arXiv subjects

Alejandro Cabo Montes de Oca

Publications and source records attributed to Alejandro Cabo Montes de Oca.

At least 19 recordsLinked to original sources

arXiv2021

On the dynamics of the contagious rate under isolation measures

The infection dynamics of a population under stationary isolation conditions is modeled. It is underlined that the stationary character of the isolation measures can be expected to imply that an effective SIR model with constant parameters should describe the infection process. Then, a derivation of this property is presented, assuming that the statistical fluctuations in the number of infection and recovered cases are disregarded. This effective SIR model shows a reduced population number and a constant $β$ parameter. The effects of also including the retardation between recovery and infection process is also considered. Next, it is shown that any solution of the effective SIR also solves the linear problem to which the SIR equations reduce when the total population is much larger than the number of the infected cases. Then, it is also argued that this equivalence follows for a specific contagious parameter $β(t)$ which time dependence is analytically derived here. Then, two equivalent predictive calculational methods for the infection dynamics under stationary isolation measures are proposed. The results represent a solutions for the known and challenging problem of defining the time dependence of the contagion parameter, when the SIR parameter $N$ is assumed to be the whole population number. Finally, the model is applied to describe the known infection curves for countries that already had passed the epidemic process under strict stationary isolation measures. The cases of Iceland, New Zealand, Korea and Cuba were considered. Although, non subject to stationary isolation measures the cases of U.S.A. and Mexico are also examined due to their interest. The results support the argued validity of SIR model including retardation.

q-bio.PE↗

arXiv2021

Dynamical gravastars from the interaction between scalar fields and matter

Gravastars are configurations of compact singularity-free gravitational objects which are interesting alternatives to classical solutions in the strong gravitational field regime. Although there are no static star-like solutions of the Einstein-Klein-Gordon equations for real scalar fields, we show that dynamical gravastars solutions arise through the direct interaction of a scalar field with matter. Two configurations presented here show that, within the internal zone, the scalar field plays a role similar to a cosmological constant, while the scalar field decays at large distances as the Yukawa potential. Like classical gravastars, these solutions exhibit small values of the temporal metric component near a transitional radial value, although this behaviour is not determined by the de Sitter nature of the internal space-time, but rather by a slowly-varying scalar field. The scalar field-matter interaction is able to define trapping forces that rigorously confine the polytropic gases to the interior of a sphere. At the surface of these spheres, pressures generated by the field-matter interaction play the role of "walls" preventing the matter from flowing out. These solutions predict a stronger scattering of the accreting matter with respect to Schwarzschild black holes.

gr-qc↗

arXiv2020

Real scalar field stars of the EKG equations including matter

Static (not stationary) solutions of the Einstein-Klein-Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of static solutions in contraposition with the case of the simpler EKG equations for real scalar fields and gravity. Surprisingly, when the considered matter is a photon-like gas, it turns out that the gravitational field intensity at large radial distances becomes nearly a constant, exerting an approximately fixed force to small bodies at any distance. The effect is clearly related with the massless character of the photon-like field. It is also argued that the gravitational field can generate a bounding attraction, that could avoid the unlimited increase in mass with the radius of the obtained here solution. This phenomenon, if verified, may furnish a possible mechanism for explaining how the increasing gravitational potential associated to dark matter, finally decays at large distances from the galaxies. A method for evaluating these photon bounding effects is just formulated in order to be further investigated.

gr-qc↗

arXiv2020

Neutrino oscillations as many-particle induced interference between distinguishable particles

