Hbar Research Articles

The photons and gluons sedimentation in the Svedberg ultracentrifuge

We consider the case of rotating black body (including the rotation of the black bath with gluons) where photons and gluons can perform the settling and sedimentation. The Planck formula for photons must be, in this situation, replaced by the Exner solution of the Lamm equation for photons.

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

CONSTRUCTING QUANTUM ANGULAR MOMENTUM L3 IN SPECIFIC DIRECTION BY USING U(1) GROUP

The purpose of this work is to investigate the mathematical structure of finite quantum angular momentum in a specific direction L3 which can be constructed from the representation of the U(1) group. The angular momentum eigenstate is invariant under Abelian rotation symmetry. The character group of U(1) is constructed to show that there exists an additive unitary operator for the angular momentum eigenstate, and the rotation eigenstate is invariant under it. The Weyl relation is proved by showing that the angle and angular momentum L3 are the canonical conjugate pair of observables.

The instant probability of object with deterministic motion. Another way to understand quantum mechanics

Usually, the idea of probability is applied only to the random motion in physics. Here, the instant probability concept is obtained by applying the probability approach to objects with deterministic motion trajectories via a coin falling to the ground as an example. Applied this concept to understand quantum mechanics, the following conclusions are inferred: The wave function/quantum state represents an instant probability distribution of physical quantities after taking into account Planck's constant; the collapse of the wave function is a special case of any function on time-dependent probability prediction has to collapse when performing measurement. The arrangement of measurements will affect the observed results; Quantum mechanics reveals the existence of non-local effects, which have nothing to do with the interaction in classical physics. Quantum mechanics cannot answer questions such as whether the cat is dead or alive before opening the box. The correct answer to this kind of question has to be from classic physics.

A problem with the conservation law observed in macroscopic quantum phenomena is a consequence of violation of the correspondence principle

Jorge Hirsch drew attention to the contradiction of the Meissner effect with Faraday’s law and the law of angular momentum conservation. This article draws attention to the fact that the angular momentum can change without any force only due to quantization in both microscopic and macroscopic quantum phenomena. But if in the first case this change cannot exceed the Planck constant, then in the second case this change is macroscopic due to a violation of the correspondence principle. To explain the violation of the correspondence principle, Lev Landau postulated in 1941 that microscopic particles in superfluid helium and superconductor cannot move separately. Quantization can change not only the angular momentum, but also the kinetic energy of a superconducting condensate on a macroscopic amount. For this reason, the Meissner effect and other macroscopic quantum phenomena contradict the second law of thermodynamics. The reluctance of physicists to admit the violation of the second law of thermodynamics provoked a false understanding of the phenomenon of superconductivity and obvious contradictions in books on superconductivity.

Perfect quantum protractors

In this paper we introduce and investigate the concept of a perfect quantum protractor, a pure quantum state |ψ⟩∈H that generates three different orthogonal bases of H under rotations around each of the three perpendicular axes. Such states can be understood as pure states of maximal uncertainty with regards to the three components of the angular momentum operator, as we prove that they maximise various entropic and variance-based measures of such uncertainty. We argue that perfect quantum protractors can only exist for systems with a well-defined total angular momentum j, and we prove that they do not exist for j∈{1/2,2,5/2}, but they do exist for j∈{1,3/2,3} (with numerical evidence for their existence when j=7/2). We also explain that perfect quantum protractors form an optimal resource for a metrological task of estimating the angle of rotation around (or the strength of magnetic field along) one of the three perpendicular axes, when the axis is not a priori known. Finally, we demonstrate this metrological utility by performing an experiment with warm atomic vapours of rubidium-87, where we prepare a perfect quantum protractor for a spin-1 system, let it precess around x, y or z axis, and then employ it to optimally estimate the rotation angle.

Theoretical Quantum Mass

In the present theoretical work, attempts have been made to find the least mass, which quantifies the discrete mass, in terms of the reduced Planck constant and cosmological constant in the Heisenberg position-momentum uncertainty relation as well as by employing the time period of oscillating universes in mass-time inequality. It has been estimated and reported that the least mass exists in the range 5.98 × 10-74 < m < 2 × 10-68 kg, which quantifies discrete masses in the universe of size < 8.64 G ly.

