arXiv subjects

Ardian Nata Atmaja

Publications and source records attributed to Ardian Nata Atmaja.

At least 19 recordsLinked to original sources

arXiv2026

Heun Spectrum, Threshold Hierarchy, and One-Loop Quantum Mass of the Christ--Lee Kink

We study the fluctuation spectrum and renormalized one-loop quantum mass of the Christ--Lee kink over the full positive range of its deformation parameter. The fluctuation equation is reduced exactly to general-Heun form, yielding parity-resolved continuum solutions and implicit quantization conditions for the discrete spectrum. At the first nontrivial continuum crossing, the odd Heun solution truncates to a polynomial, giving the exact threshold $ε_1=\sqrt{\sqrt{3}-1}$. For small deformation, the kink separates into two widely spaced $ϕ^6$-like interfaces and the fluctuation operator develops a long central cavity. This geometry explains the logarithmic growth of the bound-state count, the asymptotically geometric hierarchy of continuum-threshold crossings, and the emergence of a soft relative-translation mode. In the opposite limit, the spectrum approaches the $ϕ^4$ Pöschl--Teller problem, while its even threshold resonance becomes a shallow bound state at finite deformation. The one-loop correction is evaluated in a fixed vacuum-normal-ordering prescription using a common-regulator spectral trace and independently through an imaginary-frequency functional determinant. The two calculations agree throughout representative finite deformations and reproduce the exact $ϕ^4$ limit. In the small-deformation regime, the extended central region produces a logarithmically enhanced negative quantum correction. These results provide a unified analytic and numerical description of how the spectral reorganization of the Christ--Lee kink controls its semiclassical quantum mass.

math-ph↗

arXiv2025

Optically Controlled Skyrmion Number Current

We propose a mechanism to control the motion of magnetic Skyrmions through the generation of a Skyrmion number current. This current is induced and tuned by an explicitly time-dependent Hamiltonian that includes a Zeeman term arising from the interaction between the spin system and circularly polarized light. To capture the effect, we apply a first-order perturbation method to the Landau-Lifshitz-Gilbert equation, using a breathing Skyrmion ansatz based on the Belavin-Polyakov profile. This approach reveals that the time-dependent deformation of the Skyrmion boundary produces an anisotropic breathing mode, which in turn generates a nonzero Skyrmion number current. The resulting dynamics in momentum space form a limit cycle, whose characteristics depend on the external magnetic field amplitude, the Heisenberg exchange coupling, and the Gilbert damping constant. Our formulation not only clarifies the topological origin of optically driven Skyrmion motion but also points to Skyrmion number currents as a low-dissipation alternative to electric currents for efficient Skyrmion control.

cond-mat.mes-hall↗

arXiv2025

Radial Stabilization of Magnetic Skyrmions Under Strong External Magnetic Field

The skyrmion number density, $q\equiv\vec{n}\cdot\left(\partial_x\vec{n}\times\partial_y\vec{n}\right)/(4π)$, is one of the key quantities that characterizes the topological properties of a magnetic skyrmion. In this work, we propose a model for a two-dimensional magnetic system with Hamiltonian that contains an interaction term proportional to $q^2$ which preserves inversion symmetry. The proposed $q^2$ term is also known as the Skyrme term and is a two-dimensional version of the well-known quartic term in models of three-dimensional Hopfions. In contrast with the usual exchange interaction, the $q^2$ term persists at the strong external magnetic field limit. Using the Landau-Lifshitz-Gilbert equation for micromagnetic calculations, we show that the minimum energy configuration of this model exhibits skyrmion properties. Furthermore, this configuration remains stable under small linear radially symmetric perturbations, and we demonstrate that the total energy of the system is bounded from below, ensuring that it remains above the vacuum energy. This implies a topologically protected configuration. Our model provides a framework for describing skyrmions in materials without broken inversion symmetry, particularly in systems subjected to strong external magnetic fields, where conventional exchange interactions are significantly weaker than the Zeeman effect.

