Modelo de Ginzburg-Landau a partir da teoria de campos a temperatura finita

Neste trabalho, utilizamos o formalismo de teorias quânticas de campos a temperatura finita, tal como desenvolvidas por Matsubara, aplicado a uma hamiltoniana de N campos escalares com autointeração quártica a N grande. Obtém-se uma expressão, na primeira aproximação quântica, para o coeficiente do termo quadrático da hamiltoniana ("massa quadrada"), renormalizado, como função da temperatura. A partir dela, estudamos o processo de quebra espontânea de simetria. Por outro lado, a mesma hamiltoniana é conhecida como modelo de Ginzburg-Landau na literatura de matéria condensada, e que permite o estudo de transições de fase em materiais ferromagnéticos. A temperatura é introduzida através do termo quadrático na hamiltoniana, de forma linear: é proporcional à diferença entre a variável de temperatura e a temperatura crítica. Tal modelo, porém, possui validade apenas na regi~ao de temperaturas próximas à criticalidade. Como resultado de nossos cálculos na teoria de campos a temperatura finita, observamos que, numa faixa de valores em torno da temperatura crítica, a massa quadrática pode ser aproximada por uma relação linear em relação à variável de temperatura. Isso evidencia a compatibilidade da abordagem de Ginzburg-Landau, na vizinhança da criticalidade, com respeito ao formalismo de campos a temperatura finita. Discutimos também os efeitos causados pela presença de um potencial químico no sistema.

Efeito Casimir em teorias de Chern-Simons

Nesta dissertação obtemos a força de Casimir a temperatura finita entre duas linhas paralelas sujeitas a condição de fronteira do tipo linhas mistas, no contexto da teoria de Maxwell- Chern-Simons em (2+1) dimensões. Além disso, analisamos a simetria de inversão de temperatura apresentada pela energia livre de Helmholtz do modelo para diferentes condições de fronteira. Iniciamos estudando aspectos gerais do formalismo de Matsubara no intuito de introduzirmos efeitos térmicos na teoria; também analisamos aspectos gerais da teoria de MCS em (2 + 1) dimensões. Posteriormente, revisitamos o cálculo da força de Casimir para o caso de duas linhas paralelas infinitamente permeáveis magneticamente a temperatura nula e finita, bem como o caso de linhas mistas a temperatura nula, onde tomamos uma linha perfeitamente condutora eletricamente e outra infinitamente permeável magneticamente. Em seguida, apresentamos novos resultados envolvendo a força de Casimir a temperatura finita com condições de fronteira do tipo linhas mistas. Por último, analisamos a simetria de inversão de temperatura associada a energia livre de Helmholtz do modelo, mostrando que mesmo para condições mistas e possível obter uma espécie de simetria residual, em analogia a resultados existentes para a eletrodinâmica em (3+1) dimensões.

Matsubara-Fradkin thermodynamical quantization of Podolsky electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A quantização da eletrodinâmica de Podolsky em equilíbrio termodinâmico no formalismo de Matsubara-Fradkin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A creature of statute: Copyright law and legal formalism

This article argues that copyright law is not just a creature of statute, but it is also a social and imaginative contruct. It evaluates a number of critiques of legal formalism. Part 1 examines whether the positive rules and principles of copyright law are the product of historical contingency and political expediency. Part 2 considers the social operation of copyright law in terms of its material effects and cultural significance. Part 3 investigates the future of copyright law, in light of the politics of globalisation and the impact of new information technologies.

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Scheme of squares: Part II. Systems formalism for sinusoidal perturbations

We extend here the formalism developed in Part I (for the potentiostatic response) to the admittance analysis of the scheme of squares. The results are applicable, as before, to several configurations of the electrode such as the rotating disk or the planar. All that one has to do is “to plug in” the appropriate matrices relating the interfacial concentrations to the fluxes.

Many-body effects in electrochemisorption : Part IV. Multi-boson formalism

Several boson subsystems may be involved in electrosorption phenomena. To accommodate this possibility, the one-boson formalism described in Parts I–III is extended to this case. The hierarchy in the superoperator scheme, the evaluation of operator averages for closure and several special cases are indicated. As an illustration, some calculations are presented to indicate the trends of many-body corrections in chemisorption.

Fluctuation phenomena in electrochemistry part I. The formalism

A unified approach to the problem of electrochemical fluctuations is presented. On the basis of the Langevin procedure, primary noise sources are introduced in the basic phenomenological equations and a discussion of the secondary noise sources arising in the expressions for the power spectra of currents is given.

A new formalism for representation of binary thermodynamic data

The applicability of a formalism involving an exponential function of composition x1 in interpreting the thermodynamic properties of alloys has been studied. The excess integral and partial molar free energies of mixing are expressed as: $$\begin{gathered} \Delta F^{xs} = a_o x_1 (1 - x_1 )e^{bx_1 } \hfill \\ RTln\gamma _1 = a_o (1 - x_1 )^2 (1 + bx_1 )e^{bx_1 } \hfill \\ RTln\gamma _2 = a_o x_1^2 (1 - b + bx_1 )e^{bx_1 } \hfill \\ \end{gathered} $$ The equations are used in interpreting experimental data for several relatively weakly interacting binary systems. For the purpose of comparison, activity coefficients obtained by the subregular model and Krupkowski’s formalism have also been computed. The present equations may be considered to be convenient in describing the thermodynamic behavior of metallic solutions.

Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Socialist Realism instead of Formalism : the Formation and Development of the Soviet Music Control System 1932-1950

Whereas it has been widely assumed in the public that the Soviet music policy system had a “top-down” structure of control and command that directly affected musical creativity, in fact my research shows that the relations between the different levels of the music policy system were vague, and the viewpoints of its representatives differed from each other. Because the representatives of the party and government organs controlling operas could not define which kind of music represented Socialist Realism, the system as it developed during the 1930s and 1940s did not function effectively enough in order to create such a centralised control of Soviet music, still less could Soviet operas fulfil the highly ambiguous aesthetics of Socialist Realism. I show that musical discussions developed as bureaucratic ritualistic arenas, where it became more important to reveal the heretical composers, making scapegoats of them, and requiring them to perform self-criticism, than to give directions on how to reach the artistic goals of Socialist Realism. When one opera was found to be unacceptable, this lead to a strengthening of control by the party leadership, which lead to more operas, one after the other, to be revealed as failures. I have studied the control of the composition, staging and reception of the opera case-studies, which remain obscure in the West despite a growing scholarly interest in them, and have created a detailed picture of the foundation and development of the Soviet music control system in 1932-1950. My detailed discussion of such case-studies as Ivan Dzerzhinskii’s The Quiet Don, Dmitrii Shostakovich’s Lady Macbeth of Mtsensk District, Vano Muradeli’s The Great Friendship, Sergei Prokofiev’s Story of a Real Man, Tikhon Khrennikov’s Frol Skobeev and Evgenii Zhukovskii’s From All One’s Heart backs with documentary precision the historically revisionist model of the development of Soviet music. In February 1948, composers belonging to the elite of the Union of Soviet Composers, e.g. Dmitri Shostakovich and Sergei Prokofiev, were accused in a Central Committee Resolution of formalism, as been under the influence of western modernism. Accusations of formalism were connected to the criticism of the conciderable financial, material and social privileges these composers enjoyed in the leadership of the Union. With my new archival findings I give a more detailed picture of the financial background for the 1948 campaign. The independent position of the music funding organization of the Union of Soviet Composers (Muzfond) to decide on its finances was an exceptional phenomenon in the Soviet Union and contradicted the strivings to strengthen the control of Soviet music. The financial audits of the Union of Soviet Composers did not, however, change the elite status of some of its composers, except for maybe a short duration in some cases. At the same time the independence of the significal financial authorities of Soviet theatres was restricted. The cuts in the governmental funding allocated to Soviet theatres contradicted the intensified ideological demands for Soviet operas.

Superoperator formalism and chemisorption theory

It is pointed out that the superoperator formalism, developed for the calculation of ionization potentials in molecular physics, is a very powerful tool in chemisorption theory. This is demonstrated by applying the formalism to the Anderson-Newns model and by showing how the different approximate solutions can be obtained by elegant and systematic procedures. It is also pointed out that using the formalism, solutions for more complicated hamiltonians can easily be obtained.

Extension of Darken's Quadratic Formalism to Dilute Multicomponent Solutions

Darken's quadratic formalism is extended to multicomponent solutions. Equations are developed for the representation of the integral and partial excess free energies, entropies and enthalpies in dilute multicomponent solutions. Quadratic formalism applied to multicomponent solutions is thermodynamically consistent. The formalism is compared with the conventional second order Maclaurin series or interaction parameter representation and the relations between them are derived. Advantages of the quadratic formalism are discussed.

Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant Xi,or X i/Xj are presented. The expression for In γsolvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.