Continuous Mass Spectrum Research Articles

Dark matter from evaporating primordial black holes in the early universe

Primordial Black Holes (PBHs) could dominate in the early universe and, evaporating before Big bang Nucleosynthesis, provide new freeze in mechanism of dark matter (DM) production. The proposed scenario is considered for two possible mechanisms of PBH formation and the corresponding continuous PBH mass spectra so that the effect of non-single PBH mass spectrum is taken into account in the results of PBH evaporation, by which PBH dominance in the early universe ends. We specify the conditions under which the proposed scenario can explain production of dark matter in very early universe.

Role of Dopants in Fine-Tuning the Electrical and Catalytic Properties of Barium Niobate Perovskites Towards High-Temperature Electrolyzer Application

Perovskite materials are being studied for high temperature electrochemical applications such as solid oxide fuel cells (SOFC) and electrolyzers due to their tunable conductivity and catalytic activity. However, high temperature operation poses significant challenges in both fabrication and durable operation that is further complicated by the operating environment.1 We studied barium niobates with various dopants such as Fe, Ni, Ca, Y, and Mg for B site doping while Sr, K, and La are studied for A site doping. These niobates showed enhanced chemical stability in SOFC relevant conditions and catalytic activity towards methane activation. Nb4+/5+ redox couple seem to be a key reason behind this chemical stability while the size and electronegativity of the dopants affect the electrical properties.2 Catalyst exsolution is explored with dopants such as Fe, Ni, and Co under reducing conditions along with surface bound metallic nanoparticles prepared by an incipient wet synthesis method. Chemical stability of these perovskites was analyzed by an in situ TGA measurements under various gas environments followed by analysis of the powders using PXRD, XPS, SEM, and TEM methodologies.3 Methane activation properties are further analyzed in a temperature programmed reaction setup while Electrochemical properties were evaluated in a home-made setup using different electrolyte materials in the temperature range of 700°C to 900°C. Cyclic voltammetry, impedance spectroscopy, and chronoamperometry measurements coupled with continuous mass spectra analysis was utilized to diagnose any correlation between product distribution and applied potential. Our results demonstrate doped barium niobates as a promising candidate for stable operation in high temperature electrochemical applications. The presentation will discuss these results and provide a correlation between dopants and catalytic activity and chemical stability of doped barium niobate perovskites. References (1) Ramaiyan, K. P.; Denoyer, L. H.; Benavidez, A.; Garzon, F. H. Selective Electrochemical Oxidative Coupling of Methane Mediated by Sr2Fe1.5Mo0.5O6-δ and Its Chemical Stability. Commun. Chem. 2021, 4 (1), 139. https://doi.org/10.1038/s42004-021-00568-1.(2) Denoyer, L. H.; Benavidez, A.; Garzon, F. H.; Ramaiyan, K. P. Highly Stable Doped Barium Niobate Based Electrocatalysts for Effective Electrochemical Coupling of Methane to Ethylene. Adv. Mater. Interfaces 2022, 9 (27), 2200796. https://doi.org/10.1002/admi.202200796.(3) Denoyer, L. H.; Benavidez, A.; Garzon, F. H.; Ramaiyan, K. P. Chemical Stability of BaMg0.33Nb0.67-XFexO3-δ in High Temperature Methane Conversion Environments. under communication - ECS Journal of Solid State Science and Technology.

Doped Barium Niobate Perovskite Based Materials for High-Temperature Electrolyzer Application and Efficient Methane Conversion

