arXiv subjects

Alex E. Bernardini

Publications and source records attributed to Alex E. Bernardini.

At least 91 records · Page 5Linked to original sources

arXiv2012

Quantum measurement schemes related to flavor-weighted energies

Reporting about the density matrix theory for a composite quantum system of flavor eigenstates, we introduce the idea of flavor-weighted energies. It provides us with the right correlation between the energies of flavor eigenstates and their measurement probabilities. In addition, the apparent ambiguities which follow from computing flavor-averaged energies are suppressed. The framework of the generalized theory of quantum measurement also provides some theoretical tools for computing the von-Neumann entropy correlated to flavor associated energies. It allows for relating flavor weighted(averaged) energies to non-selective (selective) quantum measurement schemes. As a final issue, the connection of such flavor associated energies with the expressions for neutrino effective mass values is investigated. It is straightforwardly verified that cosmological background neutrino energy densities could be obtained from the coherent superposition of mass eigenstates. Our results show that the non-selective measurement scheme for obtaining flavor-weighted energies is consistent with the predictions from the single-particle quantum mechanics.

hep-ph↗

arXiv2012

Accretion of non-minimally coupled generalized Chaplygin gas into black holes

The mass evolution of Schwarzschild black holes by the absorption of scalar fields is investigated in the scenario of the generalized Chaplygin gas (GCG). The GCG works as a unification picture of dark matter plus dark energy that naturally accelerates the expansion of the Universe. Through elements of the quasi-stationary approach, we consider the mass evolution of Schwarzschild black holes accreted by non-minimally coupled cosmological scalar fields reproducing the dynamics of the GCG. As a scalar field non-minimally coupled to the metrics, such an exotic content has been interconnected with accreting black holes. The black hole increasing masses by the absorption of the gas reflects some consistence of the accretion mechanism with the hypothesis of the primordial origin of supermassive black holes. Our results effectively show that the non-minimal coupling with the GCG dark sector accelerates the increasing of black hole masses. Meanwhile some exotic features can also be depicted for specific ranges of the non-minimal coupling in which the GCG dynamics is substantially modified.

gr-qc↗

arXiv2011

Exotic Dark Spinor Fields

Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Cech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group H^1(M, Z_2). The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the full topological analysis must be evaluated. Since exotic dark spinor fields also satisfy Klein-Gordon propagators, the dynamical constraints related to the exotic term in the Dirac equation can be explicitly calculated. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender --- from the dynamics of dark spinor fields --- constraints in the spacetime metric structure. Meanwhile, such constraints may be alleviated, at the cost of constraining the exotic spacetime topology. Besides being prime candidates to the dark matter problem, dark spinor fields are shown to be potential candidates to probe non-trivial topologies in spacetime, as well as probe the spacetime metric structure.

hep-th↗

arXiv2011

Reproducing neutrino effects on the matter power spectrum through a degenerate Fermi gas approach

Modifications on the predictions about the matter power spectrum based on the hypothesis of a tiny contribution from a degenerate Fermi gas (DFG) test-fluid to some dominant cosmological scenario are investigated. Reporting about the systematic way of accounting for all the cosmological perturbations, through the Boltzmann equation we obtain the analytical results for density fluctuation, $δ$, and fluid velocity divergence, $θ$, of the DFG. Small contributions to the matter power spectrum are analytically obtained for the radiation-dominated background, through an ultra-relativistic approximation, and for the matter-dominated and $Λ$-dominated eras, through a non-relativistic approximation. The results can be numerically reproduced and compared with those of considering non-relativistic and ultra-relativistic neutrinos into the computation of the matter power spectrum. Lessons concerning the formation of large scale structures of a DFG are depicted, and consequent deviations from standard $Λ$CDM predictions for the matter power spectrum (with and without neutrinos) are quantified.

astro-ph.CO↗

arXiv2011

Degenerate Fermi gas perturbations at standard background cosmology

The hypothesis of a tiny fraction of the cosmic inventory evolving cosmologically as a degenerate Fermi gas test fluid at some dominant cosmological background is investigated. Our analytical results allow for performing preliminary computations to the evolution of perturbations for relativistic and non-relativistic test fluids. The density fluctuation, $δ$, the fluid velocity divergence, $θ$, and an explicit expression for the dynamics of the shear stress, $σ$, are obtained for a degenerate Fermi gas in the background regime of radiation. Extensions to the dominance of matter and to the $Λ$CDM cosmological background are also investigated and lessons concerning the formation of large structures of degenerate Fermi gas are depicted.

