arXiv subjects

E. da Hora

Publications and source records attributed to E. da Hora.

At least 19 recordsLinked to original sources

arXiv2026

Oscillons from $Q$-balls in generalized models

We study the oscillon/$Q$-ball relation in an extended model with non-canonical kinematics. The model contains a single real scalar field whose kinetic term is enlarged to include a generalizing function. We approximate the real sector up to the third order in a book-keeping parameter. In this context, we implement the Renormalization Group Perturbation Expansion (RGPE), from which we conclude that the relation between oscillons and underlying $Q$-balls holds even in the presence of nontrivial kinematics. We apply our results to the study of three different effective cases. In all of them, our expressions mimic the numerical evolution of nonstandard oscillons with great accuracy, especially for small and moderate amplitudes. As the initial amplitude increases, the numerical profile develops a modulated behavior, and we use a two $Q$-balls solution to seed our analytical oscillon. We discuss how our non-canonical construction allows the existence of a well-behaved oscillon in connection to the simplest $\phi^2$-potential. This novel profile behaves in the same general way as the previous ones. So, we argue that they belong to the same universality class. Finally, we extend our analysis to consider those contributions up to the fifth order in the approximation expansion. We explore an exotic $\phi^6$-scenario, and conclude that the relation between generalized oscillons and underlying $Q$-balls now belongs to a different universality class.

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arXiv2026

Exact BPS double-kinks in generalized $ϕ^4$, $ϕ^6$ and sine-Gordon models

We consider a $(1+1)$-dimensional theory with a single real scalar field $ϕ$ whose kinematics is modified by a generalizing function $f(ϕ)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a particular $f(ϕ)$ to obtain analytic BPS double-kink solutions in three different models governed by the $ϕ^4$, $ϕ^6$, and sine-Gordon superpotentials. In all cases, the resulting double-kinks approach the boundaries by following an exponential decay, with the generalizing function controlling its dependence on $x$ and mass. We also calculate the BPS bound explicitly and study how the double kinks behave near the origin. The energy distribution of the novel BPS states engenders symmetric two-lump profiles for the $ϕ^4$ and sine-Gordon superpotentials. Whereas, for the $ϕ^6$ superpotential, the BPS energy profiles form asymmetric two-lumps.

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arXiv2025

Geometrically constrained sine-Gordon field: BPS solitons and their collisions

We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $ϕ$ and $χ$ whose scalar potential $V(ϕ,χ)$ has a standard $χ^4$ sector and a sine-Gordon one for $ϕ$. These fields are coupled through a generalizing function $f(χ)$ that appears in the scalar potential and controls the nontrivial dynamics of $ϕ$. We minimize the effective energy via the implementation of the BPS technique. We then obtain the Bogomol'nyi bound for the energy and the first-order equations whose solutions saturate that bound. We solve these equations for a nontrivial $f(χ)$. As the result, BPS kinks with internal structures emerge. They exhibit a two-kink profile. i.e. an effect due to geometrical constrictions. We consider the linear stability of these new configurations. In this sense, we study the existence of internal modes that play an important role during the scattering process. We then investigate the kink-antikink collisions, and present the numerical results for the most interesting cases. We also comment about their most relevant features.

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arXiv2025

Sine-Gordon kink lattice

We consider an extended model with two real scalar fields, $ϕ(x,t)$ and $χ(x,t)$. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the $χ^4$ one. The fields mutually interact via a nontrivial coupling function $f(χ)$ that also changes the kinematics of $ϕ$. We briefly review the implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. We then solve the resulting BPS equations for two different interactions $f$. The first one leads to a single kink-kink configuration, while the second one gives rise to a inhomogeneous sine-Gordon kink lattice. We study the linear stability of these new solutions, focusing on their translational modes. We also explore how the strength of the mutual interaction affects the BPS profiles. In particular, we show that a homogeneous lattice with identical kinks is attained in the regime of extremely strong interactions.

