Renormalized coordinate approach to the thermalization process

We consider a particle in the harmonic approximation coupled linearly to an environment. modeled by an infinite set of harmonic oscillators. The system (particle--environment) is considered in a cavity at thermal equilibrium. We employ the recently introduced notion of renormalized coordinates to investigate the time evolution of the particle occupation number. For comparison we first present this study in bare coordinates. For a long ellapsed time, in both approaches, the occupation number of the particle becomes independent of its initial value. The value of ocupation number of the particle is the physically expected one at the given temperature. So we have a Markovian process, describing the particle thermalization with the environment. With renormalized coordinates no renormalization procedure is required, leading directly to a finite result.Comment: 16 pages, LATEX, 2 figure

Magnetite and its transformation to hematite in a soil derived from steatite.

O presente trabalho objetivou caracterizar o mineral magnetico e identificar suas rotas pedogeneticas de transformacao em um solo formado sobre esteatito, de Minas Gerais, Brasil. O oxido de ferro isoestrutural ao espinelio foi identificado e caracterizado por analises quimicas, difracao de raios X, espectroscopia Mossbauer e medidas de magnetizacao de saturacao. Na rocha fresca, foi encontrada magnetita estequiometrica e bem cristalizada, com parametro da rede cubica, ao = 0.8407(5) nm. Nas fracoes areia e silte, foram detectadas magnetita parcialmente alterada e hematita estequiometrica e bem cristalizada, com parametros de rede hexagonal, a = 0.5036(3) nm e c = 1.375(4)nm. A ocorrencia dessas hematitas deveu-se principalmente a oxidacao do Fe2+ a Fe3+, no sitio octaedrico de magnetita, durante a pedogenese. Esse processo foi caracterizado pelo aparecimento de pequena quantidade de Fe3+ eletronicamente desacoplada, encontrada nas magnetitas parcialmente oxidadas, cujas formulas para as diferentes estequiometrias foram propostas. Verificou-se tambem pequena quantidade de ilmenita nas amostras de rocha e de solo

Perfect category-graded algebras

In a perfect category every object has a minimal projective resolution. We give a criterion for the category of modules over a categorygraded algebra to be perfect.Comment: A sufficient condition is replaced by a criterion. Several references added. 17 page