arXiv subjects

Azadeh Mohammadi

Publications and source records attributed to Azadeh Mohammadi.

At least 19 recordsLinked to original sources

arXiv2026

Optical properties of gravitating strings

We study the optical properties of gravitating Abelian-Higgs cosmic strings and compare them with those of the idealized infinitely thin string. We analyze the structure of the corresponding vortex solutions, characterizing their width, curvature profile, and approach to the ideal string limit. By investigating photon propagation in the string spacetime, we show that the finite core of the vortex gives rise to distinctive observational signatures absent in the ideal string approximation, including a characteristic triple-imaging configuration, strong demagnification of the central image, and a nontrivial Shapiro time delay between external and internal images. We determine how these effects depend on the parameters of the Abelian-Higgs model and show that the sign of the time delay is controlled by the ratio of the gauge boson mass to the Higgs boson mass, causing the string core to behave as either a temporal shortcut or a temporal barrier. Our results demonstrate that lensing effects can reveal information about the vortex formation and internal structure.

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arXiv2026

Collision Dynamics of False-Vacuum Oscillons

We study the collision dynamics of localized oscillons in two classes of $(1+1)$-dimensional scalar field theories with metastable false vacua, a normal class with a positive quartic self-interaction term and an inverted class with a negative quartic term. We construct small-amplitude oscillon solutions around the false vacuum using the Fodor {\emph{et al.}} expansion, and show that the force between oscillons decays exponentially at large separation, with a strength modulated by their relative phase. Numerical simulations of two-oscillon collisions exhibit reflection, crossing, and formation of excited oscillons. Resonance windows occur, similar to those found in kink-antikink collisions. In the normal theory, if the oscillons have sufficient energy, the field can pass over a sphaleron barrier and evolve into a kink-antikink pair, initiating a phase transition to the true vacuum. We also simulate the collision of oscillons evolved from a slightly perturbed sphaleron.

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arXiv2026

Generalized BPS magnetic monopoles in inhomogeneous Yang-Mills-Higgs models

We present a non-Abelian model for magnetic monopoles in inhomogeneous media, based on a generalization of the standard 't~Hooft-Polyakov model. The medium is described by spatially dependent couplings in the gauge and scalar sectors, constrained by $P(|Φ|,r)M(|Φ|,r)=1$ so that the Bogomol'nyi-Prasad-Sommerfield (BPS) bound is preserved. For static spherically symmetric configurations, we study the first-order monopole equations for the class of generalized permeabilities $M(H,r)=f(r)/H^α$. For the power-law profile $f(r)=r^β$, we determine the domain in the $(α,β)$ plane where regular BPS solutions exist. On the line $α=1$, the system becomes exactly integrable, with closed-form monopole solutions in an inhomogeneous background. Away from this analytical sector, the solutions are constructed numerically. The model supports a rich spectrum of configurations, including effectively point-like monopoles, compact-core monopoles, hollow monopoles, shell-like structures, and multi-shell monopoles characterized by multiple concentric peaks in the energy density.

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arXiv2025

Resonance with quasinormal modes in long-range kinks' collisions

We consider a rational scalar field model in (1+1)-dimensions where the long-range character of the kinks is controllable. We show via numerical simulations that kinks with long-range tails on both sides can exhibit resonance windows. The resonant energy exchange mechanism occurs via the excitation of quasinormal modes, which we obtain via a spectral analysis. Additionally, we locate a resonance window in a family of $ϕ^{10}$ models with long-range tails on both sides. Moreover, we propose a new algorithm for initializing long-range kink collisions, based on convection-diffusion dynamics.

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arXiv2025

Scalar and spinor fields in gravitating cosmic string spacetimes

We study the scattering behavior of scalar and spinor fields in the background of a gravitating cosmic string spacetime. The model explored here for the background vortex is non-abelian, becoming abelian in an appropriate limiting case. We adopted the formalism we developed in \cite{silva2021scattering}, modifying the standard partial wave approach. We apply the method for a scalar and also a fermion field interacting with the background spacetime with a nontrivial asymptotic structure. The spacetime metric, obtained numerically in \cite{de2015gravitating}, forms the basis of our state-of-the-art numerical study. We make an exhaustive analysis and compare all the results in the non-abelian model with the corresponding abelian one for both massless and massive fields. We analyze the field configuration's total cross-section and angular profile at small and large distances from the core. We show that the total cross-section oscillates with the incident momentum of the wave, as anticipated in \cite{silva2021scattering}, and also, the angular profile can be explained reasonably well with a Fraunhofer diffraction pattern, especially for the scalar field scattering.