astro-ph.CO↗

arXiv2011

Quantum flavor oscillations extended to the Dirac theory

This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first and second quantization theories. In this scenario, the use of the Dirac equation is required for a satisfactory evolution of fermionic mass-eigenstates since in the standard treatment of oscillations the mass-eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. Within first quantized theories, besides flavor oscillations, chiral oscillations automatically appear when we set the dynamic equations for a fermionic Dirac-type particle. The left-handed chiral nature of created and detected neutrinos can be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. In the context of a causal relativistic theory of a free particle, one of the two effects should be present in flavor oscillations: (a) rapid oscillations or (b) initial flavor violation. Concerning second quantized approaches, a simple second quantized treatment exhibits a tiny but inevitable initial flavor violation without the possibility of rapid oscillations. Such effect is a consequence of an intrinsically indefinite but approximately well defined neutrino flavor. The violation effects are shown to be much larger than loop induced lepton flavor violation processes, already present in the standard model in the presence of massive neutrinos with mixing. The conclusions of this report lead to lessons concerning flavor mixing, chiral oscillations, interference between positive and negative frequency components of Dirac equation solutions, and the field formulation of quantum oscillations.

hep-ph↗

arXiv2010

Dynamical neutrino masses in the generalized Chaplygin gas scenario with mass varying CDM

Neutrinos coupled to an underlying scalar field in the scenario for unification of mass varying dark matter and cosmon-{\em like} dark energy is examined. In the presence of a tiny component of mass varying neutrinos, the conditions for the present cosmic acceleration and for the stability issue are reproduced. It is assumed that {\em sterile} neutrinos behave like mass varying dark matter coupled to mass varying {\em active} neutrinos through the {\em seesaw} mechanism, in a kind of {\em mixed} dark matter sector. The crucial point is that the dark matter mass may also exhibit a dynamical behavior driven by the scalar field. The scalar field mediates the nontrivial coupling between the mixed dark matter and the dark energy responsible for the accelerated expansion of the universe. The equation of state of perturbations reproduce the generalized Chaplygin gas (GCG) cosmology so that all the effective results from the GCG paradigm are maintained, being perturbatively modified by neutrinos.

astro-ph.CO↗

arXiv2010

Equilibrium and stability of neutrino lumps as TOV solutions

We report about stability conditions for static, spherically symmetric objects that share the essential features of mass varying neutrinos in cosmological scenarios. Compact structures of particles with variable mass are held together preponderantly by an attractive force mediated by a background scalar field. Their corresponding conditions for equilibrium and stability are given in terms of the ratio between the total mass-energy and the spherical lump radius, $M/R$. We show that the mass varying mechanism leading to lump formation can modify the cosmological predictions for the cosmological neutrino mass limits. Our study comprises Tolman-Oppenheimer-Volkoff solutions of relativistic objects with non-uniform energy densities. The results leave open some questions concerning stable regular solutions that, to an external observer, very closely reproduce the preliminary conditions to form Schwarzschild black holes.

astro-ph.CO↗

arXiv2010

Naturalness and stability of the generalized Chaplygin gas in the seesaw cosmon scenario

The seesaw mechanism is conceived on the basis that a mass scale, $ξ$, and a dimensionless scale, $s$, can be fine-tuned in order to control the dynamics of active and sterile neutrinos through cosmon-type equations of motion: the seesaw cosmon equations. This allows for sterile neutrinos to be a dark matter candidate. In this scenario, the dynamical masses and energy densities of active and sterile neutrinos can be consistently embedded into the generalized Chaplygin gas (GCG), the unified dark sector model. In addition, dark matter adiabatically coupled to dark energy allows for a natural decoupling of the (active) mass varying neutrino (MaVaN) component from the dark sector. Thus MaVaN's turn into a secondary effect. Through the scale parameters, $ξ$ and $s$, the proposed scenario allows for a convergence among three distinct frameworks: the cosmon scenario, the seesaw mechanism for mass generation and the GCG model. It is found that the equation of state of the perturbations is the very one of the GCG background cosmology so that all the results from this approach are maintained, being smoothly modified by active neutrinos. Constrained by the seesaw relations, it is shown that the mass varying mechanism is responsible for the stability against linear perturbations and is indirectly related to the late time cosmological acceleration.

hep-ph↗

arXiv2010

k-deformed Poincare algebras and quantum Clifford-Hopf algebras

The Minkowski spacetime quantum Clifford algebra structure associated with the conformal group and the Clifford-Hopf alternative k-deformed quantum Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra U_q(so(3,2)), when the associated Clifford-Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah-Bott-Shapiro theorem.

math-ph↗

arXiv2010

Stationary condition in a perturbative approach for mass varying neutrinos

A perturbative approach for arbitrary choices of the equation of state of the universe is introduced in order to treat scenarios for mass varying neutrinos (MaVaN's) coupled to the dark sector. The generalized criterion for the applicability of such an approach is expressed through a constraint on the coefficient of the linear perturbation on the dark sector scalar field. This coefficient depends on the ratio between the variation of the neutrino energy and the scalar field potential. Upon certain conditions, the usual {\em stationary condition} found in the context of MaVaN models together with the perturbative contribution can be employed to predict the dynamical evolution of the neutrino mass. Our results clearly indicate that the positiveness of the squared speed of sound of the coupled fluid and the model stability are not conditioned by the {\em stationary condition}.

