Non-linear generalization of the sl(2) algebra

We present a generalization of the sl(2) algebra where the algebraic relations are constructed with the help of a general function of one of the generators. When this function is linear this algebra is a deformed sl(2) algebra. In the non-linear case, the finite dimensional representations are constructed in two different ways. In the first case, which provides finite dimensional representations only for the non-linear case, these representations come from solutions to a dynamical equation and we show how to construct explicitly these representations for a general quadratic non-linear function. The other type of finite dimensional representation comes from solutions to a cut condition equation. We give examples of solutions of this type in the non-linear case as well.Comment: 13 pages, 3 EPS figures, Late

New aspects on Current enhancement in Brownian motors driven by non Gaussian noises

Recent studies on Brownian motors driven by colored non Gaussian noises have shown that the departure of the noise distribution from Gaussian behavior induces an enhancement of its current and efficiency. Here we discuss some new aspects of this phenomenon focusing in some analytical results based in an adiabatic approximation, and in the analysis of the long probability distribution tails' role.Comment: 11 pages, 4 figs. Physica A (in press

Generalized quantum field theory: perturbative computation and perspectives

We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we construct a quantum field theory that creates at any space-time point particles described by a q-deformed Heisenberg algebra and we compute the propagator and a specific first order scattering process. Concerning the second one, we draw attention to the possibility of constructing this theory where each state of a generalized Heisenberg algebra is interpreted as a particle with different mass.Comment: 19 page

Construction of a non-standard quantum field theory through a generalized Heisenberg algebra

We construct a Heisenberg-like algebra for the one dimensional quantum free Klein-Gordon equation defined on the interval of the real line of length $L$. Using the realization of the ladder operators of this type Heisenberg algebra in terms of physical operators we build a 3+1 dimensional free quantum field theory based on this algebra. We introduce fields written in terms of the ladder operators of this type Heisenberg algebra and a free quantum Hamiltonian in terms of these fields. The mass spectrum of the physical excitations of this quantum field theory are given by $\sqrt{n^2 \pi^2/L^2+m_q^2}$, where $n= 1,2,...$ denotes the level of the particle with mass $m_q$ in an infinite square-well potential of width $L$.Comment: Latex, 16 page

Distributivity and deformation of the reals from Tsallis entropy

We propose a one-parameter family \ $\mathbb{R}_q$ \ of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish a one-parameter family of field isomorphisms \ $\tau_q$ \ between \ $\mathbb{R}$ \ and \ $\mathbb{R}_q$ \ through which an absolute value on \ $\mathbb{R}_q$ \ is introduced. This turns out to be a quasisymmetric map, whose metric and measure-theoretical implications are pointed out.Comment: 16 pages, Standard LaTeX2e, To be published in Physica

Generating statistical distributions without maximizing the entropy

We show here how to use pieces of thermodynamics' first law to generate probability distributions for generalized ensembles when only level-population changes are involved. Such microstate occupation modifications, if properly constrained via first law ingredients, can be associated not exclusively to heat and acquire a more general meaning.Comment: 6 pages, no figures, Conferenc

O cavalo e a jovem rapariga

A história do cavalo e da jovem rapariga é contada por Ésquines no contexto de um caso jurídico. Esta comunicação propõe mostrar que a história contada no Contra Timarco tem vários níveis de leitura. A interpretação moralista que o próprio Ésquines oferece revela que o seu significado último já se tinha perdido no séc. IV a. C. Os eventos narrados têm elementos muito antigos ligados às ideias sobre o feminino e às transgressões de tabus sexuais. A leitura que oferecemos defende o ponto de vista de que a donzela e o cavalo são arquétipos intemporais do ser humano.The story of the horse and the maiden is told by Aeschines in the context of a case of court litigation. This paper has the intention of showing that the story told in the speech Contra Timarchum has several levels of interpretation. The moral interpretation that Aeschines himself offers does reveal that the ultimate meaning had already been lost in the fourth century B. C. The events narrated in the speech have very old meanings connected to the ideas about the feminine and the transgressions of sexual taboos. The interpretation that is offered by the present authors defends the point of view that the maiden and the horse are timeless archetypes of the human being