Teorias fermiônicas efetivas sob condições extremas

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Física, Florianópolis, 2009Nesta tese utilizamos o método analítico não perturbativo, conhecido por teoria de perturbação otimizada junto com o princípio de mínima sensitividade, para estudar os diagramas de fases associados aos modelo de Gross-Neveu, em 2 + 1 dimensões, e ao modelo de Nambu-Jona-Lasinio, na versão U (1), em 3 + 1 dimensões. Nossas abordagens são feitas através do cálculo da densidade de energia livre de Landau (ou potencial efetivo) em temperaturas e densidades finitas. Uma atenção especial é dedicada a revisão destes modelos calculados na chamada aproximação de N- grande tendo como principal motivação o fato de que nossos resultados introduzem correções de N finito. Os principais resultados apresentados, associados ao modelo de Gross-Neveu, são a localização precisa do ponto tricrítico e de uma fase mista "líquido-gás". Com relação ao modelo de Nambu-Jona-Lasinio mostramos que nossas primeiras correções contribuem nos caso em que a densidade é diferente de zero produzindo resultados que, na aproximação de N-grande, apenas são obtidos ao custo da introdução de um termo extra

Fundamental connections in differential geometry : quantum field theory, electromagnetism, chemistry and fluid mechanics

This work presents novel hydrodynamic formulations that reconcile the continuum hypothesis with the emergence of electromagnetic interactions among molecules from fundamental principles. Two models are proposed: a relativistic version of the Navier-Stokes equations derived from commutation relations, and a Helmholtz-like system obtained by applying the Hodge operator to the extended Navier-Stokes equations. Preliminary analysis suggests that the second model, with its nonlinear terms serving as a generalized current, can reproduce microscopic quantum effects. It shows promise for generating self-consistent field equations via Bäcklund transformations, remaining valid across all scales despite the breakdown of the continuum hypothesis

A quantum toy-model for inelastic scattering and catalysis based on Bäcklund transformations

This work presents a scalar self-consistent quantum model for molecular simulation. This model employs Bäcklund transformations to eliminate the wave function from Klein-Gordon and Schrödinger-type equations. The nonlinear PDE obtained after coupling the quantum model with the Gauss law of electromagnetism contains only the interaction potential. The analytical solutions obtained reproduce some relevant effects related to the evolution of the electronic clouds induced by nonlinear scattering. One of the most relevant results obtained from this new formulation is to confirm and fully justify the fact that Cl2 molecules do not react directly with aromatic rings. This result cannot be reproduced by classical models for molecular simulation. On the other hand, quantum chemistry only furnishes indicia that such electrophilic reactions may not occur, but does not shows explicitly how the electronic clouds evolve along the chemical process

Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter

Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a $1/N_c$ suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential $\mu$, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite $N_c$ contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For $\mu \gtrsim \mu_c$ the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value $G/(2N_c)$, where $G$ is the scalar coupling, and then increases with $\mu$ in a well-determined manner.Comment: 9 pages, 5 figures. In press Int. J. Mod. Phys. E (2012

Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions

The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross-Neveu model in 2+1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.Comment: 7 pages, 2 eps figures. Replaced with the version that matches the published one (PLB