arXiv subjects

Jorge Romero

Publications and source records attributed to Jorge Romero.

13 recordsLinked to original sources

arXiv2026

$\mathcal{N}$-bein formalism for degenerate states in the parameter space of quantum geometry

Recently, we introduced a geometric object analogous to an orthonormal frame in the Cartan formalism to study the parameter space of quantum systems; we called it $\mathcal{N}$-bein, with $\mathcal{N}$ being the number of parameters that characterize the quantum system. Acting as the ``square root'' of the quantum geometric tensor (QGT), the $\mathcal{N}$-bein allows us to define new tensors to improve our understanding of the structure beneath the parameter space of quantum mechanics. In this work, we extend this mathematical framework surrounding the $\mathcal{N}$-bein to analyze the parameter space of quantum systems with degenerate spectra. As in the non-degenerate case, we define a non-Abelian two-state QGT to identify possible transitions between degenerate states after two consecutive parameter variations. Additionally, using the Wilczek-Zee connection, we introduce a torsion-like tensor as the covariant derivative of the $\mathcal{N}$-bein. This torsion captures the noncommutativity of successive parameter variations and coincides with the antisymmetric part of the two-state QGT. We also present a geometrical formulation using differential forms and discuss the physical implications of the newly defined tensors. Furthermore, we construct several gauge-invariant observables from the $\mathcal{N}$-bein and its derivatives to highlight the utility of the new tensors. Finally, to illustrate the convenience and applications of this formalism, we apply the theoretical framework to a system of coupled harmonic oscillators immersed in an electric field. The coupling between the oscillators results in a degenerate system. Thus, using the new formalism, we found correlations among the quantum states quantified by the new invariants.

quant-ph↗

arXiv2024

$N$-bein formalism for the parameter space of quantum geometry

This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it $N$-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the $N$-bein behaves like a ``square root'' of the quantum geometric tensor. Using it, we present a quantum geometric tensor of two states that measures the possibility of moving from one state to another after two consecutive parameter variations. This new tensor determines the commutativity of such variations through its anti-symmetric part. In addition, we define a connection different from the Berry connection, and combining it with the $N$-bein allows us to introduce a notion of torsion and curvature à la Cartan that satisfies the Bianchi identities. Moreover, the torsion coincides with the anti-symmetric part of the two-state quantum geometric tensor previously mentioned, and thus, it is related to the commutativity of the parameter variations. We also describe our formalism using differential forms and discuss the possible physical interpretations of the new geometrical objects. Furthermore, we define different gauge invariants constructed from the geometrical quantities introduced in this work, resulting in new physical observables. Finally, we present two examples to illustrate these concepts: a harmonic oscillator and a generalized oscillator, both immersed in an electric field. We found that the new tensors quantify correlations between quantum states that were unavailable by other methods.

quant-ph↗

arXiv2024

High-precision mass measurements of neutron deficient silver isotopes probe the robustness of the $N$ = 50 shell closure

High-precision mass measurements of exotic $^{95-97}$Ag isotopes close to the $N = Z$ line have been conducted with the JYFLTRAP double Penning trap mass spectrometer, with the silver ions produced using the recently commissioned inductively-heated hot cavity catcher laser ion source at the Ion Guide Isotope Separator On-Line facility. The atomic mass of $^{95}$Ag was directly determined for the first time. In addition, the atomic masses of $β$-decaying 2$^+$ and 8$^+$ states in $^{96}$Ag have been identified and measured for the first time, and the precision of the $^{97}$Ag mass has been improved. The newly measured masses, with a precision of $\approx$ 1 keV/c$^2$, have been used to investigate the $N =$ 50 neutron shell closure confirming it to be robust. Empirical shell-gap and pairing energies determined with the new ground-state mass data are compared with the state-of-the-art \textit{ab initio} calculations with various chiral effective field theory Hamiltonians. The precise determination of the excitation energy of the $^{96m}$Ag isomer in particular serves as a benchmark for \textit{ab initio} predictions of nuclear properties beyond the ground state, specifically for odd-odd nuclei situated in proximity to the proton dripline below $^{100}$Sn. In addition, density functional theory (DFT) calculations and configuration-interaction shell-model (CISM) calculations are compared with the experimental results. All theoretical approaches face challenges to reproduce the trend of nuclear ground-state properties in the silver isotopic chain across the $N =$50 neutron shell and toward the proton drip-line.

