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We consider the massless Rarita-Schwinger (RS) LV QED. In this theory, we introduce the gauge fixing to obtain the propagator for the RS field, and calculate the Carroll-Field-Jackiw term, which turns out to be finite and ambiguous, and only in one calculation scheme, based on the nonlinear gauge framework, the gauge independence of the result is achieved., Comment: 15 pages

We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with $\nu$ decreasing with lattice dimensionality, $d$, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.

The entire classical cosmological history between two extreme de Sitter vacuum solutions is discussed based on Einstein's equations and non-equilibrium thermodynamics. The initial non-singular de Sitter state is characterised by a very high energy scale which is equal or smaller than the reduced Planck mass. It is structurally unstable and all the continuous created matter, energy and entropy of the material component comes from the irreversible flow powered by the primeval vacuum energy density. The analytical expression describing the running vacuum is obtained from the thermal approach. It opens a new perspective to solve the old puzzles and current observational challenges plaguing the cosmic concordance model driven by a rigid vacuum. Such a scenario is also modelled through a non-canonical scalar field. It is demonstrated that the resulting scalar field model is shown to be step by step a faithful analytical representation of the thermal running vacuum cosmology., Comment: 12 pages, 3 figures

The potential role of a cosmic vacuum dark component in the properties of neutron stars is investigated. It is assumed that the static, spherically symmetric distribution of matter within neutron stars is supported by two distinct components: ordinary matter and a vacuum fluid. For normal matter we use a set of state-of-the-art nuclear matter equations of state, each grounded in nuclear physics experiments. The vacuum energy component is inhomogeneously distributed within the star and obeys the standard equation of state ($p_v = -\epsilon_v$). This is characterized by an energy density fraction $y = \epsilon_m/ (\epsilon_m + \epsilon_v)$, which we model as either a constant or radius-dependent. Our findings reveal that the inclusion of vacuum energy significantly affects the mass-radius relationships in neutron stars, influencing both the maximum achievable masses and the qualitative form of these relationships. Some constraints from current multimessenger observational data limiting the amount of vacuum energy within neutron stars are also discussed., Comment: 13 pages, 5 figures

The main purpose of this paper is to provide formulas for the Hilbert-Kunz multiplicity of fiber products and idealization rings. We calculate the Hilbert-Kunz multiplicity of a fiber product $R \times_T S$, with $R$, $S$ and $T$ being Noetherian local rings with common characteristic and residue field. Inspired by a work of Strazzanti and Armengou we calculate the Hilbert-Kunz multiplicity of an idealization ring $R \ltimes M$, where $M$ is a finite $R$-module. We explore certain examples and structural consequences and obtain some bounds for the Hilbert-Kunz multiplicity., Comment: 16 pages - Comments are welcome!

In this paper we introduce new classes of gluing of complex analytic spaces germs, called weakly large, large and strongly large. We give a description of their Poincar\'e series and, as applications, we give numerical criteria to determine when these classes of gluing of germs of complex analytic spaces are smooth, singular, complete intersections and Gorenstein in terms of their Betti numbers. In particular, we show that the gluing of the same germ of complex analytic space along of any subspace is always a singular germ.

The present paper deals with the investigation of the structure of general fiber product rings $R\times_TS$, where $R$, $S$ and $T$ are local rings with common residue field. We show that the Poincar\'e series of any $R$-module over the fiber product ring $R\times_TS$ is bounded by a rational function. In addition, we give a description of ${\rm depth}(R\times_TS)$, which is an open problem in this theory. As a biproduct, using the characterization of the Betti numbers over $R\times_TS$ obtained, we provide certain cases of the Cohen-Macaulayness of $R\times_TS$ and, in particular, we show that $R\times_TS$ is always non-regular. Some positive answers for the Buchsbaum-Eisenbud-Horrocks and Total rank conjectures over $R\times_TS$ are also established., Comment: Comments and suggestions are welcome

Let $M$ be a finitely generated module over a local ring $(R,\mathfrak{m})$. By $\mathcal{S}_j(M)$, we denote the $j$th symmetric power of $M$ ($j$th graded component of the symmetric algebra $\mathcal{S}_R(M)$). The purpose of this paper is to investigate the minimal free resolutions $\mathcal{S}_j(M)$ as $R$-module for each $j\geq 2$ and determine the Betti numbers of $\mathcal{S}_j(M)$ in terms of the Betti numbers of $M$. This has some applications, for example for linear type ideals $I$, we obtain formulas of the Betti numbers $I^j$ in terms of the Betti numbers of $I$. In addition, we establish upper and lower bounds of Betti numbers of $\mathcal{S}_j(M)$ in terms of Betti numbers of $M$. In particular, obtain some applications of the famous Buchsbaum-Eisenbud-Horrocks conjecture.