We investigate the causes of the curious property of neutrino oscillations of looking as an interference between fully distinguishable particles. The sources of this effect are identified as to be determined by the many particle nature of space of states of the quantum field theory. It is firstly underlined that in order to explain the observed oscillations, the neutrino subspace of states should not be interpreted as the direct product of the three neutrinos Fock spaces, which is equivalent to imposing a superselection rule. Further, it is argued that the linear completion of such a direct product space of states permits to describe the measured oscillations. Thus, the space of states of te Standard Model (SM) should be interpreted as the linear completion of the direct product of all the Fock spaces (boson or fermions ones) associated to the distinguishable particles. Then, it follows that the neutrino oscillations are determined as interference between independent particles, which are generated by states being outside the direct product of the neutrino Fock spaces. This interpretation seems to imply a large amount of interference observations between distinguishable particles in Particle as well as in Condensed Matter Physics. For seeking clearness, the discussion is done in the framework of a simple Quantum Field Theory (QFT) model of two relativistic free massive neutrinos.

hep-ph↗

arXiv2020

Modelos SIR modificados para la evolución del COVID19

We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal evolution of the rate of contagion $β^*$. A semi-empirical model for this dynamics is formulated, where reaching $β^*\approx0$ due to isolation is achieved after the mean duration of the disease $τ=1/γ$, in which the number of infected in the confined families has decreased. It is considered that $β^*(t)$ should have an abrupt decrease on the day of initiation of confinement and decrease until canceling at the end of the interval $τ$. The analysis describes appropriately the infection curve for Germany. The model is applied to predict an infection curve for Cuba, which estimates a maximum number of infected as less than 2000 in the middle of May, depending on the rigor of the isolation. This is suggested by the ratio between the daily detected cases and the total. We consider the ratio between the observed and real infected cases (k) less than unity. The low value of k decreases the maximum obtained when $β^*-γ>0$. The observed evolution is independent of k in the linear region. The value of $β^*$ is also studied by time intervals, adjusting to the data of Cuba, Germany and South Korea. We compare the extrapolation of the evolution of Cuba with the contagion rate until 16.04.20 with that obtained by a strict quarantine at the end of April. This model with variable $β^*$ correctly describes the observed infected evolution curves. We emphasize that the desired maximum of the SIR infected curve is not the maximum standard with constant $β^*$, but one achieved due to quarantine when $\tilde R_0=β^*/γ<1$. For the countries controlling the epidemic the maxima are in the region in which SIR equations are linear.

q-bio.PE↗

arXiv2017

A stochastic version of the Noether Theorem

A stochastic version of the Noether Theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

cond-mat.stat-mech↗

arXiv2017

A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics

A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Peña and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to search for Lorentz invariance. The covariant form of the set of iterative equations for the joint coordinate and momentum distribution function $Q(x,p)$ is derived and expanded in power series of the charge of the particle. Then, solutions of the zeroth order in the charge of the iterative equations for $Q(x,p)$ are considered. For them, it follows that the space-time probability density $ρ(x)$ and the function $S(x)$ which gradient defines the mean value of the momentum at the space time point $x$, define a complex function $ψ(x)$ which exactly satisfies the Klein-Gordon (KG) equation. It is argued that when the KG solution is either of positive or negative energy, the total number of particles conserves in the random motion. It follows that the total number of particles conserves when $ψ(x)$ composed alternatively of pure positive or negative energy modes. In addition, solutions for the joint distribution function in lowest order, satisfying the positive condition are also found. They suggests a possible link with the Couder's experiments on droplet movements over oscillating liquid surfaces.

quant-ph↗

arXiv2017

A QCD Lagrangian including renormalizable NJL terms

A local and gauge invariant version of QCD Lagrangian is introduced. The model includes Nambu-Jona-Lasinio (NJL) terms within its action in a surprisingly renormalizable form. This occurs thanks to the presence of action terms which at first sight, look as breaking power counting renormalizability. However, those terms also modify the quark propagators, to become more decreasing that the Dirac one at large momenta, indicating power counting renormalizability. The approach, can also be interpreted as generalized renormalization procedure for massless QCD. The free propagator, given by the substraction between a massive and a massless Dirac ones, in the Lee-Wick form, suggests that the theory also retains unitarity. The appearance of finite quark masses already in the tree approximation in the scheme is determined by the fact that the new action terms explicitly break chiral invariance. The approach looks as being able to implement the Fritzsch Democratic Symmetry breaking ideas about the quark mass hierarchy. Also, a link of the theory with the SM seems that can follow after employing the Zimmermann's couplings reduction scheme. The renormalized Feynman diagram expansion of the model is written here and the formula for the degree of divergence of the diagrams is derived. The primitive divergent graphs are identified. We start their evaluation through the calculation of the divergence of the gluon polarization operator. The divergent part of the gluon selfenergy results to be transverse as required by gauge invariance and also independent of the new couplings appearing. The calculations of the rest of primitive divergences will be presented elsewhere.

