El mundo en una fórmula.

Se trata la aportación de Heisenberg al mundo de la física, con su mecánica cuántica matricial, que contribuye a la explicación del mundo microscópico.

Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l (1) of absolutely summable lattice potentials to the optimal class l (2) of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l (1) case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l (2) in the Bernoulli case. Open problems are discussed.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

The magnetic phase diagram of Gd(2)Sn(2)O(7)

Measurements of the magnetic susceptibility of the frustrated pyrochlore magnet Gd(2)Sn(2)O(7) have been performed at temperatures below T = 5 K and in magnetic fields up to H = 12 T. The phase boundaries determined from these measurements are mapped out in an H-T phase diagram. In this gadolinium compound, where the crystal-field splitting is small and the exchange and dipolar energy are comparable, the Zeeman energy overcomes these competing energies, resulting in at least four magnetic phase transitions below 1 K. These data are compared against those for Gd(2)Ti(2)O(7) and will, we hope, stimulate further studies.

2-(4,5,6,7-tetrafluorobenzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, a hydrogen-bonded organic quasi-1D ferromagnet

The title radical (F4BlmNN) is a stable nitronylnitroxide that forms hydrogen-bonded NH center dot center dot center dot ON chains in the solid state. The chains assemble the F4BlmNN molecules to form stacked contacts between the radical groups, in a geometry that is expected to exhibit ferromagnetic (FM) exchange based on spin polarization (SP) models. The experimental magnetic susceptibility of F4BlmNN confirms the expectation, showing 1-D Heisenberg chain FM exchange behavior over 1.8-300 K with an intrachain exchange constant Of J(chain)/k = +22 K. At lower temperatures, ac magnetic susceptibility and variable field heat capacity measurements show that F4BlmNN acts as a quasi-1-D ferromagnet. The dominant ferromagnetic exchange interaction is attributable to overlap between spin orbitals of molecules within the hydrogen-bonded chains, consistent with the SP model expectations. The chains appear to be antiferromagnetically exchange coupled, giving cusps in the ac susceptibility and zero field heat capacity at lower temperatures. The results indicate that the sample orders magnetically at about 0.7 K. The magnetic heat capacity ordering cusp shifts to lower temperatures as external magnetic field increases, consistent with forming a bulk antiferromagnetic phase below a Neel temperature of T-N(0) = 0.72 K, with a critical field of H-c approximate to 1800 Oe. The interchain exchange is estimated to be zJ/k congruent to (-)0.1 K.

Isostructural M(RL)(2)(hfac)(2) complexes with RL=5-(4-[N-tert-butyl-N-aminoxyl]phenyl)pyrimidine

5-(4-(N-tert-Butyl-N-aminoxylphenyl)) pyrimidine (RL, 4PPN) forms crystallographically isostructural and isomorphic pseudo-octahedral M(RL)(2)(hfac)(2) complexes with M(hfac)(2), M = Zn, Cu, Ni, Co, and Mn. Multiple close contacts occur between sites of significant spin density of the organic radical units. Magnetic behavior of the Zn, Cu, Ni, Co complexes appears to involve multiple exchange pathways, with multiple close crystallographic contacts between sites that EPR (of 4PPN) indicates to have observable spin density. Powder EPR spectra at room temperature and low temperature are reported for each complex. Near room temperature, the magnetic moments of the complexes are roughly equal to those expected by a sum of non-interacting moments (two radicals plus ion). As temperature decreases, AFM exchange interactions become evident in all of the complexes. The closest fits to the magnetic data were found for a 1-D Heisenberg AFM chain model in the Zn(II) complex (J/k = (-)7 K), and for three-spin RL-M-RL exchange in the other complexes (J/k = (-)26 K, (-)3 K, (-) 6 K, for Cu(II), Ni(II), and Co(II) complexes, respectively). (C) 2008 Elsevier B.V. All rights reserved.

