q-Deformed Kink Solutions

The q-deformed kink of the $\lambda\phi^4-$model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. From such a bosonic zero-mode the q-deformed potential in 1+1 dimensions is found, and we show that the q-deformed kink solution is a kink displaced away from the origin.Comment: REvtex, 11 pages, 2 figures. Preprint CBPF-NF-005/03, site at http://www.cbpf.br. Revised version to appear in International Journal of Modern Physics

Three dimensional Lifshitz black hole and the Korteweg-de Vries equation

We consider a solution of three dimensional New Massive Gravity with a negative cosmological constant and use the AdS/CTF correspondence to inquire about the equivalent two dimensional model at the boundary. We conclude that there should be a close relation with the Korteweg-de Vries equation.Comment: 4 page

On Matrix Superpotential and Three-Component Normal Modes

We consider the supersymmetric quantum mechanics (SUSY QM) with three- component normal modes for the Bogomol'nyi-Prasad-Sommerfield (BPS) states. An explicit form of the SUSY QM matrix superpotential is presented and the corresponding three-component bosonic zero-mode eigenfunction is investigated.Comment: 17 pages, no figure. Paper accepted for publication in Journal of Physics A: Mathematical and Theoretica

On Useful Conformal Tranformations In General Relativity

Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical purposes and represents a collection of exercises concerning local conformal transformations and dimensional reduction. To be published in "Gravitation and Cosmology

A semiquantitative approach to the impurity-band-related transport properties of GaMnAs nanolayers

We investigate the spin-polarized transport of GaMnAs nanolayers in which a ferromagnetic order exists below a certain transition temperature. Our calculation for the self-averaged resistivity takes into account the existence of an impurity band determining the extended ("metallic" transport) or localized (hopping by thermal excitation) nature of the states at and near the Fermi level. Magnetic order and resistivity are inter-related due to the influence of the spin polarization of the impurity band and the effect of the Zeeman splitting on the mobility edge. We obtain, for a given range of Mn concentration and carrier density, a "metallic" behavior in which the transport by extended carriers dominates at low temperature, and is dominated by the thermally excited localized carriers near and above the transition temperature. This gives rise to a conspicuous hump of the resistivity which has been experimentally observed and brings light onto the relationship between transport and magnetic properties of this material