arXiv subjects

D. Bazeia

Publications and source records attributed to D. Bazeia.

At least 19 recordsLinked to original sources

arXiv2026

Large lumps

We introduce a procedure to obtain lump solutions via the formation of a kink-antikink pair, consisting of the superposition of kinks whose distance from the origin is controlled by a single parameter $a$. For large values of $a$, a wide plateau appears in the solution, which we call a large lump. The procedure involves the use of a first-order equation that allows the construction of the potential associated with the lump solution. We then investigate several known scalar field models where the parent kinks are capable of giving rise to novel lumps. The lump inherits the tails of the parent kink, allowing for either short-range exponential profiles or long-range profiles characterized by distinct power-law decays. We also show how to verify if an arbitrary lump solution can be obtained via our method and illustrate this possibility with a novel vacuumless lump.

hep-th↗

arXiv2026

Scalar fields, impurities and supersymmetry

We develop a rigid $\mathcal{N}=(1,1)$ superspace formulation for multifield scalar models coupled to localized impurities through spurion superfields in two-dimensional spacetime. The spurionic completion gives a manifestly supersymmetric action and provides a systematic framework for describing interacting scalar fields in the presence of impurity backgrounds. In this setting, supersymmetry acts as an organizing principle for a controlled bosonic half-BPS sector, with the preserved projector selecting the impurity-compatible first-order equations. We derive the corresponding coupled BPS equations, energy density, boundary conditions, and Bogomol'nyi bound, showing that localized impurities deform the BPS profiles and redistribute the local energy density while leaving the total BPS energy fixed by the topological boundary term. We illustrate the formalism through representative one-, two-, and three-field models, analyzing the resulting BPS configurations and their local energy density profiles.

hep-th↗

arXiv2026

Geometrically constrained multi-kink configurations in generalized impurity-doped field theories

This short communication investigates impurity coupling in generalized field theories where scalar coupling is introduced directly at the level of the kinetic and gradient contributions of the energy. We show that the fundamental aspects of the original theory, which has been previously investigated in the impurity-free setting, can be extended to the inhomogeneous scenario. In particular, an interpretation in terms of geometrically-constrained effective one-field theories with impurities is possible in the separable case. We show that BPS multi-kink configurations are possible in the model, as well as in the usual half-BPS scalar theories.

hep-th↗

arXiv2026

Compact structures in impurity-doped vacuumless systems

We investigate novel structures which arise from the compactification of vacuumless kinks in scalar field models coupled to impurities that preserve half the BPS sectors, described by first-order equations. We also investigate the behavior of the energy density and linear stability of the solutions. We show that compact vacuumless kinks cannot be obtained in impurity-free canonical models. By considering two distinct impurities, we study the conditions needed to induce compactification. In this scenario, stable half-compact or compact solutions are shown to emerge from the systems.

hep-th↗

arXiv2026

Half-BPS Impurity Backgrounds and Supersymmetry

We develop a rigid $\mathscr{N} =(1,1)$ superspace framework for spatially inhomogeneous impurity deformations in $D=1+1$ dimensions by embedding the impurity profile into a real background superfield (spurion). This spurionic completion provides a manifestly supersymmetric description at the level of the action and offers a systematic route to identify which inhomogeneous backgrounds preserve a nontrivial subset of supercharges. Focusing on static interface-type configurations, we determine the half-BPS condition on the spurion background and the corresponding supersymmetry projector. In the resulting half-BPS sector we derive the associated first-order BPS equation for static bosonic matter configurations and establish an exact Bogomol'nyi completion of the static energy, yielding a sharp bound saturated by BPS solutions. We further comment on how explicit coordinate dependence and derivative-dependent impurity couplings can obstruct the Bogomol'nyi structure, thereby motivating spurionic extensions that retain supersymmetric control over inhomogeneous deformations.

hep-th↗

arXiv2025

Exact solutions for a complex scalar field under discrete symmetry

We report on the presence of families of exact solutions for a complex scalar field that behaves according to the rules of discrete $Z_N$ symmetry. Since the family of models is exactly solved, the results appear to be of interest to integrability, to build junctions and networks of localized structures and to describe scalar dark matter in high energy physics.