Understanding the natural units and their hidden role in the laws of physics

The natural units of measure lauded by Max Planck more than 100 years ago are underutilized today. Many physical constants, including the Planck constant, the gravitational constant, the speed of light, vacuum permittivity, and vacuum permeability consist of natural units in their unit dimensions. The natural units are present in all formulas containing these constants. The defining characteristic of the natural units is an alignment of unit values at the Planck scale. This alignment gives a computational basis of proportionality from which the correlated properties and dynamics of elementary particles, including wavelength, period, mass, momentum, and energy, manifest in equal or inversely proportional ratios of the Planck scale. These correlations explain many of the defining equations of quantum mechanics, classical gravity, and electromagnetism.

On the Speed of Light as a Key Element in the Structure of Quantum Mechanics

We follow the assumption that relativistic causality is a key element in the structure of quantum mechanics and integrate the speed of light, c, into quantum mechanics through the postulate that the (reduced) Planck constant is a function of c with a leading order of the form ℏc∼Λ/cp for a constant Λ>0, and p>1. We show how the limit c→∞ implies classicality in quantum mechanics and explain why p has to be larger than 1. As the limit c→∞ breaks down both relativity theory and quantum mechanics, as followed by the proposed model, it can then be understood through similar conceptual physical laws. We further show how the position-dependent speed of light gives rise to an effective curved space in quantum systems and show that a stronger gravitational field implies higher quantum uncertainties, followed by the varied c. We then discuss possible ways to find experimental evidence of the proposed model using set-ups to test the varying speed of light models and examine analogies of the model based on electrons in semiconductor heterostructures.

(Digital Presentation) The Intermediate Electron Bond. Half-Reactions and the Electronic Structure of Atoms

The transfer of electrons ne from the intermediate state (Ox1 ← ne → Ox2) is associated with formation of a chemical bond with one Ox-form. Consequently, chemical bonds of electrons with Ox - forms should be formed Ox + ne + H2O→ Red or broken Red + H2O → Ox + ne in half-reactions. Then, there should be concluded some electronic state and bond without a specific chemical component. This electronic bond was determined as a definite coulomb bond, intermediate from metallic to non-metallic specific bonds. Ionization potential of intermediately bound electrons is determined I interm. = 5.19 eV [1-4].The chemical energy released in half-reactions-interactions is spent at once on separation of formed oppositely charged electrons and ions, polarization of water molecules of formed intermediate complexes. External potential differences appear between charged particles (double layers). Electrons and ions acquire electrochemical potentials, and electrochemical equilibriums are established.Exchange of formed electrons with electrons of electrodes stabilizes half-reactions. At that, a contact potential drop (not associated with interaction) appears in the electrode surface. However, only potential drops in double layers need to be taken into account. The rates of half-reactions-interactions change with changes in potential drops in double layers during electrical polarization.An important determination of ionization energy I interm. = 5.19 eV based on the found linear relationships between the first ionization potentials I of elements (related to the main groups) and their reversal covalent atomic radii 1/ r atom (Fig. 1). The linear relations cross when I interm. = 5.19 eV at 1/ r atom = 0.35 Ằ-1 ( r atom = 2.79 Ằ). It is concluded, that a specific electron bond formation with wave overlap begins with r atom = 2.79 Ằ at I interm. = 5.19 eV. Taking r interm. = 2.79 Ằ, ionization potential I interm. was calculated as coulomb energy of attraction between electron and polarized positive charge on Ox - form [2 - 4] I interm. =- e 2/ r interm. = - (4.8.10-10 e.s.u.)2 / 1.6.10-12 erg/eV . r interm. .10-8 cm == - 14.4 . 10-8eV.cm/2.79.10-8cm = - 5.19 eV (1)According to linear relations (Fig.1), for similar elements, the first ionization potentials I are equal I = 5.19 eV + Δ I (2)when energies of formation of specific electronic bonds Δ I are changed by quanta. The quantum linear oscillator model is applied Δ I = (Δ n + ½) h ν o (3)where h is Plank constant, ν o is the natural frequency of electron - wave, Δ n are numbers of quantum jumps, Δ I = ½ hν o is the point zero energy [4,5].It is concluded, that quantum jumpsΔ n = 8 - n = 1, 2, 3... should be counted from the orbital n = 8 on which electron localization and specific bonding is absent (8th period is absent in the Periodic System). However, the coulomb non-specific electronic bonding ( I interm. = 5.19 eV) must be preserved (Figh.1). Indeed, the first ionization potentials of elements of the 7th period are ~ 5 eV (5.17 eV for Ac).Therefore, Δ n = 1, Δ n = 2, Δ n = 3 ... correspond to one, two, three electron jumps necessary to reach the localization orbital related to the 7th, 6th, 5th .... (and so on) periods. First, using these Δ n , close natural frequencies ν o of electron waves were calculated for similar atoms as ν o = I - 5.19 eV / (Δ n + ½) h (4)For example, calculated ν o are for I (0.364.1015 s-1), Br (0.358.1015 s-1), Cl (0.344.1015 s-1), F (0.347 .1015 s-1).Using even the average natural frequency (0.35.1015 s-1), the first ionization potentials I (close to reference) were then calculated as the sums (Eqn.2). I = 5.19 eV + Δ I = 5.19 eV + (Δ n + ½) hν o (5)for most of elements. For example, for elements of the 7th main groups: I 10.3 eV (10.4 eV), Br 11.75 eV (11.8 eV), Cl 13.1 eV (13.0 eV), F 17.5 eV (17.4 eV). Emission wavelengths are also determined [4].Therefore, the quantum-mechanical oscillator model can be applied to electron localization in atoms and to formation and breaking of specific chemical electron bonds with Ox - forms in half-reactions. In both cases, electron - waves pass to (or from) the intermediate state I interm. = 5.19 eV corresponding to the absence of specific bond formation. References A.I Chernomorskii, Russian Journal of Physical Chemistry, 55(2)1981.A.I. Chernomorskii, Thermodynamics of Electrodes (FAN,Tashkent,1993);A.I Chernomorskii, Journal of The Electrochemical Society, 2021, 168, 116514A.I Chernomorskii, The intermediate electron bond and half-reactions (Scientific Resources, N-Y) (1999).P. Atkins, Julio de Paula, Physical Chemistry (W.H. Freeman and company,2006). Figure 1

