states is then submitted to the van Loock-Furusawa entanglement criterion, confirming that, under certain conditions, genuine entanglement occurs.
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    Condutância em nanofios magnéticos diluídos
    (Universidade Federal de Goiás, 2010) Mendes, Udson Cabra; Leão, Salvino de Araújo; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637
    We investigate core-shell nanowires of diluted magnetic semiconductors (DMS) with remote n-type modulation doping. The incorporation of Mn2 ions acting as spin 5/2 impurities in the core region of the wire gives rise to a strong s-d exchange coupling between electrons in the wire and those of the d levels of the Mn2 ions. Applying an external magnetic eld along the axis of the wire, within the mean eld approximation, the s-d exchange generates a spin-dependent core potential. A gate voltage is applied radially to wire, to obtain some control over the density of the wire. Electronic strucutre of the wire was calculated within the e?ective mass approximation, in both approximations Hartree and spin density functional theory. We calculated the conductance of wire using the Landauer-B?uttiker formulation in the linear response regime, which generally results in a total conductance with well-de ned plateaus in GT = 2; 6; 10G0 (G0 = e2=h is the quanta of conductance), which occurred because in the system investigated the rst level is twofold degenerated (spin degenerescence) and the others are fourfold degenerated (spin degenerescence and orbital angular momentum). In the absence of a magnetic eld we observe that when we take into account the e?ects of exchange and correlation, the states with eigenvalues of Lz nonzero will be polarized while those with l = 0 isn't polarized. This unpolarized level with eigenvalue of Lz null suggests that, perhaps, the 0.7 anomaly (the emergence of two plateau at G = 0:7G0 and the other in G = G0) quantum wires on existing geometry of split-gate is related to the geometry of the wire. The results for total energy show that there are a competition between the ferromagnetic and paramagnetic states.
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    Sobre os formalismos matemáticos da mecânica quântica: Dirac, von Neumann e álgebra C*
    (Universidade Federal de Goiás, 2013-09-30) Pfrimer, Frederico Rodrigues; Avelar, Ardiley Torres; http://lattes.cnpq.br/3273295678164245; Avelar, Ardiley Torres; Santana, Ademir Eugênio de; Piacente, Giovanni
    (Sem resumo)
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    Simulação óptica de uma partícula livre quântica relativística
    (Universidade Federal de Goiás, 2016-03-22) Silva, Thais de Lima; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Avelar, Ardiley Torres; Toscano, Fabricio; Walborn, Stephen Patrick
    Among the first attempts towards the unification of quantum and special relativity theories that which more highlighted was the Dirac’s electron theory. Amongst its achievements is the accurated calculation of the hydrogen spectrum and the antiparticles prediction. Even though it provides good results, some difficulties arise in this theory such as the existence of negative energy states for free particles. At the same time that it allows for the antiparticle discovery, it leads to questions like the trembling motion of a free electron (zitterbewegung). It is not a consensus whether this motion is real or just a theoretical failure in describing the reality. In this work we present a proposal to simulate the Dirac electron dynamics and, therefore, zitterbewegung, by means of a transformation of a paraxial light beam. The same transformation as is carried out on the vector state by the Dirac’s evolution operator is implemented in the transverse beam profile using wave plates and spatial light modulator. The proposal includes the cases of one and two spatial dimensions by simulating the spatial degrees of freedom into the transverse coordinates of the light beam, which offers a difficulty in simulating the three dimensional dynamics in general case. However, we show that it is possible for particular initial states. Our simulation presents some advantages over previously ones, namely: it does not require the construction of specificaly designed devices; the adjustable parameters are present on phases printed by the modulator and can be arbitrarily changed; it permits the measurement of the mean as well as the standard position operators; it permits the simulation in two and three spatial dimensions.
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    Traço parcial em sistemas relativísticos: uma nova visão
    (Universidade Federal de Goiás, 2013-11-08) Taillebois, Emile Raymond Ferreira; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Toscano, Fabrício; Walborn, Stephen Patrick
    In this dissertation, the use of the partial trace of momentum degrees of freedom in the construction of spin reduced density matrices for relativistic massive systems is analyzed. In the regime considered here, massive particles can be described by irreducible unitary representations of the Poincar e group, and the base states are labeled by the dynamical variables of momentum and spin. The reduced density matrices obtained by the partial trace of momenta have unusual properties, since they are not covariant under the action of restricted Lorentz transformations. That behavior produces some important consequences in the study of quantum information in relativistic systems. However, recent arguments have been presented against the use of those matrices in the description of processes involving the transfer of information stored in spin degrees of freedom of relativistic massive particles. Those criticisms are discussed in this dissertation and a connection with the structure of the space of states associated with a given unitary representation is established through a detailed study of the induced representation method applied to the Poincar e group. This allows rewriting the criticisms in literature without the need of a speci c model of interaction for the spin measurement. Besides that, the analysis performed here allows to establish a new method to construct e ective spin reduced density matrices. The presented approach allows recovering the results in the literature and, at the same time, to incorporate the criticisms in a consistent way. However, it is necessary to abandon the usual partial trace of the momentum degrees of freedom and the interpretation in the literature for the spin reduced density matrices. The examples presented in the arguments against the usual spin reduced density matrices are studied using the approach proposed in this dissertation.
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    Campos escalares aplicados em cosmologia
    (Universidade Federal de Goiás, 2018-07-13) Vieira, Lucas Elias; Avelar, Ardiley Torres; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4766756E0; Avelar, Ardiley Torres; Cardoso, Wesley Bueno; Brito, Francisco de Assis de
    In this work, we study topological defects in classical field theory aiming applications in cosmology. Topological and non-topological solutions were investigated in two dimensions, where we also analyzed the stability of some of these. We consider models of one and two real scalar fields, whose solutions were obtained via quadrature, BPS and orbit methods. The stability of these solutions also were investigated in some cases. In order to apply scalar field theory in cosmology, we revisit some topics of general relativity, such that the principle of equivalence, Einstein's field equations and Schwarzschild's solution for Einstein's equation. We also present some topics in cosmology, relevant to the present work, such that the cosmological principle, Hubble's law and cosmological inflation. We discuss the solutions of the Einstein's equations in the FRW metric in the so-called Hot Big Bang model-the universe composed of matter and radiation. In order to solve some problems of initial conditions of the universe, we introduce the inflationary theory, which supposes that the primordial universe was underwent an accelerated expansion guided by a scalar field. In sequence, we introduce the standard cosmological model, which states that the universe is in accelerated expansion driving by a cosmological constant, named dark energy, which constitutes about seventy percent of the universe energy. Finally, we present a first order formalism for cosmology and discuss two model describing the standard and tachyonics dynamics for scalar field that represent the dark energy.