Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions

The phase structures of Nambu-Jona-Lasinio models with one or two flavours have been investigated at non-zero values of $\mu$ and $H$, where $H$ is an external magnetic field and $\mu$ is the chemical potential. In the phase portraits of both models there arise infinitely many massless chirally symmetric phases, as well as massive ones with spontaneously broken chiral invariance, reflecting the existence of infinitely many Landau levels. Phase transitions of first and second orders and a lot of tricritical points have been shown to exist in phase diagrams. In the massless case, such a phase structure leads unavoidably to the standard van Alphen-de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density. In the massive case we have found an oscillating behaviour not only for thermodynamical quantities, but also for a dynamical quantity as the quark mass. Besides, in this case we have non-standard, i.e. non-periodic, magnetic oscillations, since the frequency of oscillations is an $H$-dependent quantity.Comment: latex, 29 pages, 8 figure

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.Comment: New references added, Published online in Foundations of Physic

Riscos e Retornos da Cafeicultura em Minas Gerais: uma análise de custos e diferenciação

O objetivo deste trabalho foi analisar, comparativamente, o desempenho dos produtores de café do Cerrado mineiro e do sudoeste do estado, de acordo com o retorno obtido e o nível de risco. Dadas as opções estratégicas adotadas nessas duas regiões, a diferenciação e os custos foram enfatizados. As margens e os potenciais de perda dos dois grupos de cafeicultores foram mensurados, o que permitiu apresentar uma relação entre risco e retorno. Os retornos foram estimados por um índice que relaciona custos e preços - margem operacional -, e a análise de riscos foi realizada a partir das estimativas do Value at Risk. Os resultados indicaram que os produtores do Cerrado, além de terem obtido melhores retornos, apresentaram menores perdas potencias que os do sudoeste. Os resultados favoráveis aos cafeicultores do Cerrado foram relacionados às diferenças dos custos produtivos e da qualidade do café. Incrementos na qualidade do produto e melhorias na gestão do processo produtivo foram os aspectos considerados relevantes para melhorar o desempenho do produtor do sudoeste. Já em relação à cafeicultura do Cerrado, destacou-se a importância de manter os esforços ligados à diferenciação e à produtividade.<br>This paper aimed to analyze the comparative performance from the Minas Gerais "Cerrado" coffee producers and the south-western conventional coffee producers, according to the returns and the risk level. Differentiation and costs were emphasized because they were the strategic options adopted by the grower in these two regions The margins and potential loss of these two producer groups were measured, in a way that a relation between risks and returns could be presented. The returns were estimated by an index that relates costs and prices - operational margin -, and risk analysis was conducted based on Value at Risk estimates. The results indicated that, besides obtaining better returns, the Minas Gerais "Cerrado" producers had smaller loss potential than those from the south-west. The favorable results obtained by the Minas Gerais "Cerrado" coffee producers were related to the differences in productive costs and coffee quality. Improved product quality and productive management were the most relevant aspects found to enhance the performance of the south-western coffee producer. As for the "Cerrado" coffee production, the importance of maintaining the efforts related to differentiation and to the productivity was pointed out