Nonrelativistic Model Research Articles

Divergent features of collective gravitational quantum excitations

In this research, we study different aspects of collective gravitational quantum excitations in the framework of the quantum multistream model. The energy dispersion of collective electrostatic (plasmon) and gravitational excitations or as we call gravity quasiparticle (GQ) are derived using the nonrelativistic and relativistic models and many parameters such as the effective mass, phase, and group speed of quasiparticle excitations are studied, in detail. It is shown that, unlike plasmons with a forbidden energy gap, all positive and negative energy values are allowed for GQs. However, unlike plasmon with a dual-tone nature of collective excitations, the GQs are found to be single-tone with either wave-like or particle-like oscillations being strongly damped. The linear phase-space evolution of GQs indicates that they evolve similarly to the classical system of particles in the center of the mass frame in which the force due to self-consistent gravitational potential plays the role of interparticle forces. It is shown that the damping of wavelike or particle-like excitations in GQ energy dispersion leads to three distinct phenomena of gravitational expansion (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E>0$$\\end{document}), stable matter (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E=0$$\\end{document}) and gravitational collapse (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E<0$$\\end{document}), respectively. The Hubble-Lemaitre-like relation is obtained from the generalized probability current for GQs. The quantum gravitational interference effect is also studied.

Spectra and decay properties of higher lying BC meson states

In this work, the spectra and decay properties of [Formula: see text] mesons [Formula: see text]) have been investigated using a nonrelativistic potential model incorporating corrections from LQCD. The nonrelativistic Schrödinger wave equation is solved numerically using the Matrix Numerov Method. Using the obtained masses and wave functions, decay widths, lifetime, branching ratios and radiative decay widths are computed for the [Formula: see text] system. Influence of the bound state effect on decay width of [Formula: see text] mesons is also analyzed. We compare the obtained results with the experimental data and with other theoretical models.

Spectroscopic study of exotic fully-heavy tetraquark states [formula omitted] ([formula omitted])

In this article, we utilize the non-relativistic potential model to investigate the mass spectra of exotic fully-heavy tetraquark states QQQ̄Q̄ (Q∈{c,b}), specifically examining [cc][c̄c̄] and [bb][b̄b̄].We treat these states as diquark–antidiquark bound systems governed by a diquark–antidiquark color Coulomb plus confining linear potential.To determine the masses of the ground state and its radially and orbitally excited states for fully-heavy tetraquark states, we incorporate perturbative spin–spin, spin–orbit and spin–tensor interaction potentials.Our results of masses of nS, nP and nD states of fully heavy tetraquark states are compared with both other theoretical predictions and experimental data.Remarkably, our results closely align with theoretical as well as experimental observations.Furthermore, our findings also support the assignment of JPC quantum numbers to the recently observed structures by ATLAS, LHCb and CMS collaborations, including X(6600), X(6900) and X(7200).

M1 radiative and spin-nonflip ππ transitions of Bc states in the Cornell potential model

In this paper, we mainly predict the rates of M1 radiative and spin-nonflip ππ transitions of the Bc-meson under the nonrelativistic Cornell potential model with a screening potential effect. We employ the numerical wave function to determine the M1 radiative transition widths of Bc excited states and utilize the Kuang-Yan proposed method for the spin-nonflip ππ transitions among Bc states. Our theoretical results are valuable for studying the M1 radiative and spin-nonflip ππ transition processes of Bc states in experiments. Published by the American Physical Society 2024

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Bayesian Survey of the Dense Matter Equation of State Built upon Skyrme Effective Interactions

The nonrelativistic model of nuclear matter (NM) with zero-range Skyrme interactions is employed within a Bayesian approach in order to study the behavior of the neutron star (NS) equation of state (EOS). A minimal number of constraints from nuclear physics and ab initio calculations of pure neutron matter (PNM) are imposed together with causality and a lower limit on the maximum mass of an NS to all our models. Our key result is that accounting for correlations among the values that the energy per neutron in PNM takes at various densities and that are typically disregarded efficiently constrains the behavior of the EOS at high densities. A series of global NS properties, e.g., maximum mass, central density of the maximum mass configuration, minimum NS mass that allows for direct URCA, and radii of intermediate and massive NSs, appear to be correlated with the value of effective neutron mass in PNM at 0.16 fm−3. Together with similar studies in the literature our work contributes to a better understanding of the NS EOS as well as its link with the properties of dense NM.