Proof of concept and new developments on a Kibble extension

Abstract This article describes the proof of concept of a Kibble extension for vacuum mass comparators and its further development. A Kibble extension is a technical extension for vacuum mass comparators to connect to the new definition of the International System of Units (SI) of 2019. A commercially available high-vacuum prototype mass comparator from Sartorius serves as the basis. It is used to compare kilogram prototypes, such as the international prototype kilogram ( K ) $(\mathfrak{K})$ , directly with other kilogram mass standards in order to realize a calibration chain. According to the new definition of the SI in 2019, the kilogram is defined by the Planck constant (h), therefore the Kibble extension is designed to enable high-vacuum mass comparators to be converted by technical modifications to allow mass to be realized according to the new definition. The aim is to realize kilogram prototypes and mass standards in the range from 1 mg to 1 kg according to the E1 standard of OIML R111-1 (2004). Initial measurement results with a prototype of the Kibble extension are presented and evaluated. Based on the experience gained, a lightweight magnet system developed with the use of simulation methods is presented. This is intended to contribute to the further development of the Kibble extension.

Validation of optical conductivity and tailing parameter

A quantum model for optical conductivity that treats light as a particle is presented. Based on this assumption, the optical characteristics of the material are calculated and compared to experimental findings. The band gap energy of a material changes with frequency and refractive index. We provided an equation of the line extrapolated in the Tauc plot. The obtained formula for optical conductivity reveals that the band tailing parameter in the Tauc formula is dependent on the speed of light, the Planck constant, and the material's refractive index. The determination of this constant helps establish the value of the band. The values of this constant are found to be consistent with various experimental results. Two electric conductivities distinguishing Abraham and Minkoswi's light momentum relationship inside materials are proposed.

Massive Dirac equation in static Bumblebee black hole space-times, detailed derivations and novel exact solutions

In this work, we construct and investigate the relativistic spin-12 fermionic fields quantum dynamics in static spherically symmetric Bumblebee black hole background. The derivation of the Dirac equation in a general static spherically symmetric black hole space-time is carried out in detail via tetrad formalism. With the help of total angular momentum operator, the angular equation can be separated from the radial part where the solution is given in terms of the spinor harmonics. The radial Dirac equation has a well-known problem due to the presence of the square root terms appearing simultaneously with the rest mass that prevents us to find exact solutions. In this work, we present exact solutions of light mass fermion's wave function and energy levels bound in the static Bumblebee black hole. We discover the exact solutions of the massive Dirac's radial equation in terms of the Confluent Heun functions. Moreover, thanks to the well-known polynomial condition of the Confluent Heun functions, we also derive the energy quantization.