Perovskite materials have helped make notable advances in many applications over the last few decades. Specifically, in high temperature electrochemical technologies such as solid oxide fuel cells (SOFC) and electrolyzers where perovskite-based electrolyte and electrode materials are playing pivotal roles. However, high temperature operation poses significant challenges in both fabrication and durable operation that is further complicated by the operating environment. For example, an electrolyte in a SOFC faces a highly oxidizing environment on the cathode while highly reducing environment on the anode and hence should possess chemical stability under these operating conditions and lifetime requirements for energy conversion technologies often times exceed 10 years of usage with no more than 20% degradation.[1]. Electrochemical oxidative coupling of methane (E-OCM) to ethylene process faces further problems associated with coke and carbonate formation along with the over oxidation of CH4 that invariably leads to CO and CO2. Here we present exciting class of barium niobate perovskites where different cations such as Mg, Ca, Y, and Fe on the niobium site was used for doping and evaluated for E-OCM application. The results are compared with another perovskite material Sr2Fe1.5Mo0.5O6- d (SFMO) that showed good catalytic activity but poor chemical stability. [2][3] Prepared perovskite material was analyzed by XPS, TGA, TPR, SEM, and TEM methodologies towards their chemical stability. Electrochemical properties were evaluated in a home-made setup using different electrolyte materials in the temperature range of 700°C to 900°C by methods such as cyclic voltammetry, impedance spectroscopy, and chronoamperometry. Electrochemical measurements coupled with continuous mass spectra analysis provided valuable insights between product distribution and applied potential. Our results demonstrate doped barium niobates as a promising candidate for stable operation in high temperature electrochemical applications.

The impact of stellar evolution on rotating star clusters: the gravothermal-gravogyro catastrophe and the formation of a bar of black holes

ABSTRACT We present results from a suite of eight direct N-body simulations, performed with nbody6++ GPU, representing realistic models of rotating star clusters with up to 1.1 × 105 stars. Our models feature primordial (hard) binaries, a continuous mass spectrum, differential rotation, and tidal mass-loss induced by the overall gravitational field of the host galaxy. We explore the impact of rotation and stellar evolution on the star cluster dynamics. In all runs for rotating star clusters, we detect a previously predicted mechanism: an initial phase of violent relaxation followed by the so-called gravogyro catastrophe. We find that the gravogyro catastrophe reaches a finite amplitude, which depends in strength on the level of the bulk rotation, and then levels off. After this phase, the angular momentum is transferred from high-mass to low-mass particles in the cluster (both stars and compact objects). Simultaneously, the system becomes gravothermally unstable and collapses, thus undergoing the so-called gravothermal-gravogyro catastrophe. Comparing models with and without stellar evolution, we find an interesting difference. When stellar evolution is not considered, the whole process proceeds at a faster pace. The population of heavy objects tends to form a triaxial structure that rotates in the cluster centre. When stellar evolution is considered, we find that such a rotating bar is populated by stellar black holes and their progenitors. The triaxial structure becomes axisymmetric over time, but we also find that the models without stellar evolution suffer repeated gravogyro catastrophes as sufficient angular momentum and mass are removed by the tidal field.

On the quantum model of a charged black hole

We study the quantum states of the black hole model in the configuration space. To this end, we investigate the properties of the configuration space of the Einstein–Maxwell set of equations in the T-region. We limit ourselves to considering the T-region, where the fields under consideration have a dynamic meaning. Based on the standard action for the of Einstein–Maxwell set of equations, we construct the reduced action for the spherical symmetry case. Using the Hamiltonian constraint, we exclude the non-dynamic degree of freedom from the reduced action, thereby passing to the configuration space. In the new representation of the system, we study the induced dynamical system in the configuration space. It turns out that the induced supermetric is reduced to a quasi-Cartesian form. The laws of charge and mass conservation, which the system contains, together with the Hamilton constraint, completely determine thestate of the black hole. They allow one to find the momenta and the action of the system in terms of field variables and conserved quantities, as well as the trajectory of motion in the configuration space. The black hole quantization is reduced to the construction of the quantum states for the system with a fixed mass and charge in a three-dimensional pseudo-Euclidean configuration space The Hamilton constraint is associated with the DeWitt equation, the latter is constructed using the Laplace–Beltrami operator, which is Hermitian with respect to the natural measure. To construct a Hermitian mass operator, it suffices to restrict ourselves to partial derivatives with their corresponding ordering. For the physical states satisfying the DeWitt equation to be also eigenfunctions of the mass operator, the compatibility conditions must be satisfied. In this case, we arrive at the corresponding ansatz. Its substitution into the DeWitt equation leads to a self-consistent solution of the quantum DeWitt equation and equation for the eigenvalue of the mass operator. The constructed model describes the quantum states of a charged black hole in the configuration space with continuous mass and charge spectra.