cond-mat.mes-hall↗

arXiv2025

Positive Mass in Scalar-Torsion Holography

We investigate the holographic renormalization of scalar-torsion gravity in a four-dimensional bulk spacetime with non-minimal derivative coupling. The asymptotic behavior of the static equations leads to an anti-de Sitter geometry for negative cosmological constants, allowing for a holographic interpretation via the AdS/CFT correspondence. The existence of unique solutions throughout the bulk is addressed. We study the effect of the non-minimal coupling parameter on the conformal dimension and the expectation value of the dual scalar operator, showing that the effective bulk mass can be tuned through the non-minimal coupling. Our results provide a formalism for finding non-tachyonic bulk scalar fields which vanish at the boundary.

hep-th↗

arXiv2025

On BPS Equations of Generalized $SU(2)$ Yang-Mills-Higgs Model with Scalars-Dependent Coupling $θ$-term

We consider a most general $SU(2)$ Yang-Mills-Higgs model consist of terms up to quadratic in first-derivative of the fields, that is the generalized $SU(2)$ Yang-Mills-Higgs with additional scalars-dependent coupling $θ$-term. Using the BPS Lagrangian method we try to find Bogomolnyi's equations for BPS monopoles and dyons by taking most general BPS Lagrangian density. We obtain more general Bogomolnyi's equations and a relation between all scalars dependent couplings. From these equations we can see there is a family of BPS monopole solutions parameterized by a real constant $γ$, while for BPS dyons there is an additional parameter which is the coupling of $θ$-term. Interestingly even for a single BPS dyon we find the value of $θ$-term's coupling only gives additional contribution to electric charge of BPS Dyons, which is in accordance with Witten's result in Phys.Lett.B 86 (1979), and thus can determine whether we get BPS monopoles or BPS dyons.

hep-th↗

arXiv2025

Topologically Stable BPS and Non-BPS States in Supersymmetric $\mathcal{N}=2$ Baby-Skyrme Model

The supersymmetric baby-Skyrme model is an interesting field theoretical model, and its BPS states have been studied using the usual methods. Here, we propose a novel method to rigorously obtain both topologically stable BPS and non-BPS states in the $\mathcal{N}=2$ baby Skyrme Model. It is observed that the BPS states found using this novel method coincide with the BPS states found using the usual methods. However, we are also able to obtain the non-BPS states, which break all of the supersymmetry of the theory. Furthermore, there exists a one-parameter family of non-BPS solutions that are connected to the half-BPS solutions, where half of the supersymmetry is restored when the parameter is set to zero. The proposed method is general, and we expect that it might be useful for investigating the topologically stable non-BPS states of other theories. Thus, this method could possibly have wide applications for the study of non-BPS states in supersymmetric theories.

hep-th↗

arXiv2024

A Unified Approach To Find The Generalized Maxwell-Chern-Simons-Higgs BPS Vortices and Their Properties

In this work, we propose that all BPS vortex solutions within the generalized Maxwell-Chern-Simons-Higgs (MCSH) model can be found from a single system of equations. This set of equations is derived using the BPS Lagrangian method, which is a more robust generalization of Bogomolnyi's trick. We show that the known spherically symmetric BPS vortices can be reproduced as certain limits of Bogomolnyi equations in the generalized MCSH Model. This provides us with a possible classification system using the auxiliary functions in the BPS Lagrangian. Furthermore, we also study the properties of each known vortex through the numerical approach where we found that all of the vortices behave similarly under variations of their free parameters and a system of well-separated MCSH vortices saturates the BPS bound.

hep-th↗

arXiv2024

Cosmic Inflation From Fluctuating Baby-Skyrme Brane

In this work, we explore the inflationary dynamics induced by small fluctuations on the Skyrme brane, characterized by a time-dependent perturbative function $\tildeϕ$. In the low-energy regime, the model successfully reproduces standard inflation, with a potential term dictated by the Skyrmion at the brane. Gravity localization is achieved at the brane, and the lowest energy scale is established at the asymptotic boundary. The model demonstrates the capability to emulate standard inflation dynamics, resembling $\tildeϕ^4$ potential characteristics under certain conditions. At higher energy levels, the behaviour of $\tildeϕ$ is contingent upon the Skyrme term coupling constant $λ$, influencing reheating phases. The wave-like nature of fluctuations allows for energy transfer, resulting in a possibly lower reheating temperature. We also discuss the prospect of $λ$ changing sign during inflation, presenting a non-standard coupling dependent on the matter field.

