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Carlos Batista

Publications and source records attributed to Carlos Batista.

At least 19 recordsLinked to original sources
arXiv2026

Field-driven helicity in solid-state high-harmonic generation

The polarization state of light plays a central role in strong-field light--matter interactions and is widely used to probe electronic structure in solids via high-order harmonic generation (HHG). In particular, helicity-resolved HHG has been interpreted as a fingerprint of crystal symmetry and topology. Here, we demonstrate deterministic and continuous control of harmonic helicity in solids using polarization-crafted beams, formed by two orthogonally polarized pulses with a controlled time delay. By tuning this delay, the polarization state of individual harmonics can be driven from linear to circular, independent of the material under investigation. We show that this behavior is robust across systems with distinct symmetry and topology, and originates from the sub-cycle modulation of the light--matter interaction mediated by the dipole coupling. Furthermore, the orthogonal configuration allows to break the dynamical symmetry of the light-matter interaction which is manifested in the generation of otherwise forbidden harmonics under standard selection rules.. These results establish harmonic helicity as a field-controlled observable rather than a direct material fingerprint.

physics.optics↗
arXiv2025

High Harmonic Spectroscopy from Lower-Order to Higher-Order Topological Insulators

Over the past decades, high-harmonic spectroscopy (HHS) has emerged as a powerful tool for all-optical probing of topological properties of solids. There are outstanding questions regarding universal nature of the spectral features of harmonics in their relationship to the non-trivial topological properties. Here, we present a systematic theoretical study of HHS in topological materials, including lower-order and higher-order topological insulators (LOTIs and HOTIs), focusing on observables such as helicity, circular dichroism, ellipticity dependence, and channel-resolved intensity yields. Using the Haldane, Kane-Mele, and breathing Kagome lattice models, we theoretically extend all-optical approaches from the LOTI to the HOTI regime by explicitly incorporating contributions from bulk, edge, and it corner states. Depending on the crystalline system, our calculations suggest that these observables can encode topological information through distinct modifications of the HHG spectra in topological phases. In particular, we identify significant enhancements of the harmonic intensity yields, reaching up to two orders of magnitude relative to trivial phases, together with distinct spectral signatures associated with edge and corner contributions revealed through channel-resolved intensity yields. These results show that channel-resolved HHS provides a promising route for probing topological states in both LOTIs and HOTIs.

cond-mat.mtrl-sci↗
arXiv2020

On the Equivalence of Spacetimes, the Cartan-Karlhede Algorithm

It is well known that in general relativity theory two spacetimes whose metrics are related by a coordinate transformation are physically equivalent. However, given two line elements, it is virtually impossible to implement the most general coordinate transformation in order to check the equivalence of the spacetimes. In this paper we present the so-called Cartan-Karlhede algorithm, which provides a finite sequence of steps to decide whether or not two metrics are equivalent. The point of this note is to illustrate the method through several simple examples, so that the reader can learn the fundamentals and details of the algorithm in practice.

gr-qc↗
arXiv2020

Two-Component Spinorial Formalism using Quaternions for Six-dimensional Spacetimes

In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components and the spin group is identified with $SL(2;\mathbb{H})$, which is a double covering for the Lorentz group in six dimensions. We present the fundamental representations of this group and show how vectors, bivectors, and 3-vectors are represented in such spinorial formalism. We also complexify the spacetime, so that other signatures can be tackled. We argue that, in general, objects built from the tensor products of the fundamental representations of $SL(2;\mathbb{H})$ do not carry a representation of the group, due to the non-commutativity of the quaternions. The Lie algebra of the spin group is obtained and its connection with the Lie algebra of $SO(5,1)$ is presented, providing a physical interpretation for the elements of $SL(2;\mathbb{H})$. Finally, we present a bridge between this quaternionic spinorial formalism for six-dimensional spacetimes and the four-component spinorial formalism over the complex field that comes from the fact that the spin group in six-dimensional Euclidean spaces is given by $SU(4)$.

hep-th↗
arXiv2020

On Conserved Quantities for the Free Motion of Particles with Spin

In the early 80's, R. Rüdiger published a pair of articles in which it was found the most general conserved charges associated to the motion of particles with spin moving in curved spacetime. In particular, it was shown that besides the well-known conserved quantity associated to Killing vectors, it is also possible to have another conserved quantity that is linear in the spin of the particle if the spacetime admits a Killing-Yano tensor. However, in these papers it was proved that in order for this new scalar to be conserved two obscure conditions involving the Killing-Yano tensor and the curvature must be obeyed. In the present paper we try to shed light over these conditions and end up proving that this conserved quantity is useless for most physically relevant spacetimes. Notably, for particles moving in vacuum (Einstein spacetimes) this conserved scalar constructed with the Killing-Yano tensor will not help on the integration of the equations of motion. Moreover, we prove that, as a consequence of these obscure conditions, the Killing-Yano tensor must be covariantly constant.

