Non BPS topological defect associated with two coupled real field

We investigate a stability equation involving two-component eigenfunctions which is associated with a potential model in terms of two coupled real scalar fields, which presents non BPS topological defect.Comment: Revtex, 6 pages, no figures. This work was presented in the XXII Brazilian National Meeting on Particles and Fields (October/2001), to appear at http://www.sbf.if.usp.b

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

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

Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

State determination: an iterative algorithm

An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.Comment: 11 pages 3 figure

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