In this paper, we demonstrate the possibility of generating a non-Abelian Carroll-Field-Jackiw (CFJ) term in the theory of a non-Abelian gauge field coupled to a spin-3/2 field in the presence of the constant axial vector field. Applying two regularization schemes, we prove that this term is finite and ambiguous, particularly vanishing within the 't Hooft-Veltman scheme., Comment: 11 pages

A macroscopic and kinetic relativistic description for a decoupled multi-fluid cosmology endowed with gravitationally induced particle production of all components is proposed. The temperature law for each decoupled particle species is also kinetically derived. The present approach points to the possibility of an exact (semi-classical) quantum-gravitational kinetic treatment by incorporating back reaction effects for an arbitrary set of dominant decoupled components. As an illustration we show that a cosmology driven by creation of cold dark matter and baryons (without dark energy) evolves like $\Lambda$CDM. However, the complete physical emulation is broken when photon creation is added to the mixture thereby pointing to a crucial test in the future. The present analysis also open up a new window to investigate the Supernova-CMB tension on the values of $H_0$, as well as the $S_8$ tension since creation of all components changes slightly the CMB results and the expansion history both at early and late times. Finally, it is also argued that cross-correlations between CMB temperature maps and the Sunyaev-Zeldovich effect may provide a crucial and accurate test confronting extended CCDM and $\Lambda$CDM models., Comment: 16 pages, 1 figure, accepted for publication in European Physical Journal C

The possibility of an expanding decelerating Universe in the distant future is investigated in the context of a quintessence scalar field cosmology. Such a conceivable evolution is tested against SNe Ia and $H(z)$ cosmic chronometers data, and also through a model independent method based on Gaussian Processes. The scalar field model is an extension of the exponential Ratra-Peebles (RP) quintessential cosmology whose potential now depends on a pair of parameters ($\alpha, \lambda)$ and predicts a decelerated expansion in the future. Different from RP approach the $\alpha$ parameter allows for a decelerating cosmology in the future thereby frustrating the inevitable evolution for a de Sitter Cosmology as predicted by the cosmic concordance model ($\Lambda$CDM). The statistical model analysis is updated with the most recent SNe Ia and $H(z)$ data thereby obtaining $H_0 = 68.6\pm3.7$ km/s/Mpc, $\Omega_{\Phi0} = 0.735^{+0.083}_{-0.069} $, $\alpha < 6.56$ and $\lambda< 0.879 $ (at $2\sigma$ c.l.). It is also found that the extended RP model allows for a future deceleration both for $H(z)$ and SNe Ia data. In the (model-independent) Gaussian Processes analysis, however, future deceleration is allowed only in the case of $H(z)$ data., Comment: 10 pages, 5 figures. Accepted for publication in Physical Review D

Context. There are recent observational evidences that RY Tau may present two different outflow stages, a quiescent one and a more active one. We try to model that phenomenon. Aims. We have performed new 2.5D magneto-hydrodynamical simulations of the possible accretion-outflow environment of RY Tau based on analytical solutions to reduce the relaxation time. Methods. We used as initial conditions the analytical self-similar solution we used to model the RY Tau micro jet. In the closed field line region of the magnetosphere we have reversed the direction of the flow and increased the accretion rate by increasing the density and the velocity. We have also implemented the heating rate and adjusted it according to the velocity of the flow. The accretion disk is treated as a boundary condition. Results. The simulations show that the stellar jet and the accreting magnetosphere attain a steady state in only a few stellar rotations, confirming the robustness and stability of self-similar solutions. Additionally, two types of behavior were observed similar to the one observed in RY Tau. Either the steady stellar outflow and magnetospheric inflow are separated by a low static force free region or the interaction between the stellar jet and the magnetospheric accretion creates coronal episodic mass ejections originating from the disk and bouncing back onto the star. Conclusions. The ratio of mass loss rate to mass accretion rate that coincides with the change of behaviour observed in RY Tau, lays within the range of ratios that have been measured during the period of the micro jet initial analysis., Comment: 14 pages, 10 figures, accepted for publication in Astronomy and Astrophysics