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arXiv2025

Finite temperature Casimir effect for a spinor field in cosmic dispiration spacetime

This study explores the finite temperature Casimir effect for a massive spinor field in cosmic dispiration spacetime, formed by the combination of a cosmic string and a screw dislocation using the generalized zeta function regularization method. First, we examine the cosmic string spacetime with a quasi-antiperiodic boundary condition, where the Casimir energy and its corrections depend on two nonzero heat kernel coefficients, one associated with the Euclidean divergence and the other with the nontrivial topology, both vanishing when renormalized. Interestingly, for specific choice of parameters the quasi-antiperiodicity effect can entirely cancel out the topological contribution, leaving only the Euclidean divergence. We then extend this analysis to cosmic dispiration spacetime. This configuration alters the spacetime topology, modifying the structure of the heat kernel coefficient related to the new nontrivial topology. In this case, the renormalized Casimir energy density can take positive or negative values and decreases exponentially as the field mass increases. Additionally, we examine the asymptotic behavior of the renormalized temperature correction term in the massless regime, showing that the spinor vacuum free energy vanishes at very high temperatures. At very low temperatures, it is dominated by the zero-temperature Casimir energy density.

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arXiv2024

On the localized and delocalized modes in kink-antikink interactions: a toy model

This study deals with a piecewise $ϕ^2$ scalar field theory in $(1+1)$ dimensions. The scalar field potential is designed with a triple-well shape, engendering kink solutions with asymmetric square-well linearized potentials. Thus, the localized and delocalized modes in this model can be obtained analytically in terms of transcendental equations. This allows us to explore kink-antikink and antikink-kink collisions with any desired number of localized and delocalized modes. We obtain new scenarios of resonance windows suppression, shedding light on the role of higher excited modes in kink scattering.

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arXiv2024

Metaverse Innovation Canvas: A Tool for Extended Reality Product/Service Development

This study investigated the factors contributing to the failure of augmented reality (AR) and virtual reality (VR) startups in the emerging metaverse landscape. Through an in-depth analysis of 29 failed AR/VR startups from 2016 to 2022, key pitfalls were identified, such as a lack of scalability, poor usability, unclear value propositions, and the failure to address specific user problems. Grounded in these findings, we developed the Metaverse Innovation Canvas (MIC) a tailored business ideation framework for XR products and services. The canvas guides founders to define user problems, articulate unique XR value propositions, evaluate usability factors such as the motion-based interaction load, consider social/virtual economy opportunities, and plan for long term scalability. Unlike generalized models, specialized blocks prompt the consideration of critical XR factors from the outset. The canvas was evaluated through expert testing with startup consultants on five failed venture cases. The results highlighted the tool's effectiveness in surfacing overlooked usability issues and technology constraints upfront, enhancing the viability of future metaverse startups.

cs.HC↗

arXiv2024

Abelian Chern-Simons vortices in the presence of magnetic impurities

This work deals with Abelian Chern-Simons vortices interacting with magnetic impurities. We compute static solutions with winding numbers zero and one. Then, we develop a numerical algorithm to simulate their collisions. Collisions between a vortex with winding number two and a magnetic impurity are also performed. All scattering results are interpreted in terms of the moduli space approximation and compared with the Abelian Maxwell-Higgs model.

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arXiv2024

Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in $xy$-plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription \text{associated} with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures.

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arXiv2024

Collisions between kinks with long-range tails: a simple and efficient method

We construct initial configurations for the scattering between kinks with long-range tails. For this purpose, we exploit kink solutions in the presence of Bogomol'nyi-Prasad-Sommerfield (BPS)-preserving impurities. This approach offers a highly efficient method and effortless implementation with a negligible computational cost. Our algorithm has a much smaller complexity than the usual minimization method, becoming more than a hundred times faster in some scenarios. Consequently, conducting kink-antikink simulations becomes remarkably straightforward.