gr-qc↗

arXiv2023

Bogomol'nyi-like Equations in Gravity Theories

Using the BPS Lagrangian method, we show that gravity theory coupled to matter in various dimensions may possess Bogomol'nyi-like equations, which are first-order differential equations, satisfying the Einstein equations and the Euler-Lagrange equations of classical fields ($U(1)$ gauge and scalar fields). In particular we consider static and spherically symmetric solutions by taking proper ansatzes and then we find an effective Lagrangian density that can reproduce the Einstein equations and the Euler-Lagrange equations of the classical fields. We consider the BPS Lagrangian density to be linear function of first-order derivative of all the fields. From these two Lagrangian desities we are able to obtain the Bogomol'nyi-like equations whose some of solutions are well-known such as Schwarzschild, Reissner-Nordström, Tangherlini black holes, and the recent black holes with scalar hair in three dimensions [Phys. Rev. D 107, 124047]. Using these Bogomol'nyi-like equations, we are also able to find new solutions for scalar hair black holes in three and four dimensional spacetime. Furthermore we show that the BPS Lagrangian method can provide a simple alternative proof of black holes uniqueness theorems in any dimension.

gr-qc↗

arXiv2023

Global Existence and Singularity Formation of Classical Solutions in Einstein-Skyrme System

In this paper, we elucidate the problem of gravitating Skyrmion governed by field equations of the Einstein-Skyrme system with no potential term in the Bondi coordinate. The spherical symmetry has to be assumed and both the metric functions and Skyrme ansatz depend on radial and retarded time coordinates which implies that the system is dynamic. We show that unique smooth solutions with arbitrary initial data exist for a certain time interval with the extra condition that the time interval must be finite in order to have a non-zero topological charge. Then, the strategy to show that global smooth solutions exist is to restrict the initial data and proceed to find suitable configurations for extending the time interval to infinity. We also discuss the possible configurations within The Einstein-Skyrme System which develop singularities in coordinate origin.

gr-qc↗

arXiv2022

Electric-dual BPS Vortices in The Generalized Self-dual Maxwell-Chern-Simons-Higgs Model

In this paper we show how to derive the Bogomolny's equations of the generalized self-dual Maxwell-Chern-Simons-Higgs model presented in \cite{Bazeia:2012ux} by using the BPS Lagrangian method with a particular choice of the BPS Lagrangian density. We also show that the identification, potential terms, and Gauss's law constraint can be derived rigorously under the BPS Lagrangian method. In this method, we find that the potential terms are the most general form that could have the BPS vortex solutions. The Gauss's law constraint turns out to be the Euler-Lagrange equations of the BPS Lagrangian density. We also find another BPS vortex solutions by taking other identification between the neutral scalar field and the electric scalar potential field, $N=\pm A_0$, which is different by a relative sign to the identification in \cite{Bazeia:2012ux}, $N=\mp A_0$. Under this identification, $N=\pm A_0$, we obtain a slightly different potential terms and Bogomolny's equations compared to the ones in \cite{Bazeia:2012ux}. Furthermore we compute the solutions numerically, with the same configurations as in \cite{Bazeia:2012ux}, and find that only the resulting electric field plots differ by sign relative to the results in \cite{Bazeia:2012ux}. Therefore we conclude that these BPS vortices are electric-dual BPS vortices of the ones computed in \cite{Bazeia:2012ux}.

hep-th↗

arXiv2022

BPS Skyrmions of Generalized Skyrme Model In Higher Dimensions

In this work we consider the higher dimensional Skyrme model, with spatial dimension $d > 3$, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, $B\geq 1$, a modified generalized hedgehog ansatz is used where we assign an integer $n_i$ for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-invariant model. The properties of the higher dimensional version of both submodels are studied and it is found that the BPS Skyrmions with $B\geq1$ exist in the first submodel but there is only $B=1$ BPS Skyrmion in the second submodel. We also study the higher dimensional version of self-duality conditions in terms of strain tensor eigenvalues and find that, in general, the scale-invariant model has a stronger self-duality condition than the BPS Skyrme model.

hep-th↗

arXiv2022

Are There BPS Dyons in The Generalized $SU(2)$ Yang-Mills-Higgs Model?

