arXiv subjects

Adalto R. Gomes

Publications and source records attributed to Adalto R. Gomes.

18 recordsLinked to original sources

arXiv2025

Half-line kink scattering in the $ϕ^4$ model with Dirichlet boundary conditions

In this work, we investigate the dynamics of a scalar field in the nonintegrable $\displaystyle ϕ^{4}$ model, restricted to the half-line. Here we consider singular solutions that interpolate the Dirichlet boundary condition $ϕ(x=0,t)=H$ and their scattering with the regular kink solution. The simulations reveal a rich variety of phenomena in the field dynamics, such as the formation of a kink-antikink pair, the generation of oscillons by the boundary perturbations, and the interaction between these objects and the boundary, which causes the emergence of boundary-induced resonant scatterings (for example, oscillon-boundary bound states and kink generation by oscillon-boundary collision) founded into complex fractal structures. Linear perturbation analysis was applied to interpret some aspects of the scattering process. We detected the presence of two shape modes near the boundary. The power spectral density of the scalar field at a fixed point leads to several frequency peaks. Most of them can be explained with some interesting insights for the interaction between the scattering products and the boundary.

hep-th↗

arXiv2024

Scattering of sine-Gordon kinks with internal structure in an extended nonlinear $O(3)$ sigma model

In this paper, we present topological defects in $(1,1)$ dimensions, described by an extended nonlinear $O(3)$ sigma model. We consider spherical coordinates $(ϕ,χ)$ in the $S^2$ isotopic space and a potential $V(ϕ,χ)$. For specific forms of the potential, it is possible to apply the Bogomol'nyi method, resulting in first-order equations of motion with solutions that minimize energy. We study a model with an explicit solution for the field $ϕ$ that resembles the ubiquitous sine-Gordon kink/antikink, but with an internal structure given by the field $χ$ with a form antilump/lump that depends on a constant $C$. The soliton-antisoliton scattering process depends on $C$ and on the initial velocity of the pair. Some results are reported, such as: one-bounce scattering for $ϕ$, or strong emission of radiation for $ϕ$, followed by i) annihilation of $χ$; ii) same pattern antilump-antilump or lump-antilump for $χ$; iii) inversion antilump-antilump to lump-lump for $χ$; iv) inversion antilump-lump to lump-antilump for $χ$. Other findings are: v) annihilation of the pair soliton-antisoliton with the emission of scalar radiation; vi) emission of pairs of oscillations around the vacuum for $ϕ$ and $χ$. The energy density shows that the defect has an internal structure as a nested defect of an antilump inside a kink. The lump core of the defect is responsible for the emission of radiation. The changing of structure of the defects during the scattering is analyzed not only with the field profiles in the physical $(1,1)$ space, but also in the internal $S^2$ space, which gives some new insight into the process.

hep-th↗

arXiv2023

Asymmetry engendered by symmetric kink-antikink scattering in a degenerate two-field model

In this paper we analyze the scattering process in a two-field model in $(1+1)$-dimensions, with the special property to have several topological solutions: i) one with higher rest mass, characterized by a nested defect (lump inside a kink), and ii) four others having lower rest mass, degenerated, and characterized by a kink inside kink. We investigate kink-antikink symmetric scattering, where the kink and antikink have higher rest mass and the same initial velocity modulus $v$. The output of scattering presents a wide range of behaviors, such as annihilation of the kink-antikink pair, the emission of radiation jets, the generation of oscillating pulses and the change of the topological sector. We show that the changing of the topological sector is favored, and only two of the four sectors are possible as outcomes. Moreover, despite the degeneracy in energy, the distribution of the final states is asymmetric in the phase space, being an effect of the presence of vibrational states.