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

Themean value of the one-loop energy-momentum tensor in thermal QED with an electric-like background that creates particles from vacuum is calculated. The problem is essentially different from calculations of effective actions ( similar to the action of Heisenberg-Euler) in backgrounds that respect the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and the duration over which one can neglect the back-reaction of created particles are established.

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

We study the influence of ferromagnetic and antiferromagnetic bond defects on the ground-state energy of antiferromagnetic spin chains. In the absence of translational invariance, the energy spectrum of the full Hamiltonian is obtained numerically, by an iterative modi. cation of the power algorithm. In parallel, approximate analytical energies are obtained from a local-bond approximation, proposed here. This approximation results in significant improvement upon the mean-field approximation, at negligible extra computational effort. (C) 2008 Published by Elsevier B.V.

Análise do modelo t-J e sua aplicação aos compostos de óxidos de cobre

Neste trabalho estudamos modelos teóricos que descrevem sistemas eletrônicos fortemente correlacionados, em especial o modelo t-J, e suas aplicações a compostos de óxidos de cobre, notadamente os compostos que apresentam supercondutividade de alta temperatura crítica e o composto Sr2CuO2Cl2. No primeiro capítulo do trabalho, fazemos uma exposição de três modelos que envolvem o tratamento das interações elétron-elétron, que são os modelos de Hubbard de uma banda, o modelo de Heisenberg e o modelo t-J. Na dedução deste último fazemos uma expansão canônica do hamiltoniano de Hubbard, no limite de acoplamento forte, levando-nos a obter um novo hamiltoniano que pode ser utilizado para descrever um sistema antiferromagnético bidimensional na presen- ça de lacunas, que é exatamente o que caracteriza os compostos supercondutores de alta temperatura crítica na sua fase de baixa dopagem.Após termos obtido o hamiltoniano que descreve o modelo t-J, aplicamos à este uma descrição de polarons de spin, numa representação de holons, que são férmions sem spin, e spinons, que são bósons que carregam somente os graus de liberdade de spin. Utilizando uma função de Green para descrever a propagação do polaron pela rede, obtemos uma equação para a sua autoenergia somando uma série de diagramas de Feynman, sendo que para este cálculo utilizamos a aproxima ção de Born autoconsistente[1]. Do ponto de vista numérico demonstramos que a equação integral de Dyson resultante do tratamento anterior não requer um procedimento iterativo para sua solução, e com isto conseguimos trabalhar com sistemas com grande número de partículas. Os resultados mostram, como um aspecto novo, que o tempo de vida média do holon tem um valor bastante grande no ponto (π,0 ) da rede recíproca, perto da singularidade de Van Hove mencionada na literatura[2]. Este aspecto, e suas implicações, é amplamente discutido neste capítulo. No capítulo 3 estudamos o modelo estendido t-t'-J, com tunelamento à segundos vizinhos e a incorporação dos termos de três sítios[3]. Fazemos a mesma formulação do capítulo anterior, e discutimos as aplicações dos nossos resultados ao óxido mencionado anteriormente. Finalmente, no último capítulo apresentamos uma aplicação original do modelo t-J à uma rede retangular, levemente distorcida, e demonstramos que os resultados do capítulo 3 são reproduzidos sem necessidade de introduzir termos de tunelamento adicionais no hamiltoniano. Esta aplicação pode se tornar relevante para o estudo das fases de tiras encontradas recentemente nesses materiais de óxidos de cobre.

Ciência como montagem, montagem como ciência

The thesis describes parallel possibilities between the knowledge built in theatre and in Science. The narrative is constructed through a reflexive observation of the process of making a threatical play, specifically O Tempo da Chuva by Grupo Beira de Teatro , in analogy to the process of making a scientific theory, specifically the one described by Werner Heisenberg in his book Physics and Beyond: encounters and conversations . It sets a dialog with authors/actors from various areas of knowledge, such as Edgar Morin, Werner Heisenberg, René Descartes, Paul Feyerabend, Paul Caro, Juremir Machado da Silva, Maria da Conceição de Almeida, Renato Ferracini, among others. It discusses the hypothesis that Science is the process of building and the theatrical process of building a play can also be systematized, likewise science. The thesis defends, as the complexities science may suggest, a method as a strategy. Developed throughout the process, such method could only be verified at the end, when the elements of the setting of atomic physics theories and theatre were correlated. Questions such as: the place of theatre and science in our contemporary society and the political and ethical role of artists and scientists are at the episthemological basis of this narrative which we have started, but it is not even close to a conclusion

