Searcharxiv⌕ Search

arXiv subjects

V. Almeida

Publications and source records attributed to V. Almeida.

5 recordsLinked to original sources
arXiv2022

Self-dual $CP(2)$ vortex-like solitons in the presence of magnetic impurities

We investigate the existence of vortex configurations in two gauged-$CP(2)$ models extended via the inclusion of magnetic impurities. In particular, we consider both the Maxwell-$CP(2)$ and the Chern-Simons-$CP(2)$ enlarged scenarios, separately. We choose a $CP(2)$-field configuration with a null topological charge not only in the simplest (free) case, but also when coupled to an Abelian gauge field. The implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism shows that the effective models for such a configuration possess a self-dual structure which looks like those inherent to the gauged sigma models. Therefore, when the $CP(2)$ field is coupled to the Maxwell term, the corresponding total energy possesses both a well-defined Bogomol'nyi bound and a quantized magnetic flux. Further, when the $CP(2)$ scenario is gauged with the Chern-Simons action, the total electric charge is verified to be proportional to the quantized magnetic flux. In addition, the analysis verifies that the magnetic impurity contributes to the BPS potentials and appears in both the models' BPS equations. Next, we introduce a Gaussian type impurity and solve the self-dual equations via a finite-difference scheme. The resulting solutions present a nonmonotonic behavior that flips both the magnetic and electric fields. Finally, we discuss the topologically trivial solutions in the limit for which the impurity becomes a Dirac $δ$-function.

hep-th↗
arXiv2021

Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting

In this paper we consider Littlewood-Paley functions defined by the semigroups associated with the operator $\mathcal{A}=-\fracΔ{2}-x\nabla$ in the inverse Gaussian setting for Banach valued functions. We characterize the uniformly convex and smooth Banach spaces by using $L^p(\mathbb{R}^n,γ_{-1})$- properties of the $\mathcal{A}$-Littlewood-Paley functions. We also use Littlewood-Paley functions associated with $\mathcal{A}$ to characterize the Köthe function spaces with the UMD property.

math.CA↗
arXiv2018

First-order vortices in a gauged $CP(2)$ model with a Chern-Simons term

We consider a gauged $CP(2)$ theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the Bogomol'nyi prescription, from which we obtain the corresponding energy lower-bound and the first-order equations the model supports. We use these expressions to introduce effective BPS scenarios, solving the resulting first-order equations by means of the finite-difference scheme, this way attaining genuine field solutions engendering topological configurations. We depict the new profiles, commenting on the main properties they engender.

hep-th↗
arXiv2017

Anisotropic Hardy-Lorentz spaces with variable exponents

In this paper we introduce Hardy-Lorentz spaces with variable exponents associated to dilation in ${\Bbb R}^n$. We establish maximal characterizations and atomic decompositions for our variable exponent anisotropic Hardy-Lorentz spaces.

math.FA↗