hep-th↗

arXiv2025

Some of the many uses of scalar fields: kinks, lumps, and geometric constraints

This perspective deals with real scalar fields in two-dimensional spacetime. We focus on models described by one and two real scalar fields, paying closer attention to kinks and lumps, which are localized structures of current interest in high energy physics and in other areas of nonlinear science. We briefly review some of the main results presented in the literature and then focus on some new issues concerning the compact and long-range behavior of solutions and the presence of geometric constraints, suggesting how they can be used in applications in other areas of nonlinear science.

hep-th↗

arXiv2025

Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints

We investigate a class of models described by two real scalar fields in two-dimensional spacetime. The study focuses mainly on the presence of exact static solutions which satisfy the first-order formalism, in models constructed to engender Lorentz symmetry violation. We start by exploring a direct connection between Lorentz breaking and geometric constraint, as experimentally examined in the case of domain walls in geometrically constrained magnetic materials. By means of a specific choice of functions, we show that imposing geometric constraint within the Lorentz-violating framework recovers the exact solutions of the corresponding Lorentz-invariant theory. Furthermore, we extend the investigation to new models that go beyond reproducing the Lorentz invariant geometrically constrained solutions, revealing that it remains possible to parametrize the first-order equation of one of the fields through a suitably redefined coordinate.

hep-th↗

arXiv2025

Magnetic monopoles in Yang-Mills-Higgs theory with impurities

In this work, BPS models built from the coupling of Yang-Mills-Higgs Lagrangian to impurities are investigated. We first consider scalar impurities, which in the BPS limit generate monopoles similar to those obtained in a previously considered class of $\mathrm{SU(2)}\times\mathrm{Z}_2$ or $\mathrm{SU(2)}\times\mathrm{SU(2)}$ models. We then focus on coupling with nonabelian impurities, defined as fixed backgrounds produced from fields transforming under the adjoint representation of SU(2), with a coupling chosen to preserve half of the BPS sectors. The nature of this coupling, the ensuing Bogomol'nyi bound and BPS equations, as well as the effect of these impurities in the abelianization that leads to the emergence of a U(1) gauge group are investigated. We study in greater detail impurities with spherical symmetry, and examine the manner in which impurity coupling changes the asymptotic behavior and range of monopole interactions. Moreover, we introduce a method that can be used to approximate solutions with the use of small perturbations around the Prasad-Sommerfield monopole, and discuss the possibility of extending the aforementioned results to dyons. In order to exemplify the most important properties of the theory, several specific impurity models are presented, with the respective monopole solutions are found numerically. These solutions present novel internal structure and multiple features that would not be possible in the original theory.

hep-th↗

arXiv2025

Kinks in generalized scalar field models and their scattering properties

This work investigates kink solutions in one-dimensional scalar field theories. We begin with a review of the formalism used to obtain these solutions, presenting the BPS formalism and linear stability analysis. Next, we explore new models involving real scalar fields, generated by distinct potentials, with a focus on the topological structures responsible for the formation of kinks. Finally, we study collisions between the solutions obtained in two distinct models, analyzing their dynamic implications.

hep-th↗

arXiv2025

Quantifying scale-free behaviors in Rock-Paper-Scissors Models as a function of Mobility

We investigate the scale-free behavior of the spatial rock-paper-scissors model with May-Leonard dynamics, analyzing specific quantifiers that engender the power-law feature. The main results show that an important parameter that drives the scale-free behavior is the mobility, which can be used to quantitatively describe several scale-free aspects of the model, such as the number of clusters, the characteristic length, the individuals' lifespan and its corresponding mean traveled distance. All of these are novel quantifiers of current practical interest for the study of biodiversity.

q-bio.PE↗

arXiv2025

Monitoring biodiversity on highly reactive rock-paper-scissors models

This work investigates how biodiversity is affected in a cyclic spatial May-Leonard model with hierarchical and non-hierarchical rules. Here we propose a generalization of the traditional rock-paper-scissors model by considering highly reactive species, i. e., species that react in a stronger manner compared to the others in respect to either competition or reproduction. These two classes of models, called here Highly Competitive and Highly Reproductive models, may lead to hierarchical and non-hierarchical dynamics, depending on the number of highly reactive species. The fundamental feature of these models is the fact that hierarchical models may as well support biodiversity, however, with a higher probability of extinction than the non-hierarchical ones, which are in fact more robust. This analysis is done by evaluating the probability of extinction as a function of mobility. In particular, we have analyzed how the dominance scheme changes depending on the highly reactive species for non-hierarchical models, where the findings lead to the conclusion that highly reactive species are usually at a disadvantage compared to the others. Moreover, we have investigated the power spectrum and the characteristic length of each species, including more information on the behavior of the several systems considered in the present work.

