Hbar Research Articles

From many-body quantum dynamics to the Hartree–Fock and Vlasov equations with singular potentials

In a combined mean-field and semiclassical regime, we consider the time evolution of N fermions interacting through singular pair interaction potentials of the form \pm |x-y|^{-a} , which includes the Coulomb and gravitational interactions. We prove that the many-body dynamics of mixed states are well approximated by solutions of the Hartree–Fock and Vlasov equations in terms of Schatten norms. The errors in these approximations are expressed in terms of the expected number of particles, N , and the Planck constant, h . For cases where a\in(0,1/2) , we obtain local-in-time results when N^{-1/2}\ll h \leq N^{-1/3} . Notably, this leads to the derivation of the Vlasov equation with singular potentials. For cases where a\in[1/2,1] , our results hold only within a small time scale or require an N -dependent cut-off. A fundamental ingredient in our analysis is the propagation of regularity for solutions to the Hartree–Fock equation uniformly in the Planck constant, which holds for a\in(0,1] .

Direct calibration of a true-rms ac voltmeter against a He-free pulsed Josephson standard

Starting from 2019 a new central role is played by quantum standards, owing to the redefined SI, where electrical units are directly linked to the fundamental constants e (elementary charge) and h (Planck constant). Thus, metrologists are nowadays trying to extend the astonishing accuracy attainable in dc measurements to ac and beyond, moving towards calibrations aiming quantum ac voltage generation. Programmable Josephson Voltage Standards are nowadays capable of fulfilling primary metrology requirements only for stepwise-approximated voltage signals up to few hundreds Hz. Pulsed Josephson standards are instead capable of generating arbitrary waveforms at higher frequencies, so are generally called Josephson Arbitrary Waveform Standards (JAWS). Despite of the lower attainable voltage, JAWS are very promising and are the subject of intense research activity. In particular, the capability of generating high spectral purity signals allows high accuracy measurements especially at the low voltage levels (<100mV rms), which are challenging to be performed by the traditional ac-dc transfer difference using thermal converters. We report in the following about our setup for quantum-based calibrations of a true-rms ac voltmeter with low uncertainty, first results obtained and unsolved issues.

About the Fine Structure Constant

This study builds on a previous publication entitled “a formula for electron mass calculation based on new fundamental concepts (ref.1), it shows that the relationship obtained between the mass of the electron and the four fundamental constants of physics, including fine structure constant, is precisely satisfied (to the millionth) if we take the inverse of the latter equal to the whole number 137. This value is interpreted as “ideal” for a Vacuum which would be free from radiation and other particles, therefore consisting exclusively of dark energy, this would imply a slight modification of the speed of light and Planck's constant, in this medium.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.

Energy-technological quantum parameters of silicon in electronics

Theoretical and experimental material on silicon is presented, which, together with formal and experimental dependencies of energy technological processes, determines the parameters of integrated electronic circuits. It is shown that the fundamentals of quantum physics, the fine structure constants of electricity and magnetism, together with theoretical and experimental data on energy technology processes, make it possible to consider patterns for electronic structural materials. The relationships between Planck's constant, gravitational constant, speed of light, electrical constant, dielectric constant, electrical charges and mass for the element silicon are considered. Methodological issues of formalizing the parameters of energy technological processes, which determine the fine structure constant of silicon, are noted.

Conserved spin operator of Dirac’s theory in spatially flat FLRW space-times

New conserved spin and orbital angular momentum operators of Dirac’s theory on spatially flat FLRW space-times are proposed generalizing thus the recent results concerning the role of Pryce’s spin operator in the flat case (Cotăescu in Eur Phys J C, 82, 1073, 2022). These operators split the conserved total angular momentum generating the new spin and orbital symmetries that form the rotations of the isometry groups. The new spin operator is defined and studied in active mode with the help of a suitable spectral representation giving its Fourier transform. Moreover, in the same manner is defined the operator of the fermion polarization. The orbital angular momentum is derived in passive mode using a new method, inspired by Wigner’s theory of induced representations, but working properly only for global rotations. In this approach the quantization is performed finding that the one-particle spin and orbital angular momentum operators have the same form in any FLRW spacetime regardless their concrete geometries given by various scale factors.

