arXiv subjects

C. Furtado

Publications and source records attributed to C. Furtado.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Topological Charge and Spinorial Holonomy in Yukawa-Regularized Graphene Disclinations

Conical geometries provide the standard description of disclinations, but they concentrate the curvature at a singular apex. We introduce a Yukawa-type regularization that replaces this singularity by a smooth curvature distribution while preserving the asymptotic topology of the defect. Exact expressions are obtained for the conformal factor, curvature, and enclosed topological charge. The resulting geometry exhibits a scale-dependent topological charge and a corresponding radius-dependent holonomy, establishing a direct connection between distributed curvature and geometric phases. We further investigate the dynamics of massless Dirac quasiparticles in this background and show that the regularized core modifies the spin connection while preserving the asymptotic topological signature of the defect. These results provide a finite-core extension of the conventional conical description and offer a natural framework for studying geometric and topological effects in graphene-like systems.

cond-mat.mes-hall↗

arXiv2026

Elastic field causing noncommutativity

We study how a uniform torsion background, modeling a continuous density of screw dislocations and induces effective spatial noncommutativity and reshapes the energy spectrum of a free quantum particle. Within the geometric theory of defects, the metric yields a first-order (magnetic-like) coupling in the transverse dynamics, equivalent to an effective magnetic field $B_{eff}$ proportional to $p_z Omega$, where $Omega$ encodes the torsion strength. In the strong-coupling (Landau) regime, the planar coordinates obey [x,y] != 0 and the spectrum organizes into Landau-like levels with a slight electric-field-driven tilt and a uniform shift. Thus, increasing $Omega$ drives the system continuously toward the familiar Landau problem in flat space, with torsion setting the noncommutativity scale and controlling the approach to the Landau limit.

cond-mat.mes-hall↗

arXiv2025

Nonrelativistic effective potential of the bumblebee model

In this paper, we explicitly obtain the nonrelativistic Breit potential in the bumblebee model arising in the weak gravity limit of the metric-affine bumblebee gravity, coupled to the spinor matter. In this theory, in the lower (second) order in the small coupling constant $\xi$ (and the second order in the LV vector $\beta_{\mu}$) it demonstrates the $1/r$ asymptotics, which naturally corresponds to the massless character of the theory, while higher orders in $\xi$ yield anisotropic modifications of the Coulomb potential due to the Lorentz symmetry breaking. For the lower-order modification of the effective potential, we calculate LV corrections to energy levels of the hydrogen atom.

hep-th↗

arXiv2025

Zero modes and geometric phase for 2D Weyl fermions on Lifshitz backgrounds

Here we investigate analytical properties of Weyl fermions in (2+1)-dimensional Lifshitz spacetimes. In particular, we are interested in obtaining geometric phases and verifying the existence of well-behaved fermionic zero modes. Using the Dirac phase method, we show how geometric phases naturally arise from the coupling between the fermionic fields and the Lifshitz geometry. We also present exact solutions of the zero modes by rewriting the Weyl equation as a system of supersymmetric equations.

hep-th↗

arXiv2025

Holonomic quantum computation on graphene from Atiyah-Singer index theorem

We investigate the emergence of geometric phases in graphene-based nanostructures through the lens of the Atiyah-Singer index theorem. By modeling low-energy quasiparticles in curved graphene geometries as Dirac fermions, we demonstrate that topological defects arising from the insertion of pentagonal or heptagonal carbon rings generate effective gauge fields that induce quantized Berry phases. We derive a compact expression for the geometric phase in terms of the genus and number of open boundaries of the structure, providing a topological classification of zero-energy modes. This framework enables a deeper understanding of quantum holonomies in graphene and their potential application in holonomic quantum computation. Our approach bridges discrete lattice models with continuum index theory, yielding insights that are both physically intuitive and experimentally accessible.

cond-mat.mes-hall↗

arXiv2025

Conformal Geometry and Regularization of Disclinations by a Cosmological Constant in $(2+1)$ Dimensions

We investigate the effect of a cosmological constant $\Lambda$ on the geometry generated by a two-dimensional disclination in a conformal metric framework. For $\Lambda>0$, we obtain an exact analytic solution of the Liouville-type equation, which regularizes the defect core, preserves the topological charge, and yields a compact space with finite volume and positive curvature. For $\Lambda<0$, the solution must be obtained numerically and asymptotically approaches $R \to 3\Lambda < 0$, producing an open hyperbolic geometry with divergent volume. In both regimes, the curvature profile is governed solely by the disclination strength $\alpha$, while the sign of $\Lambda$ dictates the global phase: compact and confined for $\Lambda>0$, hyperbolic and delocalized for $\Lambda<0$. This establishes a clear geometric dichotomy and shows that the cosmological constant provides a natural analytic regularization beyond cutoff-based treatments, with implications for analog gravity and two-dimensional condensed matter systems.