q-bio.PE↗

arXiv2025

Generalized scalar field models in the presence of impurities

We study generalized scalar field models coupled to impurities in Minkowski spacetime with arbitrary dimensions. The investigation concerns a class of models that depends explicitly on the spacetime coordinates and also, it reveals the presence of a second-order tensor that can have null divergence if a first-order equation and a constraint are satisfied. We obtain the conditions to get compatibility between the equation of motion and the first-order equation, within a framework that is also used in the static case, to show that the introduction of an auxiliary function may allow to describe the energy density of the solution as a divergence. Stability of the solution under rescale of argument, translation in the space and small fluctuations are also fully investigated. We further illustrate the procedure considering the canonical model and also, the $k$-field and Born-Infeld-like models. The results show that stable solutions can be obtained in arbitrary dimensions, and the stability seems to be related to the first-order equation that emerges from imposing null divergence of the aforementioned tensor.

hep-th↗

arXiv2025

Entangled states from simple quantum graphs

Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to generate entangled states through coherent control operations between two simple quantum graphs. A controlled operation is defined such that the scattering behavior of one quantum graph dynamically modifies the other. Our analysis reveals the precise conditions under which maximal entanglement or separability arises, including configurations that can be implemented via phase shifts in graph structures. Our findings demonstrate that the maximal entanglement in this system is closely related to recent results on randomized quantum graphs. These results provide new pathways for engineering entanglement using simple quantum graphs and suggest experimental feasibility using microwave networks.

quant-ph↗

arXiv2025

Radially symmetric scalar field solutions in the presence of cuscuton term

In this work, we investigate radially symmetric solutions in arbitrary dimensions in scalar field models in the presence of the cuscuton term. We introduce a first-order formalism compatible with the equation of motion which supports field configurations engendering minimum energy and show that the cuscuton term does not induce instabilities in the solutions. To illustrate the general results, we study two distinct classes of models and present analytical solutions and the corresponding energy densities.

hep-th↗

arXiv2025

Scalar fields with impurities in arbitrary dimensions: first-order framework and exact solutions

We study a class of scalar field models coupled to impurities in arbitrary spacetime dimensions. The system admits the introduction of a second-order tensor that can be forced to obey an equality, if a first-order differential equation is satisfied, compatible with the equation of motion when the potential engenders a very specific form. In the case of static solutions, the energy density of the system can equal the divergence of an auxiliary vector function, which is included to help us solve the model. Stability of the field configuration under rescale of argument is investigated, and the procedure is illustrated considering distinct canonical models. The results show that exact solutions can be obtained in arbitrary dimensions, related to the presence of the first-order equation.

hep-th↗

arXiv2025

Cuscuton-like contribution to dark energy evolution

This work deals with the presence of the cuscuton term in the otherwise standard dark energy evolution under the usual FLRW background. We disclose a first-order framework similar to the Hamilton-Jacobi formalism, which helps us to solve the equations of motion and find analytical solutions. We explore several possibilities, concentrating mainly on how the cuscuton-like contribution works to modify cosmic evolution. Some results are of current interest since they describe scenarios capable of changing the evolution, adding or excluding possible distinct phases during the Universe's expansion history. Additionally, we present interesting constraints on the cuscuton-like contribution for the dark energy evolution using a set of homogeneous geometrical observational probes. Finally, based on the Akaike Information Criterion (AIC), we perform a statistical comparison of the cuscuton-like model with $\Lambda$CDM, and find strong support for our model.

astro-ph.CO↗

arXiv2024

Geometrically constrained localized configurations engendering non-topological profile

This work deals with two real scalar fields in two-dimensional spacetime, with the fields coupled to allow the study of localized configurations. We consider models constructed to engender geometric constrictions, and use them to investigate solutions of the lump type, which attain no topological properties. We show how to modify the internal structure of the field configurations and the corresponding energy densities in several distinct ways, making them thinner, thicker and also, in the form of a multi-lump solution composed of two or more lumps or asymmetrically distributed around their associated centers. The results appear to be of current interest in high energy physics and may, in particular, be used to study bright solitons in optical fibers and in Bose-Einstein condensates.

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