Galaxy dynamics tracing quantum cosmology beyond [formula omitted]CDM below the de Sitter scale of acceleration

It is proposed that the baryonic Tully–Fisher relation (bTFR) and JWST ’Impossible galaxies’ at cosmic dawn are unified in weak gravity by the trace J of the Schouten tensor below the Sitter scale of acceleration adS=cH, where c is the velocity of light and H is the Hubble parameter. Across adS, J parametrizes short-period galaxy rotation curves and fast gravitational collapse beyond the predictions of ΛCDM. The sensitivity of weak gravitation to J=16R, where R is the Ricci scalar tensor, is derived in infrared gravitation from a consistent limit to quantum gravity, reducing to general relativity in the limit of a small Planck constant. For the first time, it identifies the exact relation a0=c2J/2π of the Milgrom parameter across all redshifts, accounting for the bTFR and early galaxy formation accelerated by a factor ∼J1/8. It predicts a0′(0)<0 at the present epoch.

Third-order nonlinear Hall effect in a quantum Hall system.

In two-dimensional systems, perpendicular magnetic fields can induce a bulk band gap and chiral edge states, which gives rise to the quantum Hall effect. The quantum Hall effect is characterized by zero longitudinal resistance (Rxx) and Hall resistance (Rxy) plateaus quantized to h/(υe2) in the linear response regime, where υ is the Landau level filling factor, e is the elementary charge and h is Planck's constant. Here we explore the nonlinear response of monolayer graphene when tuned to a quantum Hall state. We observe a third-order Hall effect that exhibits a nonzero voltage plateau scaling cubically with the probe current. By contrast, the third-order longitudinal voltage remains zero. The magnitude of the third-order response is insensitive to variations in magnetic field (down to ~5 T) and in temperature (up to ~60 K). Moreover, the third-order response emerges in graphene devices with a variety of geometries, different substrates and stacking configurations. We term the effect third-order nonlinear response of the quantum Hall state and propose that electron-electron interaction between the quantum Hall edge states is the origin of the nonlinear response of the quantum Hall state.

On quantum states for angular position and angular momentum of light

In the present paper we construct a properly defined quantum state ψ(θ) expressed in terms of elliptic Jacobi theta functions for the self-adjoint observables angular position θ and the corresponding angular momentum operator L=−id/dθ in units of ℏ=1 . The quantum uncertainties Δθ and ΔL for the state are well-defined and are shown to give a lower value of the uncertainty product ΔθΔL in contrast to the so called minimal uncertainty states as discussed in Franke-Arnold et al (2004 New J. Phys. 6 103-1-8). The mean value ⟨L⟩ of the state ψ(θ) is not required to be an integer. In the case of any half-integer mean value ⟨L⟩ the state constructed exhibits a remarkable critical behavior with upper and lower bounds Δθ=π2/3−2 and ΔL=1/2 .

Dirac Theory in Noncommutative Phase Spaces

Based on the position and momentum of noncommutative relations with a noncanonical map, we study the Dirac equation and analyze its parity and time reversal symmetries in a noncommutative phase space. Noncommutative parameters can be endowed with the Planck length and cosmological constant such that the noncommutative effect can be interpreted as an effective gauge potential or a (0,2)-type curvature associated with the Plank constant and cosmological constant. This provides a natural coupling between dynamics and spacetime geometry. We find that a free Dirac particle carries an intrinsic velocity and force induced by the noncommutative algebra. These properties provide a novel insight into the Zitterbewegung oscillation and the physical scenario of dark energy. Using perturbation theory, we derive the perturbed and nonrelativistic solutions of the Dirac equation. The asymmetric vacuum gaps of particles and antiparticles reveal the particle–antiparticle symmetry breaking in the noncommutative phase space, which provides a clue to understanding the physical mechanisms of particle–antiparticle asymmetry and quantum decoherence through quantum spacetime fluctuation.