The glass transition as a boundary layer problem of the energy landscape kinetic master equations and its relationship with quantum path integrals

The glass transition is a process in which a non-periodic solid is obtained by fast cooling a melt. In this work, an analysis is made of the energy landscape kinetic equations that allow to describe such phenomena. In particular, it is shown that the glass transition occurs at the boundary layer of the energy landscape kinetic master equations, as solutions always have steep gradients and are very sensitive to the initial conditions. Moreover, it is discussed that the evolution operator is given by a path integral where the cooling rate plays a role akin to the Planck constant in a quantum mechanical problem. As an example, the kinetic equation properties of a two-level fully connected energy landscape system, capable of exhibiting both a glass and a thermodynamic phase transition, both of which are analytically solvable, are analysed in detail.

The Transformative Role of Group Theory in Physics

This article investigates the significant impact of Group Theory within the field of physics, having a particular focus on its application in comprehending difficult physical systems and phenomena. This report centers on the application of Lie groups, rotational groups, the Poincaré and Lorentz groups in order explain complicated features of physics. The report methodically discusses the role of the SU (2) group in Lie groups, the exploration of the rotational symmetries of the SO(3) group, and the significance of Lorentz transformations in special relativity with results demonstrate how Group Theory explains the nature of angular momentum in quantum mechanics and the limitations of the Schrödinger equation under Lorentz transformations. In addition, how the Poincaré group in special relativity is utilized. However, the scope of Group Theory's applications in physics is vast and multifaceted, making it challenging to encapsulate all its facets in a single report. This expansive field continues to evolve, promising further insights and innovations in the understanding of the physical universe.

Space time energy equivalence

Space–time–energy equivalence is the principle that everything that has space and time (in the presence of a constant force with an impact point) has an equivalent amount of energy, and vice versa. This equivalence is widespread in physics and astrophysics. Five examples (Stoney units, Planck units, Newton's law and Interaction of light rays, standard gravitational parameter and Coulomb's law) of the algebraic notation of this principle show its universality. Five examples (repetitions) of the same principle should justify the universality of the new principle and its use in physics and astrophysics. The proposed equivalence reveals the functional relationship between physical constants: Planck's constant, electric charge of an electron, vacuum permittivity and vacuum permeability. The realization of this equivalence will allow, through deepening the understanding of the nature of space–time, to take a fresh look at physics, when describing natural laws and principles.

A balanced quantum Hall resistor

The quantum anomalous Hall effect in magnetic topological insulators has potential for use in quantum resistance metrology applications. Electronic conductance is quantized to e2/h (where e is the elementary charge and h is the Planck constant) due to the effect, which persists down to zero external magnetic field and is compatible with the quantum standard of voltage. However, metrological applications of the quantum anomalous Hall effect are currently restricted by the need for low measurement currents and low temperatures. Here we report a measurement scheme that increases the robustness of a zero-magnetic-field quantum anomalous Hall resistor and extends its operating range to higher currents. In the scheme, we simultaneously inject current into two disconnected perimeters of a multi-terminal Corbino device, which is based on V0.1(Bi0.2Sb0.8)1.9Te3, to balance the electrochemical potential between the edges. This screens the electric field that drives backscattering through the bulk and thus improves the stability of the quantization at increased currents. Our approach could also be applied to existing quantum resistance standards that rely on the integer quantum Hall effect.

Sayed`s Theory of Dark Energy and Dark Matter Forces Nature

Allah (God) is the Creator of the wonderful accelerated expansion of universe. The nature of Dark energy (DE) and matter (DM) is enigmatic mystery of the modern astrophysics. This article is a theory establishes the nature and laws of DE and DM forces. They are among the forces controlling the universe harmony and homogeneity. The derived equations were based on the published Sayed quantum gravity force formula. The Sayed`s Dark energy force (SDEF) formulas indicate that they are function in quantum gravity force (FQG), energy density(ρ), cosmological (Ʌ), Hubble (H), and Planck (h) constants. The formulas were verified and validated. For Planck and cosmos scales, the Dark energy force, energy density, and Ʌ were calculated and found to be 2.538x1084 N, 10-26 Kg/m3, and 10-52 m-2 respectively. These values are in high concordance with the declared values. The results obtained show that the DE force represents more than ¾ of the universe forces as the observations. The disputed Hubble constant was also calculated and found to be in the range; ~2.2 x10-18 s-1. It can also be stated and emphasized that the light speed violation (E≠mc2) is a must to solve the DE nature and many other universe mysteries.

Infinite Quantum Twisting at the Cauchy Horizon of Rotating Black Holes.