gr-qc↗

arXiv2025

New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective

We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation for the conformal factor, we analyze how smooth defect densities -- such as Gaussian, exponential, and power-law profiles -- regularize curvature singularities and encode nontrivial topological information. Each distribution yields a well-defined geometry that interpolates between localized curvature near the defect core and asymptotic flatness. We compute the Ricci scalar and total curvature, confirming consistency with the Gauss-Bonnet theorem. Our results provide a unified geometric description of regularized disclination-like defects and offer insights into analog gravity, crystalline materials, and two-dimensional systems with emergent curvature.

gr-qc↗

arXiv2025

Geometric Modeling of a Line of Alternating Disclinations: Application to Grain Boundaries in Graphene

We develop a conformal geometric model for grain boundaries in graphene based on a periodic line of alternating disclinations. Within the framework of (2+1)-dimensional gravity, we solve a reduced form of the Einstein equations to determine the conformal factor, from which the induced metric, scalar curvature, and holonomy are obtained analytically. Each pentagon-heptagon pair is modeled as a disclination dipole, forming a continuous distribution that captures the geometric signature of experimentally observed 5-7 grain boundaries. We show that the curvature is localized near the defect line and that the geometry becomes asymptotically flat, with trivial holonomy at large distances. This construction provides a tractable and physically consistent realization of the Katanaev-Volovich framework, connecting topological defect theory with atomistic features of graphene.

gr-qc↗

arXiv2025

Geometric and Topological Aspects of Quadrupoles of Disclinations: Conformal Metrics and Self-Forces

We study the geometric and physical effects of quadrupolar configurations of disclinations using a conformal metric approach in $(2+1)$ dimensions. Two cases are considered: a linear quadrupole, inducing anisotropic curvature with a $\cos(2\theta)$ as profile, and a square quadrupole, yielding a more isotropic field with higher angular harmonics. We solve the Poisson equation for the conformal factor and compute the corresponding Green functions. Using these configurations, we evaluated the electrostatic and magnetostatic self-energies and self-forces for linear sources. The results reveal how symmetry and curvature influence self-interaction effects, with the magnetostatic self-force exhibiting a sign reversal compared to the electrostatic case. Connections with previous models of dislocations and cosmic strings are discussed, with potential applications in graphene, nematics, and gravitational analogs.

gr-qc↗

arXiv2025

Gravitational lensing by $k-n$ generalized black-bounce space-times

We study gravitational lensing by $k-n$ generalized black-bounce space-times both in regimes of weak and strong field approximations. These metrics interpolate between regular black holes and one-way or traversable wormholes. First, we investigate the light-like geodesic trajectories and derive an analytical expression for the deflection angle in terms of the bounce parameter in the weak-field gravitational regime. We then turn to the strong-field gravitational regime and display the behavior of the bending angle as a function of both the impact parameter and the bounce parameter. Next, using the lens equations, we analyze how the observables for \textit{Sagittarius} A* behave concerning the bounce parameter. We obtain the shadow's radii for some black-bounce metrics and plot the graph of their sizes, comparing them with the Schwarzschild one.

gr-qc↗

arXiv2025

Uncertainty Quantification in Multiscale Modeling of Polymer Composite Materials Using Physically Recurrent Neural Networks

This study investigates whether Physically Recurrent Neural Networks (PRNNs), a recent surrogate model for heterogeneous materials, trained on a micromodel with fixed material parameters, can maintain accuracy for varying material properties without retraining, and propagate uncertainty in a multiscale framework. Unlike conventional RNNs, where parameter changes require training or explicit inclusion of material properties as extra input features, PRNNs embeds material models in their material layer that allow for modification of material parameters after training. When adjusting material properties dynamically according to the input during testing, PRNN shows high accuracy across a wide range of parameters. Therefore the surrogate can be applied to multiscale uncertainty quantification (UQ). Compared to the full-order simulations on an overly coarse mesh, the PRNN-driven model reduces simulation time by over 7000 times while accurately capturing highly nonlinear evolution of the probability density for the macroscopic response as a result of a given distribution for microscale material parameters. A PRNN-driven UQ is demonstrated on a more accurate finer mesh that would be computationally infeasible with the full-order model.

cond-mat.dis-nn↗

arXiv2025

Contribution of Geometry and Non-Abelian Gauge Fields to Aharonov-Bohm Scattering of Massless Fermions in Graphene with Disclinations