hep-th↗

arXiv2015

Is a generalized NJL model the effective action of massless QCD?

A local and gauge invariant alternative version of QCD for massive fermions introduced in previous works, is considered here to just propose a theory which includes Nambu-Jona-Lasinio (NJL) terms in its defining action in a renormalizable form. The Lagrangian includes a special kind of new vertices which at first sight, look as breaking power counting renormalizability. However, these terms also modify the quark propagators, to become more decreasing that the Dirac propagator at large momenta, indicating that the theory is renormalizable. Therefore, it follows the surprising conclusion that the added NJL four fermions terms does not break renormalizability. The approach, can also be interpreted as a slightly generalized renormalization procedure for massless QCD, which seems able to incorporate the mass generating properties for the quarks of the NJL model, in a renormalizable way. The structure of the free propagator, given by the substraction between a massive and a massless Dirac one in the Lee-Wick form, also suggests that the theory retains unitarity, if the radiative corrections make the massless quarks become non propagating. The appearance of finite masses in the theory is justified by the fact that the new action terms break chiral invariance. The scheme looks as being able to implement the Fritzsch Democratic Symmetry breaking approach to quark mass hierarchy. It seems also possible to further link the theory with the SM after employing the Zimmermann's coupling constant reduction scheme in a similar way as the Top quark condensation model had been approximately reformulated as a Higgs field one.

hep-th↗

arXiv2014

Optimization of a model for the CuO planes in La2CuO4

The results of a previous work, where it was considered the effect of hole doping on a simple model of the CuO2 planes in La2CuO4, are extended. The parameters are adjusted with the objective to fix the known values of the gap of 2 eV for this material and its dielectric constant of 21. We find again indications of a "hidden" phase transition beneath the superconductor dome. The transition is a second order one, and is associated with an energetic coincidence of a ground insulator state (AFA)with an excited paramagnetic state showing a pseudogap (PPG), at a critical point of the hole concentration around xc=0.2. The evolution as a function of doping of the band structures and the Fermi surface of the system in the phases AFA and PPG, is shown. In the zone of low doping, the holes begin to occupy the states located at the mid of the sides of the Brillouin zone, that in the AFA states have the strongest antiferromagnetic character. Around the critical doping the results show that in both phases, the Fermi surfaces and the energy spectrum of the filled electronic states tend to coincide.

cond-mat.supr-con↗

arXiv2013

Newton-like equations for a radiating particle

Second order Newton equations of motion for a radiating particle are presented. It is argued that the trajectories obeying them also satisfy the Abraham-Lorentz-Dirac (ALD) equations for general 3D motions in the non-relativistic and relativistic limits. The case of forces only depending of the proper time is here considered. For these properties to hold, it is sufficient that the external force to be infinitely smooth and that a series formed with its time derivatives converges. This series define in a special local way the effective forces entering the Newton equations. When the external force vanishes in an open vicinity of a given time, the effective one also becomes null. Thus, the proper solutions of the effective equations can not show runaway or pre-acceleration effects. The Newton equations are numerically solved for a pulsed force given by an analytic function along the proper time axis. The simultaneous satisfaction of the ALD equations is numerically checked. Further, a set of modified ALD equations for almost everywhere infinitely smooth forces, but including step like discontinuities in some points is also presented for the case of collinear motions. The form of the equations supports the statement argued in a previous work, about that the causal Lienard-Wiechert field solution surrounding a radiating particle, implies that the effective force on the particle should instantaneously vanish when the external force is retired. The modified ALD equations proposed in the previous work are here derived in a generalized way including the same effect also when a the force is instantly connected.