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arXiv2025

Vacuum state perturbed by an oscillon: composite configurations in $ϕ^4$ model

We examine the evolution of a vacuum configuration when perturbed by an oscillon. We consider the $ϕ^4$ scenario with a single scalar field only. For highly excited oscillons, we find that new composite solutions appear. They are formed by multiple antikink-kink pairs and a centered reminiscent oscillon. The overall process gives rise to a resonant structure whose pattern resembles that of a genuine kink-antikink scattering. We then approximate the initial oscillon by a lumplike profile constructed as a kink-antikink pair. We map the numerical results previously obtained. The developments proposed here may contribute to the understanding of the mechanism through which an oscillon decay reproduces the structure typically related to a kink-antikink collision.

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arXiv2024

Restricted baby Skyrme-Maxwell theory in a magnetic medium: BPS configurations and some properties

We study the existence of BPS configurations in a restricted baby Skyrme-Maxwell enlarged via the inclusion of a nontrivial magnetic permeability. In order to attain such a goal, we use the Bogomol'nyi-Prasad-Sommerfield prescription, which allows us to obtain the lower bound for the energy and the BPS equations whose [electrically neutral] solutions saturate that bound. During the energy minimization procedure, we find a differential constraint which involves the self-dual potential, the superpotential itself and also the magnetic permeability. In order to solve the BPS system, we focus our attention on those solutions with rotational symmetry. For that, we fix the magnetic permeability and select two BPS potentials which exhibit a similar behavior near to the vacuum. We depict the resulting profiles and proceed to an analytical description of the properties of the BPS magnetic field. Furthermore, we consider some essential aspects of our model, such as the conditions for the overall existence of the BPS solutions, and how the permeability affects the magnetic flux. Finally, we present a family of exact BPS solutions.

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arXiv2024

BPS chiral vortices in a Maxwell-Higgs electrodynamics

We investigate the existence of BPS structures in a Maxwell-Higgs electrodynamics immersed within a chiral medium, whose electromagnetic properties are described by both the Chern-Simons term and a neutral scalar field. The implementation of the Bogomol'nyi-Prasad-Sommerfield's technique provides the BPS potential and the self-dual equations whose solutions saturate the Bogomol'nyi bound. In such a context, we look for vortices in two chiral media: the first one engenders localized vortices with an exponential decay similar to that of the Abrikosov-Nielsen-Olesen solutions, whereas the second medium generates delocalized profiles whose tail follows a power-law decay. Once we have solved the BPS systems, we comment on the effects induced by the presence of the chiral medium on the Maxwell-Higgs vortices.

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arXiv2022

BPS solitons with internal structures in a restricted baby Skyrme-Maxwell theory in a magnetic medium

We consider a restricted baby Skyrme-Maxwell scenario enlarged via the inclusion of a nontrivial magnetic permeability. We then proceed with the minimization of its total energy by means of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription, from which we get that the self-dual potential now depends on the magnetic permeability itself. As a result, we obtain not only the lower bound for the energy, but also the self-dual equations whose solutions saturate that bound. In such a context, we focus our attention on those time-independent gauged skyrmions with radial symmetry and no electric charge. We solve the effective self-dual equations numerically for different choices of the magnetic permeability, from which we obtain BPS magnetic fields whose internal structures form concentric rings. We also explain analytically the formation of these structures based on the values of a single real parameter which characterizes the respective magnetic permeabilities.

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arXiv2022

Maxwell-$CP(2)$ vortices in the presence of magnetic impurities

We consider a Maxwell-$CP(2)$ model extended to include a magnetic impurity. We focus our attention on the time-independent configurations with radial symmetry, from which we minimize the corresponding energy by following the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. We use the general first-order expressions in order to introduce modified scenarios in which the impurity plays a relevant role. We then solve the effective first-order equations numerically by means of a finite-difference scheme, from which we comment on the main changes on the shape of the final solutions caused by the presence of a localised impurity. We also discuss the limit when the impurity becomes a delta function.

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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.

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arXiv2020

BPS Maxwell-Chern-Simons vortices with internal structures: the Abelian Higgs and the gauged $CP(2)$ cases

We investigate the existence of first-order vortices inherent to both the Maxwell-Chern-Simons-Higgs and the Maxwell-Chern-Simons-$CP(2)$ models extended via the inclusion of an extra scalar sector which plays the role of a source field. For both cases, we focus our attention on the time-independent configurations with radial symmetry which can be obtained through the implementation of the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. In this sense, in order to solve the corresponding first-order differential equations, we introduce some particular scenarios which are driven by the source field whose presence, we expect, must change the way the resulting vortices behave. After solving the effective first-order system through a finite-difference algorithm, we comment about the main new effects induced by the presence of the source field in the shape of the final configurations.