This work examines the effect of disclinations on the scattering of quasipaticles in graphene with the presence of a topological defect. Using the tight-binding method, the electronic properties of graphene with disclination are described, where the topological defects are introduced in the lattice via geometric theory. The massless Dirac equation is modified to account for the curvature induced by these defects, incorporating a gauge field. The results show that disclinations significantly affect the scattering process, altering phase shifts and interference patterns. The differential cross-section and its dependence on the scattering angle are analyzed, highlighting the role of geometric factors like the parameter {\alpha} in shaping the scattering dynamics.

cond-mat.mes-hall↗

arXiv2025

Missing Aharonov-Casher geometric quantum phase

From the interaction of the permanent magnetic dipole moment of a neutral particle with an electric field inside a long non-conducting cylindrical shell of inner radius $r_{a}$ and outer radius $r_{b}$, we show that a geometric quantum phase stems from the missing electric charge per unit length. Thus, we discuss the possibility of existing Aharonov-Bohm-type effects with regard to this geometric quantum phase. Further, we discuss the persistent spin currents.

quant-ph↗

arXiv2024

Rotation effects on the graphene wormhole energy levels

In this work, we are interested in how spinning effects influence the electronic properties of the graphene wormhole. For this purpose, we have described the graphene by the wormhole background based on the model developed by Gonz\'alez and his co-workers. By applying a coordinate transformation in the metric of graphene wormhole, we can introduce rotating effects. In the continuum limit, by solving the massless Dirac equation in the context of a rotating wormhole background, we obtain the Landau levels for the rotating graphene wormhole. We still have exposed the analogy between the graphene wormhole and fermions on the G\"odel-type spacetime.

cond-mat.mes-hall↗

arXiv2024

Physically Recurrent Neural Networks for Computational Homogenization of Composite Materials with Microscale Debonding

The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially powerful approach for this purpose, but its widespread adoption is prevented by its excessive computational costs. A popular approach to address this computational bottleneck is using surrogate models, which have been used to successfully predict a wide range of constitutive behaviors. However, applications involving microscale damage and fracture remain largely unexplored. This work aims to extend a recent surrogate modeling approach, the Physically Recurrent Neural Network (PRNN), to include the effect of debonding at the fiber-matrix interface while capturing path-dependent behavior. The core idea of the PRNN is to implement the exact material models from the micromodel into one of the layers of the network. In this work, additional material points with a cohesive zone model are integrated within the network, along with the bulk points associated to the fibers and/or matrix. The limitations of the existing architecture are discussed and taken into account for the development of novel architectures that better represent the stress homogenization procedure. In the proposed layout, the history variables of cohesive points act as extra latent features that help determine the local strains of bulk points. Different architectures are evaluated starting with small training datasets. To maximize the predictive accuracy and extrapolation capabilities of the network, various configurations of bulk and cohesive points are explored, along with different training dataset types and sizes.

math.NA↗

arXiv2024

Landau levels for massive disclinated graphene-based topological insulator

In this work, we investigate the massive Kane-Mele model for graphene in the presence of disclination and an external magnetic field, where graphene behaviors as a topological insulator. In the low-energy limit, the effective field equation for graphene is described by a Dirac equation with three different degrees of freedom. We succeed to decouple the set of eight components of the Dirac equation by using the spin projector \hat{C} in the disclinated geometry. As consequence, we obtain the Landau levels in this framework, in which we note the emergence of zero modes as edge states due to the inversion symmetry breaking. We also note that for different sites in sublattices \mathcal{A/B}, one can have different values of gap width.

cond-mat.mes-hall↗

arXiv2022

On the missing magnetic flux and topological effects of a screw dislocation on a charged particle in an inhomogeneous magnetic field

We study the interaction of an electron/hole with inhomogeneous magnetic field in the presence of a screw dislocation. We consider the internal structure of the defect, i.e., we consider the core that gives rise to a finite size to the defect. In addition, we assume that this core determines a forbidden region for the electron/hole. Then, we solve the Schr\"odinger equation and show that an Aharonov-Bohm-type effect arises from the influence of the topological defect and the missing magnetic flux on the eigenvalues of energy.

quant-ph↗

arXiv2020

Strong gravitational lensing in a spacetime with topological charge within the Eddington-inspired Born-Infeld gravity

In this work we calculate the angular deflection of light in the strong field limit in two spacetimes which were previously studied within the Eddington-inspired Born-Infeld gravity (EiBI), namely, a black hole and a wormhole, both with topological charge. We show that the presence of the parameters characterizing EiBI and the topological charge promote significant changes in the angular deflection of light with respect to that one obtained in Schwarzschild spacetime. Using the expression for angular deflection in the strong field limit, we calculate the position and magnification of the respective relativistic images.

gr-qc↗