Heat always flows from hotter to a colder temperature until thermal equilibrium be finally restored in agreement with the usual (zeroth, first and second) laws of thermodynamics. However, Tolman and Ehrenfest demonstrated that the relation between inertia and weight uniting all forms of energy in the framework of general relativity implies that the standard equilibrium condition is violated in order to maintain the validity of the first and second law of thermodynamics. Here we demonstrate that the thermal equilibrium condition for a static self-gravitating fluid, besides being violated, is also heavily dependent on the underlying spacetime geometry (whether Riemannian or non-Riemannian). As a particular example, a new equilibrium condition is deduced for a large class of Weyl and f(R) type gravity theories. Such results suggest that experiments based on the foundations of the heat theory (thermal sector) may also be used for confronting gravity theories and prospect the intrinsic geometric nature of the spacetime structure., Comment: 5 pages, no figures. Accepted for publication in Physical Review D

In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures $T_c(q)$, for $q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are less dependent on finite size effects, while still being able to distinguish between first and second order phase transitions. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions., Comment: Added computation of critical exponents; exposition improved

We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO$_2$ lattice; in three dimensions it can be generalized to a layered Lieb lattice (LLL) or to a perovskite lattice (PL). Emergent electronic phenomena, such as topological states and ferrimagnetism, have been predicted to occur in these systems, which may be realized in optical lattices as well as in solid state. Since the study of the interplay between quantum fluctuations and disorder in these systems requires the availability of accurate estimates of geometrical critical parameters, such as percolation thresholds and correlation length exponents, here we use Monte Carlo simulations to obtain these data for Lieb lattices when a site (or bond) is present with probability $p$. We have found that the thresholds satisfy a mean-field (Bethe lattice) trend, namely that the critical concentration, $p_c$, increases as the average coordination number decreases; our estimates for the correlation length exponent are in line with the expectation that there is no change in the universality class., Comment: 5 pages, 5 figures

The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical reduction to a finite ideal gas. In the limit where the thermofractal has no internal structure, it is found that it reproduces the basic properties of a nonextensive ideal gas with a finite number of particles as recently discussed (Lima \& Deppman, Phys. Rev. E 101, 040102(R) 2020). In particular, the entropic $q$-index is calculated in terms of the number of particles both for the nonrelativistic and relativistic cases. In light of such results, the possible nonadditivity or additivity of the entropic structures are also critically analysed and new expressions to the entropy (per particle) for a composed system of thermofractals and its limiting case are derived., Comment: 6 pages, no figures

We define a stochastic reaction-diffusion process that describes a consensus formation in a non-sedentary population. The process is a diffusive version of the Majority Vote model, where the state update follows two stages: in the first stage, spins are allowed to hop to neighbor nodes with different probabilities for the respective spin orientation, and in the second stage, the spins in the same node can change its values according to the majority vote update rule. The model presents a consensus formation phase when concentration is greater than a threshold value, and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. The threshold vanishes for unequal diffusion probabilities, which means that the system has a consensus state for all values of population densities. The stationary collective opinion is dominated by the individuals that diffuse more., Comment: 13 pages, 6 figures

Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative description of the conduction electrons' behavior. The confinement process of a quantum particle to a curve or surface leads us, in the so-called "confining potential formalism" (CPF), to a geometry-induced potential (GIP) in the effective Schr\"odinger equation. With these considerations, this work aims to study in detail the consequences of constraining a quantum particle to a helix, catenary, helicoid, or catenoid, exploring the relations between these curves and surfaces using differential geometry. Initially, we use the variational method to estimate the energy of the particle in its ground state, and thus, we obtain better approximations with the use of the confluent Heun function through numerical calculations. Thus, we conclude that a quantum particle constrained to an infinite helix has its angular momentum quantized due to the geometry of the curve, while in the cases of the catenary, helicoid, and catenoid the particle can be found either in a single bound state or in excited states which constitute a continuous energy band. Additionally, we propose measurements of physical observables capable of discriminating the topologies of the studied surfaces, in the context of topological metrology.