ON THE STRUCTURE OF THE CONFIGURATION SPACE OF CHARGED BLACK HOLES

Some properties of the configuration space (CS) of charged black holes (BH) we are considered. A reduced action for the spherically symmetric configuration of the gravitational and electromagnetic fields is constructed. We restrict ourselves to considering of T-region, where the studied fields have a dynamic meaning. Using the Hamiltonian constraint, we exclude the nondynamic degree of freedom. This leads to the action of the system in the CS with the corresponding supermetric. It turns out that the CS is flat, and its metric admits a twoparametric group of motions. This group generates conservation laws for the geodesic equations. The first law is the charge conservation law, and second is the mass conservation law (the mass function). Using the Hamiltonian constraint, they allow one to find momenta as a function of the field variables andcalculate the action as a function of the conserved quantities and field variables in CS. We emphasize that to find this action, we use only the integrability condition for a differential form. The quantization of the system is reduced to the uantization of a free particle in a three-dimensional pseudo-Euclidean space. The natural measure corresponding to the CS metric is used to construct the Hermitian DeWitt and mass operators. Based on the self-consistent solution of quantum DeWitt equations and equations for the eigenvalues of the mass and charge operators, the wave function for the spherically symmetric configuration of the gravitational and electromagnetic fields in the T- region is constructed. As a result, we get a model of charged BH with continuous mass and charge spectra.

КОМПОНЕНТ ТЕМНОЇ МАТЕРІЇ І СОНЦЕ

Some consequences from the hypothesis of the origin of particles of one of the components of dark matter are presented. The reason for the hypothesis was the observational data of stellar radiation, considered through the prism of the relationship of all phenomena in Nature and the law of conservation of energy. It is argued that a part of the stellar electromagnetic radiation, which does not participate in the interaction with baryonic matter, will not wander forever in space. This radiation will interact with a subtle level of matter, continuously giving it its energy, shifting to the microwave region. In this frequency region, two quanta of close energies can form a neutral boson of spin 0, or spin 2, on opposite “courses”. Based on the observed spectrum of cosmic microwave radiation, it is assumed that these Bose particles have a continuous mass spectrum. These light nonrelativistic bosons are precisely the component of the thin medium that interacts with stellar radiation, taking energy from it. Bose particles participate in gravitational interactions. This means that in addition to the distribution of dark matter around galaxies, an increased concentration of particles in the form of large clouds can be observed in it. If an internal shock wave appears in such a cloud, located far from galactic streams of baryon particles, it will destroy the particles of the cloud, creating “strange radio circles” visible exclusively in the radio range. The gravitational interaction causes dark particles to drift towards large clusters of visible matter. The process of their drift to massive objects will be accompanied by resistance from the outgoing stellar radiation. Therefore, near the surface of a burning star, these particles themselves will resist the outgoing radiation, shifting it towards longer wavelengths. The plasma ejected by the star, with sufficient energy of its particles, is capable of destroying the particles of the dark component, creating pairs of photons and providing itself with "seed" quanta for bremsstrahlung. Free quanta remaining from the decay of dark particles will give microwave radiation. Therefore, burning stars should exhibit a redshift in the emission spectra and microwave radiation. Taking a certain model in the distribution of the dark component of matter near the Sun, it is possible to predict the nature of the redshift in the spectra of its radiation as the observation point moves along the solar disk from its center to the limb. A similar conclusion is made regarding the intensity of microwave radiation near the surface of the star. The galactic movement of the Sun should lead to some temperature effects associated with a denser counter flow of dark particles to the corresponding area of the solar surface. Knowing the direction of motion of the Sun in the Galaxy, based on the results of the temperature deviation on the surface of the star, one can determine the local speed and direction of movement of the cloud of the dark component of matter.