nucl-ex↗

arXiv2023

Linking the ADM formulation to other Hamiltonian formulations of general relativity

We obtain the Arnowitt-Deser-Misner formulation of general relativity in $n$ dimensions ($n \geq 3$) from its either $SO(n-1,1)$ [$SO(n)$] or $SO(n-1)$ Palatini Hamiltonian formulations and vice versa [we recall that $SO(n-1,1)$ [$SO(n)$] requires no gauge fixing whereas $SO(n-1)$ involves the time gauge]. Similarly, the Hamiltonian formulation of general relativity in terms of Ashtekar-Barbero variables can also be directly obtained from the Arnowitt-Deser-Misner Hamiltonian formulation and vice versa, which is an alternative approach to the way followed by Barbero. We give the relevant maps among the phase-space variables and relate the corresponding symplectic structures and the first-class constraints.

gr-qc↗

arXiv2022

Fermions coupled to the Palatini action in $n$ dimensions

We study minimal and nonminimal couplings of fermions to the Palatini action in $n$ dimensions ($n\geq 3$) from the Lagrangian and Hamiltonian viewpoints. The Lagrangian action considered is not, in general, equivalent to the Einstein-Dirac action principle. However, by choosing properly the coupling parameters, it is possible to give a first-order action fully equivalent to the Einstein-Dirac theory in a spacetime of dimension four. By using a suitable parametrization of the vielbein and the connection, the Hamiltonian analysis of the general Lagrangian is given, which involves manifestly Lorentz-covariant phase-space variables, a real noncanonical symplectic structure, and only first-class constraints. Additional Hamiltonian formulations are obtained via symplectomorphisms, one of them involving half-densitized fermions. To confront our results with previous approaches, the time gauge is imposed.

gr-qc↗

arXiv2021

Hamiltonian analysis of fermions coupled to the Holst action

We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimally coupled fermion fields to the Holst action. These formulations are achieved by making a suitable parametrization of both the tetrad and the Lorentz connection, which allows us to integrate out some auxiliary fields without spoiling the local Lorentz symmetry. They have the peculiarity that their noncanonical symplectic structures as well as the phase-space variables for the gravitational sector are real. Moreover, two of these Hamiltonian formulations involve half-densitized fermion fields. We also impose the time gauge on these formulations, which leads to real connections for the gravitational configuration variables. Finally, we perform a symplectomorphism in one of the manifestly Lorentz-invariant Hamiltonian formulations and analyze the resulting formulation, which becomes the Hamiltonian formulation of fermion fields minimally coupled to the Palatini action for particular values of the coupling parameters.

gr-qc↗

arXiv2020

Canonical analysis of Holst action without second-class constraints

We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the involved variables from the very outset. After integrating out the nondynamical variables associated with the connection, we obtain the description of phase space in terms of manifestly $SO(3,1)$ [or $SO(4)$, depending on the signature] covariant canonical variables and first-class constraints only. We impose the time gauge on them and show that the Ashtekar-Barbero formulation of general relativity emerges. Later, we discuss a family of canonical transformations that allows us to construct new $SO(3,1)$ [or $SO(4)$] covariant canonical variables for the phase space of the theory and compare them with the ones already reported in the literature, pointing out the presence of a set of canonical variables not considered before. Finally, we resort to the time gauge again and find that the theory, when written in terms of the new canonical variables, either collapses to the $SO(3)$ ADM formalism or to the Ashtekar-Barbero formalism with a rescaled Immirzi parameter.

gr-qc↗

arXiv2020

Canonical analysis of $n$-dimensional Palatini action without second-class constraints