Toward More Accurate Synthetic Reflection Spectra: Improving the Calculations of Returning Radiation

We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation. Assuming a lamppost coronal geometry, we simulate simultaneous observations of NICER and NuSTAR of bright Galactic black holes and we fit the simulated data with the latest version of relxill (modified to read the table of reflionx, which is the nonrelativistic reflection model used in our calculations). We find that relxill with returning radiation cannot fit well the simulated data when the black hole spin parameter is very high and the coronal height and disk’s ionization parameter are low, and some parameters can be significantly overestimated or underestimated. We can find better fits and recover the correct input parameters as the value of the black hole spin parameter decreases and the value of the coronal height increases.

Perfect fluid coupled to a solenoidal field which enjoys the ℓ-conformal Galilei symmetry

A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to a solenoidal field in arbitrary spatial dimension is considered. It contains an arbitrary parameter κ and in the particular case of κ=1 it describes a perfect fluid coupled to a magnetic field. For a special value of κ, the theory admits the Schrödinger symmetry group which is consistent with the magnetic case in two spatial dimensions only. Generalization to the case of the ℓ-conformal Galilei group for an arbitrary half-integer parameter ℓ is constructed.

Mass splitting and spin alignment for ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons in a magnetic field in NJL model

Based on the Nambu–Jona–Lasinio (NJL) model, we develop a framework for calculating the spin alignment of vector mesons and applied it to study ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons in a magnetic field. We calculate mass spectra for ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons and observe mass splitting between the longitudinally polarized state and transversely polarized states. The ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} meson in a thermal equilibrium system is preferred to occupy the state with spin λ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =0$$\\end{document} than those with spin λ=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =\\pm 1$$\\end{document}, because the former state has a smaller energy. As a consequence, we conclude that the spin alignment will be larger than 1/3 if one measures along the direction of the magnetic field, which is qualitatively consistent with the recent STAR data. Around the critical temperature TC=150MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{C}=150~\\hbox {MeV}$$\\end{document}, the positive deviation from 1/3 is proportional to the square of the magnetic field strength, which agrees with the result from the non-relativistic coalescence model. Including the anomalous magnetic moments for quarks will modify the dynamical masses of quarks and thus affect the mass spectra and spin alignment of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} mesons. The discussion of spin alignment in the NJL model may help us better understand the formation of hadron’s spin structure during the chiral phase transition.

Mathematical definition of the fine-structure constant: A clue for fundamental couplings in astrophysics

Astrophysical tests of the stability—or not—of fundamental couplings (e.g., can the numerical value ∼1/137 of the fine-structure constant α = e2/ℏc vary with astronomical time?) are a very active area of observational research. Using a specific α-free non-relativistic and nonlinear isotropic quantum model compatible with its quantum electrodynamics (QED) counterpart yields the 99% accurate solution α = 7.364 × 10−3 vs its experimental value 7.297 × 10−3. The ∼1% error is due to the deliberate use of mean-field Hartree approximation involving lowest-order QED in the calculations. The present theory has been checked by changing the geometry of the model. Moreover, it fits the mathematical solution of the original nonlinear integro-differential Hartree system by use of a rapidly convergent series of nonlinear eigenstates [G. Reinisch, Phys. Lett. A 498, 129347 (2024)]. These results strongly suggest the mathematical transcendental nature—e.g., like for π or e—of α’s numerical value of ∼1/137 and, hence, its astrophysical as well as its cosmological stability.

Hydrodynamic and kinetic representation of the microscopic classic dynamics at the transition on the macroscopic scale

An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

Neutron skin of 27Al with Skyrme and Korea-IBS-Daegu-SKKU density functionals

Recent measurement of the parity-violating (PV) asymmetry in the elastic electron scattering on [Formula: see text]Al target evokes the interest in the distribution of the neutron in the nucleus. In this work, we calculate the neutron skin thickness ([Formula: see text]) of [Formula: see text]Al with nonrelativistic nuclear structure models. We focus on the role of the effective mass, symmetry energy and pairing force. Models are selected to have effective masses in the range (0.58–1.05) M where M is the nucleon mass in free space, and stiffness of the symmetry energy is varied by choosing the slope of the symmetry energy in the range 9.4–100.5[Formula: see text]MeV. Effect of pairing force is investigated by calculating nuclear properties with and without pairing. With constant force pairing, we obtain [Formula: see text]–0.013[Formula: see text]fm. The result is independent of the effective mass and symmetry energy. However, [Formula: see text] is negative when the pairing force is switched off, so the pairing force plays an essential role to make [Formula: see text] positive and constrained in a narrow range. We also calculate the PV asymmetry ([Formula: see text]) in the elastic electron-[Formula: see text]Al scattering in the Born approximation at the kinematics of the Qweak experiment. We obtain a very narrow-ranged result [Formula: see text]. The result is consistent with the experiment and insensitive to the effective mass and symmetry energy.

