arXiv subjects

F. Méndez

Publications and source records attributed to F. Méndez.

7 recordsLinked to original sources

arXiv2024

Resonance of Gravitational Axions-like Particles

The motion of gravitational axion-like particles (ALP) around a Kerr black hole is analyzed, paying attention to resonance and distribution of spectral radiation. We first discuss the computation of $\sqrt{g}{\tilde R}_{μνρρσ}R^{μνρσ}$ and its implications with Pontryagin's theorem and a detailed analysis of Teukolsky's master equation is done. After carefully analyzing the Teukolsky master equation, we show that this system exhibits resonance when $ω\gtrsim μ$ where $μ$ is the mass of the ALP. A skew-normal distribution can approximate the energy distribution, and we can calculate the mean lifetime of the resonance for black holes with masses between 100 to 1000 $M_{\odot}$. This range corresponds to a duration between $10^{-1}$s and $10^{41}$s, the observation range used in LIGO data.

hep-th↗

arXiv2022

Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.

hep-ph↗

arXiv2020

Deformed Quantum Mechanics and the Landau Problem

A deformation of the Landau problem based on a modification of Fock algebra is considered. Systems with Hamiltonians f(H) where H is the Landau Hamiltonian in the lowest level are discussed. The case $f(H) = α H + b H^2$ is studied and it is shown that in this particular example, parameters of the problem can be fixed by using the quadratic Zeeman effect data and the Breit- Rabi formula. The proposed approach allows to solve exactly Landau-like families of problems not previously discussed in the literature.

hep-th↗

arXiv2018

Meissner Effect from Landau Problem

The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen-Olesen vortices are established. Firstly we show that the Landau problem with non-homogeneous magnetic fields exhibits Meissner effect that is unstable unless two-body interactions are added and vortices emerge. Using the scaling freedom we can write the Schrödinger equation in terms of the scales ratio $κ={ E}/{ m }\propto 1- T/T_c $ where the last identification is realised simply by using the Gizburg-Landau theory. We find our equations are valid in the superconducting regime, and it is not possible for the Cooper pairs amplitude to reach to a constant, non-zero value, and therefore the theory is unstable. The supersymmetric quantum mechanics version, by completeness, is also considered.

hep-th↗

arXiv2017

Inflation without Inflaton: A Model for Dark Energy

The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $Λ_a$ and $Λ_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {\cal P}_α, {\cal P}_β ] =ε_{αβ}\fracκ{G}$, where $G$ is Newton's gravitational constant and $κ$ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $κ$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $κ\ll1 $ is also studied.

gr-qc↗

arXiv2015

On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential. PACS: 03.65.-w; 03.65.Fd MSC: 81R05; 20C35; 22E70

math-ph↗

arXiv2012

Noncommutativity in (2+1)-dimensions and the Lorentz group

In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schrödinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to no-commutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.

hep-th↗