We use the well-known Bogomolny's equations, in general coordinate system, for BPS monopoles and dyons in the $SU(2)$ Yang-Mills-Higgs model to obtain an explicit form of BPS Lagrangian density under the BPS Lagrangian method. We then generalize this BPS Lagrangian density and use it to derive several possible generalized Bogomolny's equations, with(out) additional constraint equations, for BPS monopoles and dyons in the generalized $SU(2)$ Yang-Mills-Higgs model. We also compute the stress-energy-momentum tensor of the generalized model, and argue that the BPS monopole and dyon solutions are stable if all components of the stress-tensor density are zero in the BPS limit. This stability requirement implies the scalar fields-dependent couplings to be related to each other by an equation, which is different from the one obtained in~\cite{Atmaja:2018cod}, and then picks particular generalized Bogomolny's equations, with no additional constraint equation, out of those possible equations. We show that the computations in~\cite{Atmaja:2018cod} are actually incomplete. Under the Julia-Zee ansatz, the generalized Bogomolny's equations imply all scalar fields-dependent couplings must be constants, whose solutions are the BPS dyons of the $SU(2)$ Yang-Mills-Higgs model~\cite{Prasad:1975kr}, or in another words there are no generalized BPS dyon solutions under the Julia-Zee ansatz. We propose two possible ways for obtaining generalized BPS dyons, where at least one of the scalar fields-dependent couplings is not constant, that are by using different ansatze, such as axially symmetric ansatz for higher topological charge dyons; and/or by considering the most general BPS Lagrangian density.

hep-th↗

arXiv2022

Static Black Holes of Higher Dimensional Einstein-Skyrme System with General Couplings

We construct hairy static black holes of higher dimensional general coupling Einstein-Skyrme theories with the scalar potential turned on and the cosmological constant is non-positive in which the scalar multiplets satisfy $O(d+1)$ model constraint where $d$ is the spatial dimension of the spacetime and $d \ge 3$. Some physical properties of solutions near the boundaries, namely, near the (event) horizon and in the asymptotic region are discussed. Then, we prove that these black hole solutions exist globally which may have finite energy for non-positive cosmological constant. Finally, we use perturbative method to perform a linear dynamical stability analysis and then, show the existence of stable and unstable solutions in the model.

gr-qc↗

arXiv2021

BPS Skyrme Submodels of The Five Dimensional Skyrme Model

In this paper, we search for the BPS skyrmions in some BPS submodels of the generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian method. We focus on the static solutions of the Bogomolny's equations and their corresponding energies with topological charge $B>0$ is an integer. We consider two main cases based on the symmetry of the effective Lagrangian of the BPS submodels, i.e. the spherically symmetric and non-spherically symmetric cases. For the spherically symmetric case, we find two BPS submodels. The first BPS submodels consist of a potential term and a term proportional to the square of the topological current. The second BPS submodels consist of only the Skyrme term. The second BPS submodel has BPS skyrmions with the same topological charge $B>1$, but with different energies, that we shall call "topological degenerate" BPS skyrmions. It also has the usual BPS skyrmions with equal energies, if the topological charge is a prime number. Another interesting feature of the BPS skyrmions, with $B>1$, in this BPS submodel, is that these BPS skyrmions have non-zero pressures in the angular direction. For the non-spherically symmetric case, there is only one BPS submodel, which is similar to the first BPS submodel in the spherically symmetric case. We find that the BPS skyrmions depend on a constant $k$ and for a particular value of $k$ we obtain the BPS skyrmions of the first BPS submodel in the spherically symmetric case. The total static energy and the topological charge of these BPS skyrmions also depend on this constant. We also show that all the results found in this paper satisfy the full field equations of motions of the corresponding BPS submodels.