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arXiv2019

Topological first-order solitons in a gauged $CP(2)$ model with the Maxwell-Chern-Simons action

We verify the existence of radially symmetric first-order solitons in a gauged $CP(2)$ scenario in which the dynamics of the Abelian gauge field is controlled by the Maxwell-Chern-Simons action. We implement the standard Bogomol'nyi-Prasad-Sommerfield (BPS) formalism, from which we obtain a well-defined lower bound for the corresponding energy (i.e. the Bogomol'nyi bound) and the first-order equations saturating it. We solve these first-order equations numerically by means of the finite-difference scheme, therefore obtaining regular solutions of the effective model, their energy being quantized according the winding number rotulating the final configurations, as expected. We depict the numerical solutions, whilst commenting on the main properties they engender.

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arXiv2019

First-order solitons with internal structures in an extended Maxwell-$CP(2)$ model

We study a Maxwell-$CP(2)$ model coupled to a real scalar field through a dielectric function multiplying the Maxwell term. In such a context, we look for first-order rotationally symmetric solitons by means of the Bogomol'nyi algorithm, i.e. by minimizing the total energy of the effective model. We perform our investigation by choosing an explicit form of the dielectric function. The numerical solutions show regular vortices whose shapes dramatically differ from their canonical counterparts. We can understood such differences as characterizing the existence of an internal structure.

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arXiv2018

Nontopological first-order vortices in a gauged $CP(2)$ theory endowed with the Chern-Simons action

We study a gauged $CP(2)$ scenario model with the Chern-Simons term, focusing our attention on those time-independent radially symmetric configurations with nontopological profile. We proceed the minimization of the effective energy in order to introduce the corresponding first-order framework, from which we define a legitimate self-dual scenario. We solve the resulting first-order equations numerically by means of the finite-difference scheme, from which we depict the nontopological solutions. We also identify a special kind of solutions which can be partially described by an analytical treatment.

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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.

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arXiv2017

Nontopological first-order vortices in a gauged $CP(2)$ model with a dielectric function

We consider nontopological first-order solitons arising from a gauged $CP(2)$ model in the presence of the Maxwell term multiplied by a nontrivial dielectric function. We implement the corresponding first-order scenario by proceeding the minimization of the total energy, this way introducing the corresponding energy lower-bound, such a construction being only possible due to a differential constraint including the dielectric function itself and the self-interacting potential defining the model. We saturate the aforementioned bound by focusing our attention on those solutions fulfilling a particular set of two coupled first-order differential equations. In the sequel, in order to solve these equations, we choose the dielectric function explicitly, also calculating the corresponding self-interacting potential. We impose appropriate boundary conditions supporting nontopological solitons, from which we verify that the energy of final structures is proportional to the magnetic flux they engender, both quantities being not quantized, as expected. We depict the new numerical solutions, whilst commenting on the main properties they present.

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arXiv2017

Topological first-order vortices in a gauged CP(2) model

We study time-independent radially symmetric first-order solitons in a CP(2) model interacting with an Abelian gauge field whose dynamics is controlled by the usual Maxwell term. In this sense, we develop a consistent first-order framework verifying the existence of a well-defined lower bound for the corresponding energy. We saturate such a lower bound by focusing on those solutions satisfying a particular set of coupled first-order differential equations. We solve these equations numerically using appropriate boundary conditions giving rise to regular structures possessing finite-energy. We also comment the main features these configurations exhibit. Moreover, we highlight that, despite the different solutions we consider for an auxiliary function $β\left( r\right) $ labeling the model (therefore splitting our investigation in two a priori distinct branches), all resulting scenarios engender the very same phenomenology, being physically equivalent.

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arXiv2016

Self-dual configurations in Abelian Higgs models with $k$-generalized gauge field dynamics

We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a $k$-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of $F_{μν}F^{μν}$. We have implemented our proposal by means of a $k$-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol'nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of $k$-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with $|ϕ|^4$-potential or $|ϕ|^6$-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the $k$-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.

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