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arXiv2023

Kink-antikink collisions in the $ϕ^8$ model: short-range to long-range journey

We studied kink-antikink collisions in (1+1)-dimensional spacetime for all $Z_2$ symmetric $ϕ^8$ models with four degenerate minima. Such a polynomial model has only one free parameter, allowing us to conduct an exhaustive analysis. We performed detailed simulations in all three sectors of the model. We observed resonance windows from both localized and delocalized modes, as well as a sector change with the formation of additional kink-antikink pairs. Furthermore, we were able to show how collisions are modified when two quadratic minima merge into a quartic one, causing the kinks to acquire a long-range character. We demonstrated that when the tail not facing the opposing kink is long-range, incoming kinks and antikinks decay directly into radiation, as suggested in \cite{campos2021interaction}, by forming a large number of small kink-antikink pairs. Finally, we briefly discussed whether our analysis could be generalized to other polynomial models.

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arXiv2023

Integrability of the Dirac Equation in the Presence of Fluxes on Product Manifolds

This paper aims to show that the Dirac equation coupled to an arbitrary inhomogeneous flux field admits separation in manifolds formed from the direct product of bidimensional spaces. As a direct application of these results, we study a spin-$1/2$ charged particle propagating in a background conformally related to a novel and complex string-inspired model in $D = 10$ spacetime dimension whose base manifold is a product of four two-dimensional unit spheres, $S^{2}$, in the presence of $1$- and $3$-form fluxes.

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arXiv2023

Fermionic spectral walls in kink collisions

We show that a spectral wall, i.e., an obstacle in the dynamics of a bosonic soliton, which arises due to the transition of a normal mode into the continuum spectrum, exists after coupling the original bosonic model to fermions. This spectral wall can be experienced if the boson or fermion field is in an excited state. Furthermore, while passing through a spectral wall, an incoming kink-fermion bound state can be separated into purely bosonic kink, which continues to move to spatial infinity and a fermionic cloud that spreads in the region before the wall.

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arXiv2022

Kink-antikink collision in the supersymmetric $ϕ^4$ model

This paper investigates a model containing $ϕ^4$ kinks interacting with fermions. The fermion back-reaction is included in the equations of motion, which affects the kink-antikink collisions. We show that the fermion field generates a force that can be either attractive or repulsive. Moreover, we investigate three different scenarios, which exhibit a wide variety of behaviors including the usual scenarios observed in the $ϕ^4$ model as well as the formation of two oscillons, reflection without contact, one-bounce resonance windows, and the creation of kink-antikink pairs. We also find evidence that the fermion field can store part of the energy responsible for the energy exchange mechanism.

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arXiv2022

Resonance mediated by fermions in kink-antikink collisions

We investigate generalizations of the $ϕ^4$ and sine-Gordon models, including interactions with Dirac Fermions. We observe new resonance phenomena by taking the fermion back-reaction into account. First, we show that the vibrational mode responsible for the resonance structure of the $ϕ^4$ model has the same frequency as the energy of the fermion excited state when the back-reaction becomes more significant. Second, we consider the sine-Gordon model with the addition of a fermion field and find that a resonant structure appears, despite the absence of a scalar vibrational mode. The vibrational frequency of the mode responsible for the exchange mechanism is again the energy of the fermion excited state. Therefore, we find a new type of resonant energy exchange mechanism which is mediated by fermions.

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arXiv2022

Thermal Casimir effect in a classical liquid in a quasi-periodically identified conical spacetime

In this paper, we study the finite-temperature quantum fluctuation of a classical liquid induced by the topology of an effective conical spacetime, as well as by a quasi-periodic boundary condition. The conical spacetime could be either a disclination or a cosmic string. In this context, we consider a phonon field representing quantum excitations of the liquid density, which obeys an effective Klein- Gordon equation with the sound velocity replaced by the light velocity. We obtain closed analytic expressions for the thermal Hadamard function, and consequently, the renormalized mean square density fluctuation of the liquid along with thermodynamics quantities such as internal energy, free energy, total energy, and entropy densities. We also discuss the limiting cases, including low and high-temperature regimes, and the situations in which there are only either the conical spacetime or quasi-periodicity.

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arXiv2021

Quasinormal modes in kink excitations and kink-antikink interactions: a toy model

We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with $Z_2$ symmetry. The field potential is designed to create a square well potential in the stability equation of the kink excitations. The stability equation is analogous to the Schrödinger equation, and therefore we use quantum mechanics techniques to study the system. We modify the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasinormal modes. We study the effect of this transition, leading to energy leak, on isolated kink excitations. Finally, we investigate kink-antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasinormal modes and compare the results.

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