gr-qc↗
arXiv2020

Spin 2 Quasinormal Modes in Generalized Nariai Spacetimes

In this work we analytically obtain the quasinormal spectrum for the gravitational perturbation on a higher-dimensional generalization of the Nariai spacetime that is comprised of the direct product of the two-dimensional de Sitter space with several two-spheres. A key step in order to attain this result is to use a suitable basis for the angular functions depending on the rank of the tensorial degree of freedom that one needs to describe. Here we define such a basis, which is a generalization of the tensor spherical harmonics that is suited for spaces that are the product of several spaces of constant curvature.

gr-qc↗
arXiv2018

A Class of Higher-Dimensional Solutions of Einstein's Vacuum Equation

A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to higher-dimensional generalizations of Kasner spacetime with a cosmological constant. On the other hand, the metrics attained when such matrix is non-diagonal have more intricate algebraic structures. Such solutions have not been presented in the literature yet.

gr-qc↗
arXiv2018

A Class of Integrable Metrics II

Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions happen to be already known, we have found a solution that, as far as we could search for, has not been attained before. We also characterize the geometric properties of this new solution, it is a Kundt spacetime of Petrov type II possessing a null Killing vector field and an isometry algebra that is three-dimensional and abelian. In particular, such solution becomes a pp-wave spacetime when the cosmological constant is set to zero.

gr-qc↗
arXiv2018

Quasinormal Modes in Generalized Nariai Spacetimes

The perturbations of fields with spin 0, 1/2, and 1 propagating in a higher-dimensional generalization of the charged Nariai spacetime are investigated. The boundary conditions leading to quasinormal modes are analyzed and the quasinormal frequencies are analytically obtained.

gr-qc↗
arXiv2017

On Spaces with the Maximal Number of Conformal Killing Vectors

It is natural to expect and simple to prove that every conformally flat space possess the maximal number of conformal Killing vector fields (CKVs). On the other hand, it is interesting to ask whether the converse is true. Is conformal flatness a necessary condition for the existence of the maximal number of CKVs? In this review article it is proven that the answer is yes, a space admits the maximal number of CKVs if, and only if, it is conformally flat.

gr-qc↗
arXiv2017

A Class of Integrable Metrics and Gauge Fields

Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is assumed that the gauge field inherits the symmetries of the background and is aligned with the principal null directions of the spacetime.

hep-th↗
arXiv2016

Generalized Charged Nariai Solutions in Arbitrary Even Dimensions with Multiple Magnetic Charges

Higher-dimensional solutions for Einstein-Maxwell equations that generalize the charged Nariai spacetime are obtained. The solutions presented here are made from the direct product of several 2-spaces of constant curvature. These solutions turn out to have many magnetic charges, contrary to the usual higher-dimensional generalization of the Nariai spacetime, which has no magnetic charge at all. These solutions are then used to generate black hole metrics. Finally, it is analyzed how these generalized Nariai solutions are modified in more general theories of gravity.

gr-qc↗
arXiv2016

Hamiltonian formulation towards minimization of viscous fluid fingering

A variational approach has been recently employed to determine the ideal time-dependent injection rate Q(t) that minimizes fingering formation when a fluid is injected in a Hele-Shaw cell filled with another fluid of much greater viscosity. However, such a calculation is approximate in nature, since it has been performed by assuming a high capillary number regime. In this work, we go one step further, and utilize a Hamiltonian formulation to obtain an analytical exact solution for Q(t), now valid for arbitrary values of the capillary number. Moreover, this Hamiltonian scheme is applied to calculate the corresponding injection rate that minimizes fingering formation in a uniform three-dimensional porous media. An analysis of the improvement offered by these exact injection rate expressions in comparison with previous approximate results is also provided.

physics.flu-dyn↗
arXiv2016

A Class of Integrable Metrics

In four dimensions, the most general metric admitting two Killing vectors and a rank-two Killing tensor can be parameterized by ten arbitrary functions of a single variable. We show that picking a special vierbien, reducing the system to eight functions, implies the existence of two geodesic and share-free, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the Goldberg-Sachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provide an straightforward connection between the most general integrable structure and the Carter family of spacetimes.

gr-qc↗
arXiv2015

Killing Spinors and Related Symmetries in Six Dimensions

Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified in two algebraic types, in the first type the scalar curvature of the spacetime must be negative, while in the second type the spacetime must be an Einstein manifold. In addition, the equations that define Killing-Yano (KY) and closed conformal Killing-Yano (CCKY) tensors are expressed in the index notation and, as consequence, all non-vanishing KY and CCKY tensors that can be generated from a Killing spinor are made explicit.

hep-th↗
arXiv2015

Conformally Invariant Spinorial Equations in Six Dimensions

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, some useful identities involving the curvature of the spinorial connection are attained and a digression about harmonic forms and more general massless fields is made.

hep-th↗
arXiv2015

Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion

The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, the issue of defining a maximally symmetric space with respect to connections with torsion is addressed.

gr-qc↗