gr-qc↗

arXiv2013

On radiation reaction and the Abraham-Lorentz-Dirac equation

It is underlined that the Lienard-Wiechert solutions indicate that after the external force is instantly removed from a small charged particle, the field in its close neighborhood becomes a Lorentz boosted Coulomb field. It suggests that the force of the self-field on the particle should instantaneously vanish after a sudden removal of the external force. A minimal modification of Abraham-Lorentz-Dirac equation is searched seeking to implement this property. A term assuring this behavior is added to the equation by maintaining Lorentz covariance and vanishing scalar product with the four-velocity. The simple Dirac constant force example does not show runaway acceleration.

gr-qc↗

arXiv2013

On the metric of the space of states in a modified QCD

The form of the resulting Feynman propagators in a proposed local and gauge invariant QCD for massive fermions suggests the existence of indefinite metric associated to quark states, a property that might relate it with the known Lee-Wick theories. Thus, the nature of the asymptotic free quark states in the theory is investigated here by quantizing the quadratic part of the quark action. As opposite to the case in the standard QCD, the free theory does not show Hamiltonian constraints. The propagation modes include a family of massless waves and a complementary set of massive oscillations. The theory can be quantized in a way that the massive modes show positive metric and the massless ones exhibit negative norms. It is remarked that, since QCD is expected to not exhibit gluon or quark asymptotic states, the presence of negative metric massless modes does not constitute a definite drawback of the theory. In addition, the fact that the positive metric quark states are massive, seems to be a good feature of the model, being consistent with the approximate existence of asymptotically free massive states in high energy processes.

hep-th↗

arXiv2012

Study of the magnetic anisotropy in a planar model of the La2CuO4

We study the anisotropy energy in a planar model for the Cu-O layers of the La2CuO4 investigated in previous works. The Tight-Binding (TB) potential of the model was extended out of the validity region with the purpose of incorporate it in the potential. Next, the spin-orbit operator was considered in the Hartree Fock solution of the full HF problem. It follows that in spite of the fact that the extended potential possesses the square symmetry of the crystalline structure, the anisotropy energy vanishes in its purely 2D formulation. The result indicates that for the prediction by the model of the observed non vanishing magnetic anisotropy at zero doping and temperature in La2CuO4, its formulation requires of a 3D representation of its Wannier orbitals and the use of d like orbitals. The consideration of more realistic 3D character of the model, by including multiple CuO planes, also could be important due to the argued absence of long range order in 2D.

cond-mat.mtrl-sci↗

arXiv2012

Quantum phase transition from a Antiferromagnetic-Insulator to a Paramagnetic-Metal laying beneath the superconducting dome

The effect of doping on the TB model of the CuO planes in the La2CuO4 constructed in previous works is investigated. Firstly, it is noted that the model employed constitutes a generalization of the Hubbard one for the same system. Thus, the former predictions of the insulator gap, antiferromagnetic character and the existence of a paramagnetic-pseudogap state, become natural ones to be expected from this more general picture. The effect of hole doping on the antiferromagnetic-insulator state (AFI) and the paramagnetic-pseudogap one, is investigated. The results predict a quantum phase transition (QPT) from the AFI state at low doping to a paramagnetic-metallic state (PM) at higher hole densities. Therefore, a clear description of the hidden QPT laying beneath the dome in high critical temperature superconducting materials is found. At low doping, the system prefers the AFI state, and at the critical value of the doping density 0.2, the energy of a metallic state becomes lower. The evolution with small doping values of the band spectrum of the AFI state, shows that the holes tend to become localized at the middle of the sides of the reduced Brillouin zone (BZ). Then, around the critical value, the holes of the AFI state move to become situated at the corners of the same reduced BZ, showing a structural change at the phase transition point. Thus, the PM state appearing at the QPT acquires the same behavior with respect to the position of holes as the pseudogap state. In the small doping limit a clear difference between the degree of convergence of the iterative self-consistent solution is associated to an even or odd number of electrons. It suggests that the Kramers degeneration in combination with the spin-spatial entangled nature of the hole states, leads to a new kind of pair interaction between two holes. The binding energy value is estimated as a function of the screening.

