M.A. Marques

From kinks to compactons

Abstract This work deals with the presence of localized structures in relativistic systems described by a single real scalar field in two-dimensional spacetime. We concentrate on kinks and compactons in models with standard kinematics, and we develop a procedure that helps us to smoothly go from kinks to compactons in the suggested scenario. We also show how the procedure works in the braneworld scenario, for flat brane in the five-dimensional spacetime with a single extra dimension of infinite extent. The brane unveils a hybrid profile when the kink becomes a compacton, behaving as a thick or thin brane, depending on the extra dimension being inside or outside a compact space.

Compact structures in standard field theory

We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential equations and illustrate how to find compact structures in models engendering standard kinematics. In particular, we study linear stability and show that all the static solutions we have found are linearly stable.

Compact Q-balls

Abstract In this work we deal with non-topological solutions of the Q-ball type in two space–time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls solutions that live in a compact interval of the real line and appear from a family of models controlled by two distinct parameters. We find analytical solutions and study their charge and energy, and show how to control the parameters to make the Q-balls classically and quantum mechanically stable.

Maxwell–Higgs vortices with internal structure

Abstract Vortices are considered in relativistic Maxwell–Higgs systems in interaction with a neutral scalar field. The gauge field interacts with the neutral field via the presence of generalized permeability, and the charged and neutral scalar fields interact in a way dictated by the presence of first order differential equations that solve the equations of motion. The neutral field may be seen as the source field of the vortex, and we study some possibilities, which modify the standard Maxwell–Higgs solution and include internal structure to the vortex.

First order formalism for generalized vortices

Abstract This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell–Higgs, the Chern–Simons–Higgs and the Maxwell–Chern–Simons–Higgs models. The investigation focuses on the construction of models that support vortices that obey the stressless condition and lead to first order differential equations which are compatible with the equations of motion. The results induce the appearance of constraints that restrict the choice of the Lagrangian densities, but help us to introduce an auxiliary function that allows to calculate the energy without knowing the explicit form of the solutions.

Compact Chern–Simons vortices

Abstract We introduce and investigate new models of the Chern–Simons type in the three-dimensional spacetime, focusing on the existence of compact vortices. The models are controlled by potentials driven by a single real parameter that can be used to change the profile of the vortex solutions as they approach their boundary values. One of the models unveils an interesting new behavior, the tendency to make the vortex compact, as the parameter increases to larger and larger values. We also investigate the behavior of the energy density and calculate the total energy numerically.

Exact solutions, energy, and charge of stable Q-balls

In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable.

New braneworld models in the presence of auxiliary fields

We study braneworld models in the presence of auxiliary fields. We use the first-order framework to investigate several distinct possibilities, where the standard braneworld scenario changes under the presence of the parameter that controls the auxiliary fields introduced to modify Einsteins equation. The results add to previous ones, to show that the minimal modification that we investigate contributes to change quantitatively the thick braneworld profile, although no new qualitative effect is capable of being induced by the minimal modification here considered.

Generalized Born-Infeld–like models for kinks and branes

In this work we deal with a non-canonical scalar field in the two-dimensional spacetime. We search for a generalized model that is twin of the standard model, supporting the same defect structure with the same energy density. We also study the stability of the defect solution under small fluctuations, which is governed by a Sturm-Liouville equation, and show how to make it stable. The model is then modified and used in the five-dimensional spacetime to construct a thick brane that engenders the first order framework and preserves the twinlike behavior, under tensorial fluctuations of the metric in its gravitational sector.

Analytic vortex solutions in generalized models of the Maxwell–Higgs type

Abstract This work deals with the presence of analytical vortex configurations in generalized models of the Maxwell–Higgs type in the three-dimensional spacetime. We implement a procedure that allows to decouple the first order equations, which we use to solve the model analytically. The approach is exemplified with three distinct models that show the robustness of the construction. In the third model, one finds analytical solutions that exhibit interesting compact vortex behavior.