Primordial black holes are analytically and numerically discussed based on the extended McVittie spacetime solution. By assuming that dark matter and radiation are the only sources of energy accreted by the forming central object, it is found that the black-hole mass evolution depends on the initial mass of the seed, the time in which the black hole emerges, and also on the average peculiar velocity of dark matter particles. Constraints on the initial conditions of the primordial black holes are derived from profiles of the black-hole accretion mechanism and cosmological environment. A large range of masses is compatible with our approach. In particular, masses of the order of $10^{10}M_{\odot}$ today may also be generated from small seeds. An incubation time for the emerging horizons is observed when the initial masses of the seeds are close to the particle-horizon mass. It is also argued that the McVittie-type description is consistent with the Schwarzschild solution as long as other astrophysical processes near the central object are neglected., Comment: 14 pages, 8 figures

The metastable dark energy scenario is revisited by assuming that the current false vacuum energy density is the remnant from a primeval inflationary stage. The zero temperature scalar field potential is here described by an even power series up to order six which depends on 3 free parameters: the mass of the scalar field ($m$), the dimensionless ($\lambda$) specifying the standard self-interaction term, and a free cutoff mass scale ($M$) quantifying all possible deviations from the degenerate false vacuum state. The current $\Lambda$CDM model is a consequence of the very long decay time of the false vacuum which although finite is much greater than the current age of the Universe. This result remains valid for arbitrary combinations of the $m/M$ ratio which can analytically be determined in the thin-wall approximation and numerically calculated outside this limit. Unlike many claims in the literature the vacuum dominance may be temporary. The finiteness of the decay time suggests that the ultimate stage of the observed Universe in such a scenario will not be driven by a de Sitter type cosmology., Comment: 9 pages, 3 figures and 4 tables

Full detector simulation was among the largest CPU consumer in all CERN experiment software stacks for the first two runs of the Large Hadron Collider (LHC). In the early 2010's, the projections were that simulation demands would scale linearly with luminosity increase, compensated only partially by an increase of computing resources. The extension of fast simulation approaches to more use cases, covering a larger fraction of the simulation budget, is only part of the solution due to intrinsic precision limitations. The remainder corresponds to speeding-up the simulation software by several factors, which is out of reach using simple optimizations on the current code base. In this context, the GeantV R&D project was launched, aiming to redesign the legacy particle transport codes in order to make them benefit from fine-grained parallelism features such as vectorization, but also from increased code and data locality. This paper presents extensively the results and achievements of this R&D, as well as the conclusions and lessons learnt from the beta prototype., Comment: 34 pages, 26 figures, 24 tables

Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the standard additive Boltzmann-Gibbs approach thereby remaining a quite controversial subject. In order to clarify some polemical concepts, the distribution function for an ideal gas with a finite number of point particles and its $q$-index are analytically determined. The two-particle correlation function is also derived. The degree of correlation diminishes continuously with the growth of the number of particles. The ideal finite gas system is usually correlated, becomes less correlated when the number of particles grows, and is finally, fully uncorrelated when the molecular chaos regime is reached. It is also advocated that both approaches can be confronted through a careful kinetic spectroscopic experiment. The analytical results derived here suggest that Tsallis q-statistics may play a physical role more fundamental than usually discussed in the literature., Comment: 5 pages, no figures

Although the Orion Nebula Cluster is one of the most studied clusters in the solar neighborhood, the evolution of the very low-mass members ($M_* < 0.25 \, M_\odot$) has not been fully addressed due to their faintness. Our goal is to verify if some young and very low-mass objects in the Orion Nebula Cluster show evidence of ongoing accretion using broadband VLT/X-Shooter spectra. For each target, we determined the corresponding stellar parameters, veiling, observed Balmer jump, and accretion rates. Additionally, we searched for the existence of circumstellar disks through available on-line photometry. We detected accretion activity in three young stellar objects in the Orion Nebula Cluster, two of them being in the very low-mass range. We also detected the presence of young transition disks with ages between 1 and 3.5 Myr., Comment: 12 pages, 6 figures (17 pages, 11 figures if appendix included). Accepted by Astronomy and Astrophysics on 24/02/2020