We present a numerical calculation of the expectation value of the quantum angular-momentum current flux density for a scalar field in the Unruh state near the inner horizon of a Kerr-de Sitter black hole. Our results indicate that this flux diverges as V_{-}^{-1} in a suitable Kruskal coordinate such that V_{-}=0 at the inner horizon. Depending on the parameter values of the scalar field and black hole that we consider, and depending on the polar angle (latitude), this flux can have different signs. In the near extremal cases considered, the angle average of the expectation value of the quantum angular momentum current flux is of the opposite sign as the angular momentum of the background itself, suggesting that, in the cases considered, quantum effects tend to decrease the total angular momentum of the spheres away from the extremal value. We also numerically calculate the energy flux component, which provides the leading order divergence of the quantum stress energy tensor, dominant over the classical stress energy tensor, at the inner horizon. Taking our expectation value of the quantum stress tensor as the source in the semiclassical Einstein equation, our analysis suggests that the spheres approaching the inner horizon can undergo an infinite twisting due to quantum effects along latitudes separating regions of infinite expansion and contraction.

Evidence of the fractional quantum spin Hall effect in moiré MoTe2.

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities1-6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0 = e2/h (with e and h denoting the electron charge and Planck's constant, respectively)7-14. Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands15,16. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials17-19.

Events as Elements of Physical Observation: Experimental Evidence.

It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space-time location X→=x→,t. Considering historic experiments, which have been groundbreaking in the evolution of our modern ideas of matter on the atomic, nuclear, and elementary particle scales, it is shown that such experiments produce as outputs streams of macroscopically observable events which accumulate in the course of time into spatio-temporal patterns of events whose forms allow decisions to be taken concerning conceivable alternatives of explanation. Working towards elucidating the physical and informational characteristics of those elementary observations, we show that these represent hugely amplified images of the initiating micro-events and that the resulting macro-images have a cognitive value of 1 bit and a physical value of Wobs=Eobsτobs≫h. In this latter equation, Eobs stands for the energy spent in turning the initiating micro-events into macroscopically observable events, τobs for the lifetimes during which the generated events remain macroscopically observable, and h for Planck's constant. The relative value Gobs=Wobs/h finally represents a measure of amplification that was gained in the observation process.

Manipulating the McGinty Equation to Create Stable Micro-Wormholes

Fractal wormholes represent a novel theoretical concept at the intersection of classical physics and quantum mechanics. This article introduces the ΨFractal equation, a theoretical construct that seeks to describe these hypothetical entities. The equation integrates fundamental constants with parameters like mass, charge, and fractal dimension, suggesting intriguing properties and interactions with the cosmos. The McGinty equation, Ψ(x,t) = ΨQFT(x,t) + ΨFractal(x,t,D,m,q,s), can be used to help explain the fractal structure of space-time. The ΨFractal(x,t,D,m,q,s) term in the equation represents the fractal properties of space-time, where D represents the fractal dimension, m represents the mass of the system, q represents the charge, and s represents the spin. By manipulating the values of these variables, scientists can create a stable micro-wormhole in a controlled environment. The fractal dimension D, for example, can be used to control the size and stability of the wormhole. A higher fractal dimension value would result in a larger and more stable wormhole, while a lower value would result in a smaller and less stable wormhole. The mass of the system, represented by the variable m, can also play a role in the stability of the wormhole. A higher mass would result in a more stable wormhole, while a lower mass would result in a less stable wormhole. The charge and spin of the system, represented by the variables q and s, respectively, can also have an effect on the stability of the wormhole. A higher charge would result in a more stable wormhole, while a lower charge would result in a less stable wormhole. Similarly, a higher spin would result in a more stable wormhole, while a lower spin would result in a less stable wormhole. By manipulating the values of these variables, scientists can create a stable micro-wormhole in a controlled environment. This leads to advancements in fractal engine technology which in turn leads to the development of practical applications for faster-than-light travel, such as faster communication and interstellar exploration. For example, if we consider the equation for a fractal wormhole, ΨFractal(x,t,D,m,q,s) = [(G * m^2 * D) / (h * q * s)] * e^-(D * m * x^2) Where G is the gravitational constant, h is the Planck constant, and x is distance. By manipulating the value of D, m, q and s, scientists can control the size and stability of the wormhole, which in turn can be used for faster than light communication and interstellar travel.

Local density distribution of confined fermi gas in various nano-scale geometries

This study aims to investigate local density variations of Fermi gases confined in various geometries at the nano-scale, revealing irregularities even in thermodynamic equilibrium. Calculations show that density of the confined gas in a nano scale domain, decreases towards zero near domain boundaries due to a quantum boundary layer linked to the Planck constant. Additionally, Friedel-like density oscillations are observed in nano-confined Fermi gases. Analytical expressions for the local density distribution are derived for degenerate and one-dimensional scenarios, while numerical computations are conducted for complex geometries and weak degeneracy conditions. In line with existing literature, it is understood that the quantum-size effects observed in the global thermodynamic properties of confined gases are attributed to these local irregularities. It becomes evident that in areas smaller than the threshold determined by the quantum boundary layer, the gas empties the part of the domain or reaches lower densities in the considered part relative to other parts of the domain, despite being in thermodynamic equilibrium. The results indicate the potential for gases to benefit from these behaviors and suggest the possibility of designing and manufacturing new nano-scale machines that are not feasible on a macro-scale.

