Modeling of interfaces in two-dimensional problems using solid finite elements with high aspect ratio

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-buson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED, with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED, with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Theta-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content. (C) 2002 Elsevier B.V. (USA).

Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional spacetime

The problem of scattering of neutral fermions in two-dimensional spacetime is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein's paradox are presented. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength. Added plausibility for the existence of bound-state solutions in a pseudoscalar double-step potential found in a recent Letter is given. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Confinement of spinless particles by Coulomb potentials in two-dimensional space-time

The problem of confinement of spinless particles in 1 + 1 dimensions is approached with a linear potential by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling. (c) 2005 Elsevier B.V. All rights reserved.

Restrictions over two-dimensional gauge models with Thirring-like interaction

Some years ago, it was shown how fermion self-interacting terms of the Thirring-type impact the usual structure of massless two-dimensional gauge theories [1]. In that work only the cases of pure vector and pure chiral gauge couplings have been considered and the corresponding Thirring term was also pure vector and pure chiral respectively, such that the vector ( or chiral) Schwinger model should not lose its chirality structure due to the addition of the quartic interaction term. Here we extend this analysis to a generalized vector and axial coupling both for the gauge interaction and the quartic fermionic interactions. The idea is to perform quantization without losing the original structure of the gauge coupling. In order to do that we make use of an arbitrariness in the definition of the Thirring-like interaction.

Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time

The problem of confinement of fermions in 1 + 1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Two-dimensional position-dependent massive particles in the presence of magnetic fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-Zeeman splitting for a spin-resolved STM with a Kondo adatom in a spin-polarized two-dimensional electron gas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

Mixing-demixing transition and collapse of a vortex state in a quasi-two-dimensional boson-fermion mixture

We investigate the mixing-demixing transition and the collapse in a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex. We solve numerically a quantum-hydrodynamic model based on a new density functional which accurately takes into account the dimensional crossover. It is demonstrated that with the increase of interspecies repulsion, a mixed state of DBFM could turn into a demixed state. The system collapses for interspecies attraction above a critical value which depends on the vortex quantum number. For interspecies attraction just below this critical limit there is almost complete mixing of boson and fermion components. Such mixed and demixed states of a DBFM could be experimentally realized by varying an external magnetic field near a boson-fermion Feshbach resonance, which will result in a continuous variation of interspecies interaction.

Two-dimensional dipolar Bose-Einstein condensate bright and vortex solitons on a one-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dipolar Bose-Einstein condensate soliton on a two-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-dimensional background field gravity: A Hamilton-Jacobi analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)