A century after observing the deflection of light emitted by distant stars during the solar eclipse of 1919, it is interesting to know the concepts emerged from the experiment and the theoretical and observational consequences for modern cosmology and astrophysics. In addition to confirming Einstein's gravitational theory, its greatest legacy was the construction of a new research area to cosmos science dubbed gravitational lensing. The formation and magnification of multiple images (mirages) by the gravitational field of a compact or extended lens are among the most striking phenomena of nature. This article presents a pedagogical view of the first genuine gravitational lens effect, the double quasar QSO 0957 + 561. We also describe the formation of rings, giant arcs, arclets and multiple Supernova images. It is also surprising that the Hubble constant and the amount of dark matter in the Universe can be measured by the same technique. Finally, the lensing of gravitational waves, a possible but still not yet detected effect, is also briefly discussed., Comment: 22 pages, 20 figures, in Portuguese

In itinerant systems, electron-electron interactions may lead to the formation of local magnetic moments and their effective exchange coupling, which in turn gives rise to long-range magnetic order. Therefore, when moment formation is weakened, such as in the single-band Hubbard model on a square lattice with the on-site repulsion being randomly switched off on a fraction $x$ of sites, magnetic order is suppressed beyond some critical $x_c$, which was found to lie below the classical percolation threshold, $x_c^\text{(perc,sq)}$. Here we study dilute magnetism in flat band systems, namely in the Hubbard model on a `Lieb' lattice. Interestingly, we show that magnetic order persists to $x$ almost twice as large as the classical percolation threshold for the lattice, thus emphasizing the central role of electron itinerancy to the magnetic response. The analysis of the orbital-resolved order parameters reveals that the contribution of the four-fold coordinated `d' sites to magnetism is dramatically affected by dilution, while the localized `p' states of the flat band provide the dominant contribution to long-range correlations. We also examine the transport properties, which suggest the existence of an insulator-to-metal transition in the same range of the critical magnetic dilution., Comment: 9 pages, 10 figures

The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, $T{\sqrt {g_{00}(x^{i})}} = constant$, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient $g_{00}(x^{i})$. By assuming the validity of Tolman-Ehrenfest "pocket temperature", Klein also proved a similar relation for the chemical potential, namely, $\mu {\sqrt {g_{00}(x^{i})}} = constant$. In this letter we prove that a more general relation uniting both quantities holds regardless of the equation of state satisfied by the medium, and that the original Tolman-Ehrenfest law form is valid only if the chemical potential vanishes identically. In the general case of equilibrium, the temperature and the chemical potential are intertwined in such a way that only a definite (position dependent) relation uniting both quantities is obeyed. As an illustration of these results, the temperature expressions for an isothermal gas (finite spherical distribution) and a neutron star are also determined., Comment: 7 pages, 2 figures, PRD accepted

There is a growing acknowledgement in the scientific community of the importance of making experimental data machine findable, accessible, interoperable, and reusable (FAIR). Recognizing that high quality metadata are essential to make datasets FAIR, members of the GO FAIR Initiative and the Research Data Alliance (RDA) have initiated a series of workshops to encourage the creation of Metadata for Machines (M4M), enabling any self-identified stakeholder to define and promote the reuse of standardized, comprehensive machine-actionable metadata. The funders of scientific research recognize that they have an important role to play in ensuring that experimental results are FAIR, and that high quality metadata and careful planning for FAIR data stewardship are central to these goals. We describe the outcome of a recent M4M workshop that has led to a pilot programme involving two national science funders, the Health Research Board of Ireland (HRB) and the Netherlands Organisation for Health Research and Development (ZonMW). These funding organizations will explore new technologies to define at the time that a request for proposals is issued the minimal set of machine-actionable metadata that they would like investigators to use to annotate their datasets, to enable investigators to create such metadata to help make their data FAIR, and to develop data-stewardship plans that ensure that experimental data will be managed appropriately abiding by the FAIR principles. The FAIR Funders design envisions a data-management workflow having seven essential stages, where solution providers are openly invited to participate. The initial pilot programme will launch using existing computer-based tools of those who attended the M4M Workshop., Comment: This is a pre-print of the FAIR Funders pilot, an outcome of the first Metadata for Machines workshop, see: https://www.go-fair.org/resources/go-fair-workshop-series/metadata-for-machines-workshops/. Corresponding author: E. A Schultes, ORCID 0000-0001-8888-635X