hep-th↗

arXiv2020

BPS Submodels of The Generalized Skyrme Model and How to Find Them

Using the BPS Lagrangian method we show that all known BPS submodels of the generalized Skyrme model, with a particular ansatz for the fields content, can be devided into three groups based on the (effective) number of derivative-terms in the BPS submodels. We are able to derive rigorously the Bogomolny's equations of those BPS submodels. The resulting Bogomolny's equations, along with possible constraint equations, are in general forms in which some of the known BPS submodels may contain other possible non-trivial (non-vacuum) solutions then the ones found in the literature. Furthermore, we derive some other new BPS submodels of the generalized Skyrme model for each of the groups and some of them yield new solutions.

hep-th↗

arXiv2019

Searching for BPS Vortices with Nonzero Stress Tensor in Generalized Born-Infeld-Higgs Model

In this article we show that the new BPS equations for vortices, with nonzero diagonal components of the stress tensor, obtained in \cite{Atmaja:2015lia} for the generalized Maxwell-Higgs model can also be derived using the BPS Lagrangian method developed in \cite{Atmaja:2015umo}. We add into the original BPS Lagrangian $L_{BPS}=\int dQ$, which is a total derivative term, two additional terms that are proportional to square of the first-derivative of scalar effective field, $f'(r)^2$, and to a function that depends only on the scalar effective field. These additional terms produce additional constraint equations coming from Euler-Lagrange equations of the BPS Lagrangian. We apply this procedure for the generalized Born-Infeld-Higgs model and show that the total static energy, for the corresponding BPS equations, is finite if the scalar potential $V< 2b^2$, with $b$ is the Born-Infeld parameter. We also compute the energy-momentum tensor and show that its diagonal spatial components in radial and angular directions are nonzero. Furthermore we show that the conservation of energy-momentum does not produce new constraint equation. We do the numerical analysis and found that for a large class of solutions the scalar and gauge effective fields, $f(r)$ and $a(r)$, behave nicely near the origin, but unfortunately they are infinite near the boundary. We suggest that incorporate gravity into the action might resolve this problem and other resolution is by considering BPS vortex in higher dimensional models. We also suggest that the BPS Lagrangian method could be used to find BPS equations for other solitons with nonzero stress tensor.

hep-th↗

arXiv2018

BPS Equations of Monopole and Dyon in $SU(2)$ Yang-Mills-Higgs Model, Nakamula-Shiraishi Models, and Their Generalized Versions from The BPS Lagrangian Method

We apply the BPS Lagrangian method~\cite{Atmaja:2015umo} to derive BPS equations of monopole and dyon in the $SU(2)$ Yang-Mills-Higgs model, Nakamula-Shiraishi models, and their Generalized versions. We argue that by identifying the effective fields of scalar field, $f$, and of time-component gauge field, $j$, explicitly by $j=βf$ with $β$ is a real constant, the usual BPS equations for dyon can be obtained naturally. We validate this identification by showing that both Euler-Lagrange equations for $f$ and $j$ are identical in the BPS limit. The value of $β$ is bounded to $|β|<1$ due to reality condition on the resulting BPS equations. In the Born-Infeld type of actions, namely Nakamula-Shiraishi models and their Generalized versions, we find a new feature that adding the energy density by a constant $4b^2$, with $b$ is the Born-Infeld parameter, will turn monopole(dyon) to anti-monopole(anti-dyon) and vice versa. In all Generalized versions there are additional constraint equations that relate the scalar-dependent couplings of scalar and of gauge kinectic terms; or $G$ and $w$ respectively. For monopole the constraint equation is $G=w^{-1}$, while for dyon is $w(G-β^2 w)=1-β^2$ which further gives lower bound to $G$ as such $G\geq|2β\sqrt{1-β^2}|$. We also write down the complete square-forms of all effective Lagrangians.

hep-th↗