arXiv subjects

Anderson Ilha

Publications and source records attributed to Anderson Ilha.

8 recordsLinked to original sources

arXiv2017

A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals

A lattice Boltzmann method is proposed based on the expansion of the equilibrium distribution function in powers of a new set of generalized orthonormal polynomials which are here presented. The new polynomials are orthonormal under the weight defined by the equilibrium distribution function itself. The D-dimensional Hermite polynomials is a sub-case of the present ones, associated to the particular weight of a gaussian function. The proposed lattice Boltzmann method allows for the treatment of semi-classical fluids, such as electrons in metals under the Drude-Sommerfeld model, which is a particular case that we develop and validate by the Riemann problem.

physics.comp-ph↗

arXiv2013

Lattice Boltzmann method for bosons and fermions and the fourth order Hermite polynomial expansion

The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded until fourth order in the Hermite polynomials.

physics.flu-dyn↗

arXiv2001

Duality equivalence between nonlinear self-dual and topologically massive models

In this report we study the dual equivalence between the generalized self-dual (SD) and topologically massive (TM) models. To this end we linearize the model using an auxiliary field and apply a gauge embedding procedure to construct a gauge equivalent model. We clearly show that, under the above conditions, a nonlinear SD model always has a duality equivalent TM action.The general result obtained is then particularized for a number of examples, including the Born-Infeld-Chern-Simons (BICS) model recently discussed in the literature.

hep-th↗

arXiv2001

Interference of Spin-2 Self-Dual Modes

We study the effects of interference between the self-dual and anti self-dual massive modes of the linearized Einstein-Chern-Simons topological gravity. The dual models to be used in the interference process are carefully analyzed with special emphasis on their propagating spectrum. We identify the opposite dual aspects, necessary for the application of the interference formalism on this model. The soldered theory so obtained displays explicitly massive modes of the Proca type. It may also be written in a form of Polyakov-Weigman identity to a better appreciation of its physical contents.

hep-th↗

arXiv2000

Topological Mass Generation as an Interference Phenomenon

It is proposed a new mechanism for the phenomenon of topological mass generation in three spacetime dimensions as the result of the interference of two opposite massless chiral modes. This mechanism, already used to produce the massive vectorial mode of the 2D Schwinger model, is here exploited to produce the gauge invariant massive mode of the Maxwell-Chern-Simons theory. Moreover the procedure is clearly dimensionally independent: a new chiral boson action is proposed for odd and even dimensional space-times to be used as the basic building blocks of the interference schemes. This is a new result that extends the two-dimensional Floreanini-Jackiw action to higher dimensional spaces and is in clear contrast with the twice odd dimensional chiral form extensions.

hep-th↗

arXiv2000

Interference Phenomenon for the Faddeevian Regularization of 2D Chiral Fermionic Determinants

The classification of the regularization ambiguity of 2D fermionic determinant in three different classes according to the number of second-class constraints, including the new faddeevian regularization, is examined and extended. We found a new and important result that the faddeevian class, with three second-class constraints, possess a free continuous one parameter family of elements. The criterion of unitarity restricts the parameter to the same range found earlier by Jackiw and Rajaraman for the two-constraints class. We studied the restriction imposed by the interference of right-left modes of the chiral Schwinger model ($χQED_{2}$) using Stone's soldering formalism. The interference effects between right and left movers, producing the massive vectorial photon, are shown to constrain the regularization parameter to belong to the four-constraints class which is the only non-ambiguous class with a unique regularization parameter.

hep-th↗

arXiv1999

Dimensionally continued Oppenheimer-Snyder gravitational collapse II: solutions in odd dimensions

The Lovelock gravity extends the theory of general relativity to higher dimensions in such a way that the field equations remain of second order. The theory has many constant coefficients with no a priori meaning. Nevertheless it is possible to reduce them to two, the cosmological constant and Newton's constant. In this process one separates theories in even dimensions from theories in odd dimensions. In a previous work gravitational collapse in even dimensions was analysed. In this work attention is given to odd dimensions. It is found that black holes also emerge as the final state of gravitational collapse of a regular dust fluid.

gr-qc↗

arXiv1996

Dimensionally continued Oppenheimer-Snyder gravitational collapse. I - solutions in even dimensions

The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued Euler characteristics of lower dimensions. The theory has many constant coefficients apparently without any physical meaning. However, it is possible, in a natural way, to reduce to two (the cosmological and Newton's constant) these several arbitrary coefficients, yielding a restricted Lovelock gravity. In this process one separates theories in even dimensions from theories in odd dimensions. These theories have static black hole solutions. In general relativity, black holes appear as the final state of gravitational collapse. In this work, gravitational collapse of a regular dust fluid in even dimensional restricted Lovelock gravity is studied. It is found that black holes emerge as the final state for these regular initial conditions.

gr-qc↗