All Charm Tetraquark Spectra in Coulombic Plus Quadratic Potential

A non-relativistic model with relativistic corrections is used to generate the mass spectra of all charm tetraquark in the diquark-antidiquark system. Fitting parameters are derived by numerically solving the Schrodinger equation for the charmonium meson using the coulombic potential and the harmonic confinement interaction potential. The mass spectra of all charm tetraquark is calculated in present work by systematically reducing a four-body problem to a two-body problem using the parameters obtained from charmonium spectra.

Effect of plasmon excitations in relativistic quantum electron gas

In this research, we use the generalized quantum multistream model to describe collective qusiparticle excitations in electron gas with arbitrary degree of degeneracy and relativity. The effective Schrödinger–Poisson and square-root Klein–Gordon–Poisson models are applied to study the energy band structure and statistical parameters of finite temperature quantum and relativistic quantum electron gas in neutralizing background charge. Based on the plasmon energy bandgap appearing above the Fermi level, a new equation of state for quasiparticle (collective) excitations with new plasma parameter definition is suggested for dense plasmas applicable to a wide range of electron temperature and density. The new criterion for quasiparticle excitations reveals some interesting aspects of relativistic quantum matter at extreme condition, such as the plasmon blackout and collective quantum pressure collapse, which are studied in the frameworks of both non-relativistic and relativistic quantum phenomena. Current quasiparticle model predicts density-temperature regimes in warm-dense matter for which collective excitations become ineffective. On the other hand, the energy band structure model predicts the quasiparticle pressure collapse in temperature–density regime close to that of white dwarf stars. The energy band structure is a powerful concept in condensed matter physics and is shown to have applications for collective quantum excitations in electron gas. It can also have direct applications in quasiparticle dielectric response and thermodynamic properties of electron gas in inertial confinement fusion, stellar core, compact stars, and charged relativistic quantum environments. It is interesting that the basic thermodynamic behavior of non-relativistic and relativistic quantum electron gases closely match up to temperature and number density of typical white dwarfs where the gravitational collapse is prone to occur. This evidently confirms the relevance of non-relativistic quantum plasmon model to study the collective excitations in warm dense matter and white dwarfs.

Nonrelativistic expansion of Green-Schwarz strings on AdS5 × S5

We perform nonrelativistic expansions of type IIB AdS5×S5 Green-Schwarz (GS) superstrings upto quadratic order in fermionic excitation. We carry out a systematic 1/c expansion both for the bosonic as well as the fermionic sector of the type IIB model and explore the LO theory in detail. We explore various global as well as local symmetries of the nonrelativistic sigma model at LO including the world-sheet supersymmetry. As a special case, we choose the flat gauge and explore the longitudinal T-duality rules for the LO theory. Finally, we comment on the NLO theory and discuss some of its interesting properties including the scale invariance.

Mass-spectra of light-heavy tetraquarks

The mass spectra of light-heavy tetraquarks [Formula: see text] ([Formula: see text]) are computed in a nonrelativistic diquark model with one-gluon exchange plus confining potential. In the diquark model, a [Formula: see text] state is regarded to be made of a light-heavy diquark ([Formula: see text]) and an antidiquark [Formula: see text] in antitriplet and triplet color configuration, respectively. The masses of charm mesons were calculated in order to fit the model parameters used to create the masses of tetraquarks and therefore enhance the model’s reliability. The masses of [Formula: see text] tetra-quark states are determined to be in the range of 3.8–4.7[Formula: see text]GeV, which is consistent with the experimentally reported charmonium-like states. In particular, the [Formula: see text], [Formula: see text] and [Formula: see text] tetraquarks, which have been seen experimentally, may all be described by our model.