On the quantization of charged black holes with allowance for the cosmological constant

The paper considers a spherically symmetric configuration of the gravitational and electromagnetic fields with allowance to the cosmological constant, and its quantization. After dimensional reduction, the original action is transformed to new variables in the R- and T-regions. The exclusion of the non-dynamic degree of freedom from the obtained action leads to an action for the geodesic in the configuration space, which proves to be conformally flat. We use the Gitman–Tyutin formalism for the obtained dynamical system, which Lagrange function is degenerate. After performing a suitable canonical transformation, the constraints found from the Lagrange function are reduced to the canonical form. Herewith the physical part of the Hamilton function vanishes. To construct quantum theory, we introduce additional physical quantities – charge and mass functions. Since Hamilton operator equals zero, it leads to the fact that the desired wave function of the system obeys only the eigenvalue equations for the mass and charge operators. The solution of these equations leads to continuous charge and mass spectra.

Additional strange resonances in Lattice QCD

Recent Lattice QCD (LQCD) studies suggest that there are missing resonances in the strange sector of the Hadron Resonance Gas (HRG) model. By adopting the continuous Hagedorn mass spectrum, we present how different medium compositions influence the HRG predictions of conserved charge fluctuations. It is shown that missing strange resonances may be partially accounted for by applying the Hagedorn mass spectrum extracted from experimentally established hadrons. On the other hand, the strange-baryonic spectra, extracted from LQCD results for fluctuations, are found to be consistent with the unconfirmed states in the Particle Data Group (PDG) database, whilst the strange-mesonic spectrum points towards yet undiscovered states in the intermediate mass region.

Matching the Hagedorn mass spectrum with lattice QCD results

Based on recent Lattice QCD (LQCD) results obtained at finite temperature, we discuss modeling of the hadronic phase of QCD in the framework of Hadron Resonance Gas (HRG) with discrete and continuous mass spectra. We focus on fluctuations of conserved charges, and show how a common limiting temperature can be used to constrain the Hagedorn exponential mass spectrum in different sectors of quantum number, through a matching of HRG and LQCD. For strange baryons, the extracted spectra are found to be consistent with all known and expected states listed by the Particle Data Group (PDG). The strange-mesonic sector, however, requires additional states in the intermediate mass range beyond that embodied in the database.

On the oscillator realization of conformal U(2, 2) quantum particles and their particle-hole coherent states

We revise the unireps. of U(2, 2) describing conformal particles with continuous mass spectrum from a many-body perspective, which shows massive conformal particles as compounds of two correlated massless particles. The statistics of the compound (boson/fermion) depends on the helicity h of the massless components (integer/half-integer). Coherent states (CS) of particle-hole pairs (“excitons”) are also explicitly constructed as the exponential action of exciton (non-canonical) creation operators on the ground state of unpaired particles. These CS are labeled by points Z (2 × 2 complex matrices) on the Cartan-Bergman domain \documentclass[12pt]{minimal}\begin{document}$\mathbb {D}_4=U(2,2)/U(2)^2$\end{document}D4=U(2,2)/U(2)2, and constitute a generalized (matrix) version of Perelomov U(1, 1) coherent states labeled by points z on the unit disk \documentclass[12pt]{minimal}\begin{document}$\mathbb {D}_1=U(1,1)/U(1)^2$\end{document}D1=U(1,1)/U(1)2. First, we follow a geometric approach to the construction of CS, orthonormal basis, U(2, 2) generators and their matrix elements and symbols in the reproducing kernel Hilbert space \documentclass[12pt]{minimal}\begin{document}$\mathcal {H}_\lambda (\mathbb {D}_4)$\end{document}Hλ(D4) of analytic square-integrable holomorphic functions on \documentclass[12pt]{minimal}\begin{document}$\mathbb {D}_4$\end{document}D4, which carries a unitary irreducible representation of U(2, 2) with index \documentclass[12pt]{minimal}\begin{document}$\lambda \in \mathbb {N}$\end{document}λ∈N (the conformal or scale dimension). Then we introduce a many-body representation of the previous construction through an oscillator realization of the U(2, 2) Lie algebra generators in terms of eight boson operators with constraints. This particle picture allows us for a physical interpretation of our abstract mathematical construction in the many-body jargon. In particular, the index λ is related to the number 2(λ − 2) of unpaired quanta and to the helicity h = (λ − 2)/2 of each massless particle forming the massive compound.