The Divine Blueprint: An In-Deth Analysis of the Quran’s Mathematical Architecture -Revealing the Golden Ratio, Solar Year Length, Universal GravitationalConstant, Speedof Light, Planck Constant, and theSignificance of the Numbers 28 and 114

There is a strong belief that Allah Almighty could reveal His existence by encoding the laws of nature and their fundamental constants in the Quran with impeccable precision. However, the mathematical frameworks and patterns embedded within the Quranic text to reveal scientific laws and constants may contain minor deviations in numerical values to empower personal exploration, accommodate diverse interpretations, and strengthen faith. This theory is based on the fact that the Quran is the word of Allah Almighty. Consequently, one would anticipate finding evidence suggesting a divine origin. Many scholars and researchers have suggested that this evidence can be found in the mathematical structure of the Quran through patterns, numerical codes, and other mathematical features within the text that are too complex to be simply attributed to human authorship. Therefore, it is believed that the Quran contains within its structure a mathematical encoding of all physical laws and constants. Verses like 20.98, which state, "He encompasses all things in knowledge," are quoted as evidence. According to this perspective, the Quran is assumed to incorporate mathematical miracles, indicating a potential correspondence between its text and the underlying order of the universe. This theory reveals many mathematical frameworks illustrating how the Quran embeds scientific knowledge. These include the identification of frequent occurrences of the golden ratio within the Quranic text and the manifestation of the golden ratio in the human body, alongside the determination of key celestial parameters such as the length of the solar year. Furthermore, this theory uncovers a numerical link between the Quran and fundamental scientific constants, notably the universal gravitational constant, the speed of light, and the Planck constant. Moreover, this theory utilizes numerical analysis to offer a compelling rationale for why the numbers 28 and 114 are used to represent the total number of Arabic letters and chapters in the Quran, respectively. Finally, this theory highlights the Quran's remarkable mathematical architecture, offering indisputable evidence of its divine composition. We behold a mathematical marvel of cosmic scale, a phenomenon defying human intelligence. Indeed, the Quranis a product of a super intelligence exceeding our comprehension.

Anomalous Fraunhofer-like patterns in quantum anomalous Hall Josephson junctions

The intriguing interplay between topology and superconductivity has attracted significant attention, given its potential for realizing topological superconductivity. In the quantum anomalous Hall insulators (QAHIs)-based junction, the supercurrents are carried by the chiral edge states, characterized by a 2Φ0 magnetic flux periodicity (Φ0=h/2e is the flux quantum, h the Planck constant, and e the electron charge). However, experimental observations indicate the presence of bulk carriers in QAHI samples due to magnetic dopants. In this study, we reveal a systematic transition from edge-state to bulk-state dominant supercurrents as the chemical potential varies from the bulk gap to the conduction band. This results in an evolution from a 2Φ0-periodic oscillation pattern to an asymmetric Fraunhofer pattern. Furthermore, a Fraunhoher-like pattern emerges due to the coexistence of chiral edge states and bulk states caused by magnetic domains, even when the chemical potential resides within the gap. These findings not only advance the theoretical understanding but also pave the way for the experimental discovery of the chiral Josephson effect based on QAHI doped with magnetic impurities. Published by the American Physical Society 2024

‘The ‘Vector-Model’ wavefunction: spatial description and wavepacket formation of quantum-mechanical angular momenta’

We introduce the concept of an asymptotic spatial angular-momentum wavefunction, Xmjφ,θ,χ=eimφδθ−θm eij+12χ, which treats j in the jm state as a three-dimensional entity; φ, θ, χ are the Euler angles, and θm is the Vector-Model polar angle, given by cosθm=m/j. A wealth of geometric information about j can be deduced from the eigenvalues and spatial transformation properties of the Xmjφ,θ,χ. Specifically, the Xmjφ,θ,χ wavefunction gives a computationally simple description of the sizes of the particle and orbital-angular-momentum wavepackets (constructed from Gaussian distributions in j and m ), given by effective wavepacket angular uncertainty relations for ΔmΔφ, ΔjΔχ, and ΔφΔθ. The Xmjφ,θ,χ also predicts the position of the particle-wavepacket angular motion in the orbital plane, so that the particle-wavepacket rotation can be experimentally probed through continuous and non-destructive j -rotation measurements. Finally, we use the Xmj(φ,θ,χ) to determine geometrically well-known asymptotic expressions for Clebsch–Gordan coefficients, Wigner d-functions, the gyromagnetic ratio of elementary particles, g=2, and the m -state-correlation matrix elements. Interestingly, for low j, even down to j=1/2, these expressions are either exact (the last two) or excellent approximations (the first two), showing that the Xmj(φ,θ,χ) give a useful spatial description of quantum-mechanical angular momentum, and provide a smooth connection with classical angular momentum.