cond-mat.str-el↗

arXiv2012

Modifying the HF procedure to include screening effects

A self-consistent formulation is proposed to generalize the HF scheme with the incorporation of screening effects. For this purpose in a first step, an energy functional is defined by the mean value for the full Hamiltonian, not in a Slater determinant state, but in the result of the adiabatic connection of Coulomb plus the nuclear (jellium charge) in the Slater determinant. Afterwards, the energy functional defining the screening approximation is defined in a diagrammatic way, by imposing a special "screening" restriction on the contractions retained in the Wick expansion. The generalized self-consisting set of equations for the one particle orbitals are written by imposing the extremum conditions. The scheme is applied to the homogeneous electron gas. After simplifying the discussion by assuming the screening as static and that the mean distance between electrons is close to the Bohr radius, the equations for the electron spectrum and the static screening properties are solved by iterations. The self-consistent results for the self-energies dispersion does not show the vanishing density of states at the Fermi level predicted by the HF self-energy spectrum. In this extreme non retarded approximation, both, the direct and the exchange potentials are strongly screened, and the energy is higher that the one given by the usual HF scheme. However, the inclusion of the retardation in the exact solution and the sum rules associated to the dielectric response of the problem, can lead to energy lowering. These effects will be considered in the extension of the work.

cond-mat.str-el↗

arXiv2012

A proposal of a local modified QCD

A local and renormalizable version of a modified PQCD introduced in previous works is presented. The construction indicates that it could be equivalent to massless QCD. The case in which only quark condensate effects are retained is discussed in more detail. Then, the appearing auxiliary fermion fields can be integrated leading to a theory with the action of massless QCD, to which one local and gauge invariant Lagrangian term for each quark flavour is added. These terms are defined by two gluon and two quark fields, in a form curiously not harming power counting renormalizability. The gluon self-energy is evaluated in second order in the gauge coupling and all orders in the new quark couplings, and the result became transversal as required by the gauge invariance. The vacuum energy was calculated in the two loop approximation and also became gauge parameter independent. The possibilities that higher loop contributions to the vacuum energy allow the generation of a quark mass hierarchy as a flavour symmetry breaking effect are discussed. However, the decision on this issue needs the evaluation of more than two loop contributions, in which more than one type of quark loops start appearing, possibly leading to interference effects in the vacuum energy.

hep-ph↗

arXiv2011

Exploring effects of strong interactions in enhancing masses of dynamical origin

A previous study of the dynamical generation of masses in massless QCD is considered from another viewpoint. The quark mass is assumed to have a dynamical origin and is substituted by a scalar field without self-interaction. The potential for the new field background is evaluated up to two loops. Expressing the running coupling in terms of the scale parameter $μ$, the potential minimum is chosen to fix $m_{top}=175$ $GeV$ when $μ_0=498 $ $MeV$. The second derivative of the potential predicts a scalar field mass of 126.76 $GeV$. This number is close to the value 114 $GeV$ which, preliminary data taken at CERN, suggested to be associated with the Higgs particle. However, the simplifying assumptions limit the validity of the calculations done, as indicated by the large value of $α=\frac {g^2}{4π}=1.077 $ obtained. However, supporting statements about the possibility of improving the scheme come from the necessary inclusion of weak and scalar field couplings and mass counterterms in the renormalization procedure, in common with the seemingly needed consideration of the massive W and Z fields, if the real conditions of the SM model are intended to be approached.

hep-ph↗