hep-th↗

arXiv2021

Scattering of metastable lumps in a model with a false vacuum

In this work we consider the scalar field model with a false vacuum proposed by A. T. Avelar, D. Bazeia, L. Losano and R. Menezes, Eur. Phys. J. C 55, 133-143 (2008). The model depends on a parameter $s>0$. The model has unstable nontopological lump solutions with a bell shape for small $s$, acquiring a flat plateau around the maximum for large $s$. For $s\to\infty$ the $ϕ^4$ model is recovered. We show that for $s\gtrsim 2$ the lump is metastable with the only negative mode very close to zero. Metastable lumps can propagate and survive long enough to produce dynamical effects. Due to their simplicity, they can be an alternative to the procedure of stabilization which requires, for instance, a complex scalar field to construct nontopological solitons. We study lump-lump collisions in this model, describing the main characteristics of the scattering products at their dependence on $s$ and the initial velocity modulus of each lump.

hep-th↗

arXiv2021

Semi-compactness and multiple oscillating pulses in kink scattering

In this work we consider model of asymmetric kinks, where the behavior of the solution in one side is different from the other side. Also, the models depend of an integer $n$ and, with the increase of $n$, the constructed kink assumes a hybrid character: a compactlike profile on one side and a kinklike profile on the other side. We investigate numerically the kink-antikink and antikink-kink dynamics, with the aim to understand the effect of the transition of the usual kink to the semi-compacton structure. The kink-antikink process shows the formation of one-bounce windows for small values of $n$. The increase of $n$ favors the breaking this structure and the appearance of oscillatory modes. For antikink-kink collisions we report the appearance of two-bounce windows for small values of the parameter. We also found an intricate structure of two-oscillation windows.

nlin.PS↗

arXiv2020

Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model

We study kink-antikink collisions in a particular case of the double sine-Gordon model depending on only one parameter $r$. The scattering process of large kink-antikink shows the changing of the topological sector. For some parameter intervals we observed two connected effects: the production of up to five antikink-kink pairs and up to three solitary oscillations. The scattering process for small kink-antikink has several possibilities: the changing of the topological sector, one-bounce collision, two-bounce collision, or formation of a bion state. In particular, we observed for small values of $r$ and velocities, the formation of false two-bounce windows and the suppression of true two-bounce windows, despite the presence of an internal shape mode.

hep-th↗

arXiv2019

Oscillons in hyperbolic models

In this work we examine kink-antikink collisions in two distinct hyperbolic models. The models depend on a deformation parameter, which controls two main characteristics of the potential with two degenerate minima: the height of the barrier and the values of the minima. In particular, the rest mass of the kinks decreases monotonically as the deformation parameter increases, and we identify the appearance of a gradual suppression of two bounce windows in the kink scattering and the production of long lived oscillons. The two effects are reported in connection to the presence of more than one vibrational state in the stability potential.

hep-th↗

arXiv2019

Kink scattering in a hybrid model

In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the $ϕ^6$ model. In each topological sector, the potential is symmetric around the local maximum. For $ϕ>0$ there is a linear map between the model and the $λϕ^4$ model. For $ϕ<0$ the potential is reflected. Linear stability analysis of kink and antikink lead to discrete and continuum modes related by a linear coordinate transformation to those known analytically for the $λϕ^4$ model. Fixing one topological sector, the structure of antikink-kink scattering is related to the observed in the $λϕ^4$ model. For kink-antikink collisions a new structure of bounce windows appear. Depending on the initial velocity, one can have oscillations of the scalar field at the center of mass even for one bounce, or a change of topological sector. We also found a structure of one-bounce, with secondary windows corresponding to the changing of the topological sector accumulating close to each one-bounce windows. The kink-kink collisions are characterized by a repulsive interaction and there is no possibility of forming a bound state.

hep-th↗

arXiv2019

Boundary scattering in the $ϕ^{6}$ model

We study the non-integrable $ϕ^{6}$ model on the half-line. The model has two topological sectors. We chose solutions from just one topological sector to fix the initial conditions. The scalar field satisfies a Neumann boundary condition $ϕ_{x}\left(0,t\right)=H$. We study the scattering of a kink (antikinks) with all possible regular and stable boundaries. When $H=0$ the results are the same observed for scattering for the same model in the full line. With the increasing of $H$, sensible modifications appear in the dynamics with of the defect with several possibilities for the output depending on the initial velocity and the boundary. Our results are confronted with the topological structure and linear stability analysis of kink, antikink and boundary solutions.

