arXiv subjects

F. C. Simas

Publications and source records attributed to F. C. Simas.

9 recordsLinked to original sources

arXiv2025

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

We consider a $(1+1)$-dimensional theory with a single real scalar field $\phi$ whose kinematics is modified by a generalizing function $f(\phi)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a particular $f(\phi)$ to obtain analytic BPS double-kink solutions in three different models governed by the $\phi^4$, $\phi^6$, 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 $\phi^4$ and sine-Gordon superpotentials. Whereas, for the $\phi^6$ superpotential, the BPS energy profiles form asymmetric two-lumps.

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arXiv2024

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

We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a generalizing function $f(\chi)$ that appears in the scalar potential and controls the nontrivial dynamics of $\phi$. 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 $f(\chi)$. 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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arXiv2018

False vacuum decay in kink scattering

In this work we consider kink-antikink and antikink-kink collisions in a modified $ϕ^4$ model with a false vacuum characterized by a dimensionless parameter $ε$. The usual $ϕ^4$ model is recovered for $ε=0$. We investigate the $ε<<1$ regime where the kink in the presence of false vacuum can be understood as a small deformation of the standard kink for the $ϕ^4$ model. We show that the attractive interaction between the kink-antikink pair leads to a rich scattering pattern, in some cases delaying considerably the false vacuum decay.

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arXiv2017

Degenerate vacua to vacuumless model and $K\bar K$ collisions

In this work we investigate a $Z_2$ symmetric model of one scalar field $ϕ$ in $(1,1)$ dimension. The model is characterized by a continuous transition from a potential $V(ϕ)$ with two vacua to the vacuumless case. The model has kink and antikink solutions that minimize energy. Stability analysis are described by a Schrödinger-like equation with a potential that transits from a volcano-shape with no vibrational states (in the case of vacuumless limit) to a smooth valley with one vibrational state. We are interested on the structure of 2-bounce windows present in kink-antikink scattering processes. The standard mechanism of Campbell-Schonfeld-Wingate (CSW) requires the presence of one vibrational state for the occurrence of 2-bounce windows. We report that the effect of increasing the separation of vacua from the potential $V(ϕ)$ has the consequence of trading some of the first 2-bounce windows predicted by the CSW mechanism by false 2-bounce windows. Another consequence is the appearance of false 2-bounce windows of zero-order.

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arXiv2016

Suppression of two-bounce windows in kink-antikink collisions

We consider a class of topological defects in $(1,1)$-dimensions with a deformed $ϕ^4$ kink structure whose stability analysis leads to a Schrödinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect of the appearance of more than one vibrational mode is the gradual disappearance of the initial two-bounce windows. The total suppression of two-bounce windows even with the presence of a vibrational mode offers a counterexample from what expected from the standard mechanism. For even larger deformation, some two-bounce windows reappear, but with a non-standard structure.

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arXiv2015

Trapping Spin-$0$ particles on $p-$balls in $(D,1)$ dimensions

p-Balls are topological defects in $(D,1)$ dimensions constructed with $\mathcal{M}\ge 1$ scalar fields which depend radially on only $2 \le p\le D-2$ spatial dimensions. Such defects are characterized by an action that breaks translational invariance and are inspired on the physics of a brane with $D-p$ extra dimensions. Here we consider the issue of localization of bosonic states described by a scalar field $Φ$ sufficiently weak to not disturb sensibly the defect configuration. After describing the general formalism, we consider some specify examples with $\mathcal{M}=1,2$ and $3$, looking for some region of parameters where bound and resonant bosonic states can be found. We investigate the way the influence of the defect structure, number of radial dimensions and coupling between the fields are related to the occurrence of bound and resonant states.

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arXiv2014

Kink-antikink collisions for twin models

In this work we consider kink-antikink collisions for some classes of $(1,1)$-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be revealed in a collision process. We consider a particular class of models known as twin theories, where different models lead to same solutions for the equations of motion and same energy density profile. The theories can be distinguished in the level of linear stability of defect structure. We study a class of k-defect theories depending on a parameter $M$ which is the twin theory of the usual $ϕ^4$ theory with standard dynamics. For $M\to\infty$ both models are characterized by the same potential. In the regime $1/M^2<<1$, we obtain analytically the spectrum of excitations around the kink solution. It is shown that with the increasing on the parameter $1/M^2$: i) the gap between the zero-mode and the first-excited mode increases and ii) the tendency of one-bounce collision between kink-antikink increases. We numerically investigate kink-antikink scattering, looking for the influence of the parameter changing for the thickness and number of two-bounce windows, and confronting the results with our analytical findings.

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arXiv2014

Trapping of Spin-0 fields on tube-like topological defects

We have considered the localization of resonant bosonic states described by a scalar field $Φ$ trapped in tube-like topological defects. The tubes are formed by radial symmetric defects in $(2,1)$ dimensions, constructed with two scalar fields $ϕ$ and $χ$, and embedded in the $(3,1)-$dimensional Minkowski spacetime. The general coupling between the topological defect and the scalar field $Φ$ is given by the potential $ηF(ϕ,χ)Φ^2$. After a convenient decomposition of the field $Φ$, we find that the amplitudes of the radial modes satisfy Schrödinger-like equations whose eigenvalues are the masses of the bosonic resonances. Specifically, we have analyzed two simple couplings: the first one is $F(ϕ,χ)=χ^2$ for a fourth-order potential and, the second one is a sixth-order interaction characterized by $F(ϕ,χ)=(ϕχ)^2$% . In both cases the Schrödinger-like equations are numerically solved with appropriated boundary conditions. Several resonance peaks for both models are obtained and the numerical analysis showed that the fourth-order potential generates more resonances than the sixth-order one.

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arXiv2013

Trapping Dirac fermions in tubes generated by two scalar fields

In this work we consider $(1,1)-$dimensional resonant Dirac fermionic states on tube-like topological defects. The defects are formed by rings in $(2,1)$ dimensions, constructed with two scalar field $ϕ$ and $χ$, and embedded in the $(3,1)-$dimensional Minkowski spacetime. The tube-like defects are attained from a lagrangian density explicitly dependent with the radial distance $r$ relative to the ring axis and the radius and thickness of the its cross-section are related to the energy density. For our purposes we analyze a general Yukawa-like coupling between the topological defect and the fermionic field $ηF(ϕ,χ)\barψψ$. With a convenient decomposition of the fermionic fields in left- and right- chiralities, we establish a coupled set of first order differential equations for the amplitudes of the left- and right- components of the Dirac field. After decoupling and decomposing the amplitudes in polar coordinates, the radial modes satisfy Schrödinger-like equations whose eigenvalues are the masses of the fermionic resonances. With $F(ϕ,χ)=ϕχ$ the Schrödinger-like equations are numerically solved with appropriated boundary conditions. Several resonance peaks for both chiralities are obtained, and the results are confronted with the qualitative analysis of the Schrödinger-like potentials.

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