Mass-loss and composition of wind ejecta in type I X-ray bursts

Context. X-Ray bursts (XRBs) are powerful thermonuclear events on the surface of accreting neutron stars (NSs) where nucleosynthesis of intermediate-mass elements occurs. The high surface gravity of an NS prevents the ejection of material by the XRB thermonuclear explosion. However, the predicted and observed XRB luminosities sometimes exceed Eddington’s value, and some of the material may escape by means of stellar wind. Aims. This work aims to determine the mass-loss and chemical composition of the material ejected through radiation-driven winds and its significance for Galactic abundances. It also reports on the evolution of observational quantities during the wind phase, which can help constrain the mass-radius relation in NSs. Methods. A non-relativistic radiative wind model was implemented, with modern opacity tables and treatment of the critical point, and linked through a new technique to a series of XRB hydrodynamic simulations that include over 300 isotopes. This allowed us to construct a quasi-stationary time evolution of the wind during the XRB. Results. In the models we studied, the total mass ejected by the wind was about 6 × 1019 g; the average ejected mass per burst represented 2.6% of the accreted mass between bursts, with 0.1% of the envelope mass ejected per burst; and approximately 90% of the ejecta was composed by 60Ni, 64Zn, 68Ge, and 58Ni. The ejected material also contained a small fraction (10−4 − 10−5) of some light p-nuclei, but not enough to account for their Galactic abundances. Additionally, the observable magnitudes during the wind phase showed remarkable correlations, partly due to the fact that photospheric luminosity stays close to the Eddington limit. Some of these correlations involve wind parameters, such as energy and mass outflows, that are determined by the conditions at the base of the wind envelope. Conclusions. The simulations resulted in the first realistic quantification of mass-loss for each isotope synthesized in the XRB. The photospheric correlations we found could be used to link observable magnitudes to the physics of the innermost parts of the envelope, close to its interface with the NS crust. This is a promising result regarding the issue of NS radius determination.

Krylov complexity in Calabi–Yau quantum mechanics

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi–Yau geometries, as well as some nonrelativistic models. We find that for the Calabi–Yau models, the Lanczos coefficients grow slower than linearly for small [Formula: see text]’s, consistent with the behavior of integrable models. On the other hand, for the nonrelativistic models, the Lanczos coefficients initially grow linearly for small [Formula: see text]’s, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope.

Accretion disc evolution in GRO J1655−40 and LMC X-3 with relativistic and non-relativistic disc models

ABSTRACT Black hole X-ray binaries are ideal environments to study the accretion phenomena in strong gravitational potentials. These systems undergo dramatic accretion state transitions and analysis of the X-ray spectra is used to probe the properties of the accretion disc and its evolution. In this work, we present a systematic investigation of ∼1800 spectra obtained by Rossi X-Ray Timing Explorer Proportional Counter Array observations of GRO J1655−40 and LMC X-3 to explore the nature of the accretion disc via non-relativistic and relativistic disc models describing the thermal emission in black hole X-ray binaries. We demonstrate that the non-relativistic modelling throughout an outburst with the phenomenological multicolour disc model DISKBB yields significantly lower and often unphysical inner disc radii and correspondingly higher (∼50–60 per cent) disc temperatures compared to its relativistic counterparts KYNBB and KERRBB. We obtained the dimensionless spin parameters of a* = 0.774 ± 0.069 and a* = 0.752 ± 0.061 for GRO J1655−40 with KERRBB and KYNBB, respectively. We report a spin value of a* = 0.098 ± 0.063 for LMC X-3 using the updated black hole mass of 6.98 M⊙. Both measurements are consistent with the previous studies. Using our results, we highlight the importance of self-consistent modelling of the thermal emission, especially when estimating the spin with the continuum-fitting method which assumes the disc terminates at the innermost stable circular orbit at all times.

Probing the soft state evolution of 4U 1543-47 during its 2021 outburst using AstroSat

ABSTRACT 4U 1543-47 underwent its brightest outburst in 2021 after two decades of inactivity. During its decay phase, AstroSat conducted nine observations of the source spanning from 2021 July 1 to September 26. The first three observations were performed with an offset of 40 arcmin with AstroSat/LAXPC, while the remaining six were on-axis observations. In this report, we present a comprehensive spectral analysis of the source as it was in the High/Soft state during the entire observation period. The source exhibited a disc-dominated spectra with a weak high-energy tail (power-law index ≥2.5) and a high inner disc temperature (∼0.84 keV). Modelling the disc continuum with non-relativistic and relativistic models, we find inner radius to be significantly truncated at &amp;gt;10 Rg. Alternatively, to model the spectral evolution with the assumption that the inner disc is at the innermost stable circular orbit, it is necessary to introduce variation in the spectral hardening in the range ∼1.5–1.9.