We carry out the canonical analysis of the $n$-dimensional Palatini action with or without a cosmological constant $(n\geq3)$ introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing an expression for the spatial components of the connection that allows us to isolate the nondynamical variables present among them, which can later be eliminated from the action by using their own equation of motion. As a result, we obtain the description of the phase space of general relativity in terms of manifestly $SO(n-1,1)$ [or $SO(n)$] covariant variables subject to first-class constraints only, with no second-class constraints arising during the process. Afterwards, we perform, at the covariant level, a canonical transformation to a set of variables in terms of which the above constraints take a simpler form. Finally, we impose the time gauge and make contact with the $SO(n-1)$ ADM formalism.

gr-qc↗

arXiv2019

Revisiting the solution of the second-class constraints of the Holst action

In this paper we revisit the nonmanifestly Lorentz-covariant canonical analysis of the Holst action with a cosmological constant. We take a viewpoint close to that of F. Cianfrani and G. Montani [Phys. Rev. Lett. 102, 091301 (2009)] and realize that the solution of the second-class constraints that the authors provide is incomplete, thus not accounting for the correct local dynamics of general relativity. We then mend their approach by adding the missing degrees of freedom to the solution and give a complete description of the resulting theory, which preserves Lorentz invariance but turns out to be endowed with a noncanonical symplectic structure. Later on and without resorting to any gauge condition, we perform a Darboux transformation to bring this theory into a canonical form. Finally, we show that in the time gauge both formulations, namely the noncanonical and the canonical ones, lead to the Ashtekar-Barbero variables.

gr-qc↗

arXiv2018

$SU(1,1)$ Barbero-like variables derived from Holst action

We work on a spacetime manifold foliated by timelike leaves. In this setting, we explore the solution of the second-class constraints arising during the canonical analysis of the Holst action with a cosmological constant. The solution is given in a manifestly Lorentz-covariant fashion, and the resulting canonical formulation is expressed using several sets of real variables that are related to one another by canonical transformations. By applying a gauge fixing to this formulation, we obtain a description of gravity as an $SU(1,1)$ gauge theory that resembles the Ashtekar-Barbero formulation.

gr-qc↗

arXiv2018

Alkoxide-intercalated NiFe-layered double hydroxides magnetic nanosheets as efficient water oxidation electrocatalysts

Alkoxide-intercalated NiFe-layered double hydroxides were synthesized via the nonaqueous methanolic route. These nanoplatelets exhibit high crystalline quality as demonstrated by atomic resolution scanning transmission electron microscopy combined with electron energy-loss spectroscopy. Moreover, the presence of the alkoxide moieties has been unambiguously demonstrated by means of thermogravimetric analysis coupled to a mass spectrometer. These NiFe-LDHs can be exfoliated in water or organic solvents and processed into homogeneous ultra-thin films (< 3nm thick) with the assistance of O2-plasma. The study of their behaviour as water oxidation electrocatalysts has shown an outstanding performance at basic pHs (small overpotential of ca. 249 mV and Tafel slopes in the range of 52-55 mV per decade).

physics.chem-ph↗

arXiv2018

Manifestly Lorentz-covariant variables for the phase space of general relativity

We present a manifestly Lorentz-covariant description of the phase space of general relativity with the Immirzi parameter. This formulation emerges after solving the second-class constraints arising in the canonical analysis of the Holst action. We show that the new canonical variables give rise to other Lorentz-covariant parametrizations of the phase space via canonical transformations. The resulting form of the first-class constraints in terms of new variables is given. In the time gauge, these variables and the constraints become those found by Barbero.

gr-qc↗

arXiv2016

Barbero's formulation from a $BF$-type action with the Immirzi parameter

Starting from a constrained real $BF$-type action for general relativity that includes both the Immirzi parameter and the cosmological constant, we obtain the Ashtekar-Barbero variables used in the canonical approach to the quantization of the gravitational field. This is accomplished by explicitly solving the second-class constraints resulting from the Hamiltonian analysis of the considered action, and later imposing the time gauge. All throughout this work the tetrad formalism is left aside, obtaining the Ashtekar-Barbero variables entirely in terms of the $B$-fields that define the action.

gr-qc↗