Música, filosofia, formação: por uma escuta sensível do mundo

La musique, plus qu`um mot et le texte écrit, a le pouvoir de produire le déplacement du sujet en relation aux contingences du temps e de l´espace. Entendre de la musique est plus que de l´amusement. Comme un artifice cognitif qui ultrapasse l´expérience analytique e métonymique, les formes tonales doublent la réalité, expandent les sens, actionent l´imagination, retotalisent les sentiments, amplient les expériences, permettent la rencontre du sujet avec les éssences des phénomènes qui ne sont pas traductibles par les mots. Nous écoutons de la musique pour restituer notre dignité e conférer à la vie plus de vérité, plus de concrétion (Santiago Kovadloff). La mélodie permet l´expérimentation des états de cohésion, de conéction pleine entre sens et intention, entre commencement et fin, de la finitude de la vie (Schopenhauer). Le phénomène musical provoque l´expréssion de la douleur, de la souffrance et, au même temps, du jubile et de la joie, réliant nature et homme (Nietzsche). Tenant comme base cette compréhension, la dissertation tient dans la musique une importante métaphore pour comprendre la complexité humaine, une fois qu´elle propicie une écoute sensible du monde et mobilise dans le sujet l´expérimentation de divers états de l´être. Nous pouvons dire que la musique est un opérateur de la conaissence parce qu´elle fait affleurer l´écoute intérieure, la rencontre du sujet avec lui même. Cet opérateur cognitif actione les pôles de l´ésprit qui font dialoguer sensibilité, éthique et esthétique, ordre et chaos, silence et bruit, mouvement et pause, repétition et inovation. Par l´expérience musicale, nous habitons des formes hibrides de sensibilité et raison. L´inachèvement, notre principal caractéristique comme humains, a, dans la musique, une image impair, parce que la musique est l´expression du dévir. Pour tisser ces arguments, la dissertation part des études de Schopenhauer et Nietzsche sur la musique, esthétique et métaphysique; Expose des fragments de la biographie de trois grands penseurs contemporains (Werner Heinsenberg, Ilya Prigogine et Edgar Morin) accentuant la présence de la musique en ses vies; et, par fin, présente ce que nous appelons biographies sonores de quatre artistes-musiciens brésiliens (Benedito Juarez et Gil Jardim, de São Paulo, et Ronaldo Ferreira de Lima et, Cleudo Freire, du Rio Grande do Norte)

Efeitos de interface em bicamadas magnéticas acopladas

We have developed a theoretical study of magnetic bilayers composed by a ferromagnetic film grown in direct contact on an antiferromagnetic one. We have investigated the interface effects in this systems due to the interfilms coupling. We describe the interface effects by a Heisenberg like coupling with an additional unidirectional anisotropy. In the first approach we assume that the magnetic layers are thick enough to be described by the bulk parameters and they are coupled through the interaction between the magnetic moments located at the interface. We use this approach to calculate the modified dynamical response of each material. We use the magnetic permeability of the layers (with corrections introduced by interface interactions) to obtain a correlation between the interface characteristics and the physical behavior of the magnetic excitations propagating in the system. In the second model, we calculated an effective susceptibility of the system considering a nearly microscopical approach. The dynamic response obtained by this approach was used to study the modifications in the spectrum of the polaritons and its consequences on the attenuated total reflection (ATR). In addition, we have calculated the oblique reflectivity. We compare our result with those obtained for the dispersion relation of the magnetostatic modes in these systems

Ondas de spin em super-redes ferromagnéticas com campo de anisotropia

Conselho Nacional de Desenvolvimento Científico e Tecnológico