hep-th↗

arXiv2019

Doppelgänger dark energy: modified gravity with non-universal couplings after GW170817

Gravitational Wave (GW) astronomy severely narrowed down the theoretical space for scalar-tensor theories. We propose a new class of attractor models for Horndeski action in which GWs propagate at the speed of light in the nearby universe but not in the past. To do so we derive new solutions to the interacting dark sector in which the ratio of dark energy and dark matter remains constant, which we refer to as doppelgänger dark energy (DDE). We then remove the interaction between dark matter and dark energy by a suitable change of variables. The accelerated expansion that (we) baryons observe is due to a conformal coupling to the dark energy scalar field. We show how in this context it is possible to find a non trivial subset of solutions in which GWs propagate at the speed of light only at low red-shifts. The model is an attractor, thus reaching the limit $c_{T}\to1$ relatively fast. However, the effect of baryons turns out to be non-negligible and severely constrains the form of the Lagrangian. In passing, we found that in the simplest DDE models the no-ghost conditions for perturbations require a non-universal coupling to gravity. In the end, we comment on possible ways to solve the lack of matter domination stage for DDE models.

gr-qc↗

arXiv2019

Kink scattering in hyperbolic models

In this work we study kink-antikink and antikink-kink collisions in hyperbolic models of fourth and sixth order. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models considered here tend to the polynomial $ϕ^4$ and $ϕ^6$ models in the limit of small values of the scalar field. We show that kinks and antikinks that interact hyperbolically with fourth order differ sensibly from those governed by the polynomial $ϕ^4$ model. The increasing of the order of interaction to the sixth order shows that the hyperbolic and polynomial models give intricate structures of scattering that differ only slightly. The dependence on the order of interaction are related to some characteristics of the models such as the potential of perturbations and the number of vibrational modes.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2015

The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions

We consider the general scalar field Horndeski Lagrangian coupled to matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problem since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.

gr-qc↗

arXiv2010

Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension

The CPT-even gauge sector of the Standard Model Extension is composed of nineteen components comprised in the tensor $(K_{F})_{μνρσ}$, of \ which nine do not yield birefringence. In this work, we examine the Maxwell electrodynamics supplemented by these nine nonbirefringent CPT-even components in aspects related to the Feynman propagator and full consistency (stability, causality, unitarity). We adopt a prescription that parametrizes the nonbirefringent components in terms of a symmetric and traceless tensor, $K_{μν},$ and second parametrization that writes $K_{μν}$ in terms of two arbitrary four-vectors, $U_μ$ and $V_ν.$ We then explicitly evaluate the gauge propagator of this electrodynamics in a tensor closed way. In the sequel, we show that this propagator and involved dispersion relations can be specialized for the parity-odd\ and parity-even sectors of the tensor $(K_{F})_{μνρσ}$. In this way, we reassess some results of the literature and derive some new outcomes showing that the parity-even anisotropic sector engenders a stable, noncausal and unitary electrodynamics.

hep-th↗

arXiv2010

Gauge propagator and physical consistency of the CPT-even part of the Standard Model Extension

In this work, we explicitly evaluate the gauge propagator of the Maxwell theory supplemented by the CPT-even term of the SME. First, we specialize our evaluation for the parity-odd sector of the tensor $W_{μνρσ}$,\ using a parametrization that retains only the three nonbirefringent coefficients. From the poles of the propagator, it is shown that physical modes of this electrodynamics are stable, non-causal and unitary. In the sequel, we carry out the parity-even gauge propagator using a parametrization that allows to work with only the isotropic nonbirefringent element. In this case, we show that the physical modes of the parity-even sector of the tensor $W$ are causal, stable and unitary for a limited range of the isotropic coefficient.

hep-th↗

arXiv2007

Influence of Lorentz-violating terms on a two-level system

The influence of Lorentz- and CPT-violating terms of the extended Standard Model on a semi-classical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state oscillations even in the absence of the electromagnetic field. The foreseen effects are used to establish upper bounds on the Lorentz-violating coefficients.

hep-th↗