No energy equipartition in globular clusters

It is widely believed that globular clusters evolve over many two-body relaxation times towards a state of energy equipartition, so that velocity dispersion scales with stellar mass as σ ∝ m−η with η = 0.5. We show here that this is incorrect, using a suite of direct N-body simulations with a variety of realistic initial mass functions and initial conditions. No simulated system ever reaches a state close to equipartition. Near the centre, the luminous main-sequence stars reach a maximum ηmax ≈ 0.15 ± 0.03. At large times, all radial bins convergence on an asymptotic value η∞ ≈ 0.08 ± 0.02. The development of this ‘partial equipartition’ is strikingly similar across our simulations, despite the range of different initial conditions employed. Compact remnants tend to have higher η than main-sequence stars (but still η < 0.5), due to their steeper (evolved) mass function. The presence of an intermediate-mass black hole (IMBH) decreases η, consistent with our previous findings of a quenching of mass segregation under these conditions. All these results can be understood as a consequence of the Spitzer instability for two-component systems, extended by Vishniac to a continuous mass spectrum. Mass segregation (the tendency of heavier stars to sink towards the core) has often been studied observationally, but energy equipartition has not. Due to the advent of high-quality proper motion data sets from the Hubble Space Telescope, it is now possible to measure η for real clusters. Detailed data-model comparisons open up a new observational window on globular cluster dynamics and evolution. A first comparison of our simulations to observations of Omega Cen yields good agreement, supporting the view that globular clusters are not generally in energy equipartition. Modelling techniques that assume equipartition by construction (e.g. multi-mass Michie–King models) are approximate at best.

RELATIVISTIC DIFFUSION OF QUARKS IN RANDOM GLUON FIELDS

We consider Wong's equations for a particle with a continuous mass spectrum in a random Yang–Mills field approximating the quantum field at finite temperature. We show that particle time evolution can be approximated by a relativistic diffusion. Kubo's generator of the relativistic diffusion is defined as an expectation value of the square of the Liouville operator.

Extended MacMahon–Schwingerʼs Master Theorem and conformal wavelets in complex Minkowski space

We construct the Continuous Wavelet Transform (CWT) on the homogeneous space (Cartan domain) D 4 = SO ( 4 , 2 ) / ( SO ( 4 ) × SO ( 2 ) ) of the conformal group SO ( 4 , 2 ) (locally isomorphic to SU ( 2 , 2 ) ) in 1 + 3 dimensions. The manifold D 4 can be mapped one-to-one onto the future tube domain C + 4 of the complex Minkowski space through a Cayley transformation, where other kind of (electromagnetic) wavelets have already been proposed in the literature. We study the unitary irreducible representations of the conformal group on the Hilbert spaces L h 2 ( D 4 , d ν λ ) and L h 2 ( C + 4 , d ν ˜ λ ) of square integrable holomorphic functions with scale dimension λ and continuous mass spectrum, prove the isomorphism (equivariance) between both Hilbert spaces, admissibility and tight-frame conditions, provide reconstruction formulas and orthonormal basis of homogeneous polynomials and discuss symmetry properties and the Euclidean limit of the proposed conformal wavelets. For that purpose, we firstly state and prove a λ-extension of Schwingerʼs Master Theorem (SMT), which turns out to be a useful mathematical tool for us, particularly as a generating function for the unitary-representation functions of the conformal group and for the derivation of the reproducing (Bergman) kernel of L h 2 ( D 4 , d ν λ ) . SMT is related to MacMahonʼs Master Theorem (MMT) and an extension of both in terms of Louckʼs SU ( N ) solid harmonics is also provided for completeness. Convergence conditions are also studied.

Un-spectral dimension and quantum spacetime phases

In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length ℓ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on the other side. We introduce the concept of un-spectral dimensionDU of a d-dimensional, euclidean (quantum) spacetime, as the spectral dimension measured by an “un-particle” probe. We find a general expression for the un-spectral dimension DU labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension dU of the un-particle probe; a critical “Planckian phase”, where four-dimensional spacetime can be effectively considered two-dimensional when dU=1; a “Trans-Planckian phase”, which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.