Classical trajectories from the zeros of the quantum potential: the 2D isotropic harmonic oscillator

In the first part of this work, using the quantum potential approach, we show that a solution to the time-independent Schrödinger equation determines a subset of classical solutions, only if the region corresponding to the zeroes of the quantum potential is tangent to the caustic region determined by the classical trajectories. Thus, the solutions of the time-independent Schrödinger equation, according to their caustic and the zeros of the quantum potential, can be classified in three different cases given by the following conditions: the two regions coincide, they are tangent at certain subset of points, and the two regions are not tangent at any point. In the second part, as examples of the first type of wave functions, we present the solutions of the Schrödinger equation for the 2D isotropic harmonic oscillator, which are eigenfunctions of both the Hamiltonian and the angular momentum operators. That is, we show that for this family of solutions, the zeroes of the quantum potential coincide with the caustic region. Furthermore, we find that the classical trajectories, determined from the quantum ones and the zeroes of the quantum potential, conform to a family of elliptical curves for a particle with energy, (2n + l + 1)ℏ ω, and orbital angular momentum l ℏ.

(Nano)Granules-Involving Aggregation at a Passage to the Nanoscale as Viewed in Terms of a Diffusive Heisenberg Relation.

We are looking at an aggregation of matter into granules. Diffusion plays a pivotal role here. When going down to the nanometer scale (the so-called nanoscale quantum-size effect limit), quantum mechanics, and the Heisenberg uncertainty relation, may take over the role of classical diffusion, as viewed typically in the mesoscopic/stochastic limit. A d-dimensional entropy-production aggregation of the granules-involving matter in the granule-size space is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg-type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive, very slow granules-including environment that, within the granule-size analogy invoked, matches the quantum limit of h/2πμ (μ-average mass of a granule; h-the Planck's constant) for the diffusion coefficient of the aggregation, first proposed by Fürth in 1933 and qualitatively foreseen by Schrödinger some years before, with both in the context of a diffusing particle. The classical quantum passage uncovered here, also termed insightfully as the quantum-size effect (as borrowed from the quantum dots' parlance), works properly for the three-dimensional (d = 3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also-granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the entropy-productive (nano)aggregation of interest.

Revealing the quantum nature of the voltage-induced conductance changes in oxygen engineered yttrium oxide-based RRAM devices

In this work, the quasi-analog to discrete transition occurring in the current–voltage characteristic of oxygen engineered yttrium oxide-based resistive random-access memory (RRAM) devices is investigated in detail. In particular, the focus of our research is not on the absolute conductance values of this characteristic but on the magnitude of its conductance changes occurring during the reset process of the device. It is found that the detected changes correspond to conductance values predominantly of the order of the quantum unit of conductance G0 = 2e2/h, where e is the electron charge and h the Planck constant. This feature is observed even at conductance levels far above G0, i.e. where electron transport is seemingly diffusive. It is also observed that such behavior is reproducible across devices comprising yttrium oxide layers with different oxygen concentrations and measured under different voltage sweep rates. While the oxygen deficiency affects the total number of quantized conductance states, the magnitude of the changes in conductance, close to 1 G0, is invariant to the oxygen content of the functional layer.

Superquantum effects on physical systems from a hydrodynamic perspective

Employing a nonlinear time-dependent Schrödinger equation that describes the transition between quantum and classical regimes, we explore superquantum effects on physical systems from a hydrodynamic point of view. The degree of quantumness, a pivotal parameter in this transition equation, gauges the impact of quantum effects arising from the quantum potential. As this parameter varies continuously between zero and one, it facilitates the gradual transformation of systems from purely classical to entirely quantum regimes. We extend our analysis by setting the degree of quantumness greater than one, thereby investigating superquantum phenomena. Notably, this transition equation can be reframed as a scaled time-dependent Schrödinger equation with a rescaled Planck constant. Through computational simulations derived from the scaled Schrödinger equation, we examine superquantum implications for two systems, including Gaussian wave packet scattering from an Eckart barrier and metastable state decay. This research suggests that the hydrodynamic formulation of the quantum–classical transition equation offers a profound understanding of superquantum influences on physical systems.