hep-ph↗

arXiv2010

Coupling active and sterile neutrinos in the cosmon plus seesaw framework

The cosmological evolution of neutrino energy densities driven by cosmon-type field equations is introduced assuming that active and sterile neutrinos are intrinsically connected by cosmon fields through the {\em seesaw} mechanism. Interpreting sterile neutrinos as dark matter adiabatically coupled with dark energy results in a natural decoupling of (active) mass varying neutrino (MaVaN) equations. Identifying the dimensionless scale of the {\em seesaw} mechanism, $m/M$, with a power of the cosmological scale factor, $a$, allows for embedding the resulting masses into the generalized Chaplygin gas (GCG) scenario for the dark sector. Without additional assumptions, our findings establish a precise connection among three distinct frameworks: the cosmon field dynamics for MaVaN's, the {\em seesaw} mechanism for dynamical mass generation and the GCG scenario. Our results also corroborate with previous assertions that mass varying particles can be the right responsible for the stability issue and for the cosmic acceleration of the universe.

hep-ph↗

arXiv2010

Perturbative approach for mass varying neutrinos coupled to the dark sector in the generalized Chaplygin gas scenario

We suggest a perturbative approach for generic choices for the universe equation of state and introduce a novel framework for studying mass varying neutrinos (MaVaN's) coupled to the dark sector. For concreteness, we examine the coupling between neutrinos and the underlying scalar field associated with the generalized Chaplygin gas (GCG), a unification model for dark energy and dark matter. It is shown that the application of a perturbative approach to MaVaN mechanisms translates into a constraint on the coefficient of a linear perturbation, which depends on the ratio between a neutrino energy dependent term and scalar field potential terms. We quantify the effects on the MaVaN sector by considering neutrino masses generated by the seesaw mechanism. After setting the GCG parameters in agreement with general cosmological constraints, we find that the squared speed of sound in the neutrino-scalar GCG fluid is naturally positive. In this scenario, the model stability depends on previously set up parameters associated with the equation of state of the universe. Our results suggest that the GCG is a particularly suitable candidate for constructing a stable MaVaN scenario.

astro-ph↗

arXiv2010

Mass varying dark matter in effective GCG scenarios

A unified treatment of mass varying dark matter coupled to cosmon-{\em like} dark energy is shown to result in {\em effective} generalized Chaplygin gas (GCG) scenarios. The mass varying mechanism is treated as a cosmon field inherent effect. Coupling dark matter with dark energy allows for reproducing the conditions for the present cosmic acceleration and for recovering the stability resulted from a positive squared speed of sound $c_{s}^{\2}$, as in the GCG scenario. The scalar field mediates the nontrivial coupling between the dark matter sector and the sector responsible for the accelerated expansion of the universe. The equation of state of perturbations is the same as that of the background cosmology so that all the effective results from the GCG paradigm are maintained. Our results suggest the mass varying mechanism, when obtained from an exactly soluble field theory, as the right responsible for the stability issue and for the cosmic acceleration of the universe.

gr-qc↗

arXiv2009

Stability of mass varying particle lumps

The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric solutions of Einstein equations for a system composed by nonbaryonic matter (neutrinos or dark matter) which forms stable structures through attractive forces mediated by a background scalar-field (dark energy). Assuming that the dark matter, or massive neutrinos, consist of a gas of weakly interacting particles, the coupling with the scalar field is translated into an effective dependence of the mass of the compounding particle on the radial coordinate of the curved spacetime. The stability analysis reveals that these static solutions become dynamically unstable for different Buchdahl limits of the ratio between the total mass-energy and the stellar radius, $M/R$. We also find regular solutions that for an external observer resemble Schwarzschild black-holes. Our analysis leaves unanswered the question whether such solutions, which are both regular and stable, do exist.

gr-qc↗

arXiv2009

Thermodynamic equilibrium conditions for mass varying particle structures

The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then follows that, such weakly interacting massive particles can form clusters of non-baryonic matter or even astrophysical objects that, at cosmological scales, are held together by gravity and by the attractive force mediated by a background scalar field. The equilibrium conditions for resultant static, spherically symmetric objects of uniform energy density are derived for the case where the particles share essential features with the mass varying mechanism in the context of cosmological scenarios. Physical solutions which result in stable astrophysical lumps are obtained and discussed.

gr-qc↗

arXiv2009

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. We notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. We investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited.

quant-ph↗

arXiv2008

Relativistic tunneling and accelerated transmission

We obtain the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation regime when the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation originated from the study based on non-relativistic dynamics of tunneling is overcome. The treatment of the problem suggests revealing insights into condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.

quant-ph↗