UNPARTICLE AS A PARTICLE WITH ARBITRARY MASS

The unparticle field operator can be expanded in terms of creation and destruction operators corresponding to particles with a continuous mass spectrum. Hence, when the four-momentum of an unparticle is measured, then the unparticle manifests as an ordinary particle with a definite (but arbitrary) mass.

Thermodynamics for a hadronic gas of fireballs with internal color structures and chiral fields

The thermodynamic partition function for a gas of color-singlet bags consisting of fundamental and adjoint particles in both $\mathrm{U}({N}_{c})$ and $\mathrm{SU}({N}_{c})$ group representations is reviewed in detail. The constituent particle species are assumed to satisfy various thermodynamic statistics. The gas of bags is probed to study the phase transition for nuclear matter in extreme conditions. These bags are interpreted as the Hagedorn states, and they are the highly excited hadronic states produced below the phase transition point to the quark-gluon plasma (QGP). The hadronic density of states has the Gross-Witten critical point and exhibits a third-order phase transition from a hadronic phase dominated by the discrete low-lying hadronic mass spectrum particles to another hadronic phase dominated by the continuous Hagedorn states. The Hagedorn threshold production is found just above the highest known experimental discrete low-lying hadronic mass spectrum. The subsequent Hagedorn phase undergoes a first-order deconfinement phase transition to an explosive QGP. The role of the chiral phase transition in the phases of the discrete low-lying mass spectrum and the continuous Hagedorn mass spectrum is also considered. It is found to be crucial in the phase transition diagram. Alternative scenarios are briefly discussed for the Hagedorn gas undergoing a higher order phase transition through multiple processes of internal color-flavor structure modification.

Statistics of Magnification Perturbations by Substructure in the Cold Dark Matter Cosmological Model

We study the statistical properties of magnification perturbations by substructures in strong lensed systems using linear perturbation theory and an analytical substructure model including tidal truncation and a continuous substructure mass spectrum. We demonstrate that magnification perturbations are dominated by perturbers found within a tidal radius of an image, and that sizable magnification perturbations may arise from small, coherent contributions from several substructures within the lens halo. We find that the root-mean-square (rms) fluctuation of the magnification perturbation is 10% to 20% and both the average and rms perturbations are sensitive to the mass spectrum and density profile of the perturbers. Interestingly, we find that relative to a smooth model of the same mass, the average magnification in clumpy models is lower (higher) than that in smooth models for positive (negative) parity images. This is opposite from what is observed if one assumes that the image magnification predicted by the best-fit smooth model of a lens is a good proxy for what the observed magnification would have been if substructures were absent. While it is possible for this discrepancy to be resolved via nonlinear perturbers, we argue that a more likely explanation is that the assumption that the best-fit lens model is a good proxy for the magnification in the absence of substructure is not correct. We conclude that a better theoretical understanding of the predicted statistical properties of magnification perturbations by CDM substructure is needed in order to affirm that CDM substructures have been unambiguously detected.

Solutions of multigravity theories and discretized braneworlds

We determine solutions to 5D Einstein gravity with a discrete fifth dimension. The properties of the solutions depend on the discretization scheme we use and some of them have no continuum counterpart. In particular, we find that the negligence of the lapse field (along the discretized direction) gives rise to a Randall–Sundrum-type metric with a negative tension brane. However, no brane source is required. We show that this result is robust under changes in the discretization scheme. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We find, however, one particular scheme which leads to an undetermined lapse reflecting the reparametrization invariance of the continuum theory. We also find other solutions, with no continuum counterpart with changes in the metric signature or avoidance of singularity. We show that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales. We also discuss some cosmological solutions.

Some Properties of Multigravity Theories and Discretized Brane Worlds

We review some properties of solutions to 5D Einstein gravity with a discrete fifth dimension. Those properties depend on the discretization scheme we use. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall–Sundrum-type metric with a negative tension brane. However, no brane source is required. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We show also that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales.