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Doctoral Thesis
DOI
10.11606/T.43.2004.tde-10032014-143742
Document
Author
Full name
Alberto Carlos Bertuola
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2004
Supervisor
Committee
Pato, Mauricio Porto (President)
Almeida, Alfredo Miguel Ozorio de
Marvulle, Valdecir
Oliveira, Mario Jose de
Teotonio Sobrinho, Paulo
Title in Portuguese
Teoria das matrizes aleatórias e o formalismo da entropia generalizada
Keywords in Portuguese
Entropia
Sistemas dinâmicos
Termodinâmica
Abstract in Portuguese
A introdução de uma nova expressão matemática para a entropia permite construir novos ensembles na Teoria das Matrizes Aleatórias. Neste trabalho, apresenta-se uma estrutura geral para construção de todos os possíveis ensemble. Portanto, os elementos das matrizes podem ser números reais, complexos ou mesmo quaternions. O principio da entropia (não-extensiva) máxima e o Cálculo Variacional são usados para realizar essa façanha. Esta tese está comprometida com a construção do Ensemble Ortogonal Generalizado, cujas matrizes aleatórias são simétricas e seus elementos são os números reais, especificamente. As distribuições das matrizes, as distribuições de um elemento da matriz e as estatísticas espectrais são obtidas, estudadas e os resultados apresentados.
Title in English
Theory of Random Matrices and the Formalism of Generalized Entropy
Keywords in English
Dynamic systems
Entropy
Thermodynamics
Abstract in English
The introduction of a new mathematical expression for the entropy allows the construction of new ensembles in Random Matrices Theory. A general structure is presented to the construction of all possible ensembles. Therefore the matrix's elements can be real numbers, complex numbers or even quaternions. The generalized of the maximum entropy (nonextensive) principle and the variational calculus are to use to realize this achievement. This thesis concerned with the construction of the Generalized Orthogonal Ensemble, whose random matrices are symetric and its elements are real numbers. The matrix distribuit ion, the distribuition of an element of the matrix and the spectrum statistical were to obtained, studied and the results presented.
 
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46480Bertuola.pdf (34.49 Mbytes)
Publishing Date
2014-03-12
 
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