Values Of Momentum Research Articles

On the electron self-energy to three loops in QED

We compute the electron self-energy in Quantum Electrodynamics to three loops in terms of iterated integrals over kernels of elliptic type. We make use of the differential equations method, augmented by an ϵ-factorized basis, which allows us to gain full control over the differential forms appearing in the iterated integrals to all orders in the dimensional regulator. We obtain compact analytic expressions, for which we provide generalized series expansion representations that allow us to evaluate the result numerically for all values of the electron momentum squared. As a by-product, we also obtain ϵ-resummed results for the self-energy in the on-shell limit p2 = m2, which we use to recompute the known three-loop renormalization constants in the on-shell scheme.

Time-dependent rovibronic wave function of H2+ by multiconfiguration theory

Abstract We simulate the time-dependent rovibronic wave function of H 2 + in an intense, few-cycle 400 nm laser field using a time-dependent multiconfiguration method. By calculating the expectation value of the total angular momentum squared, the time-dependent expectation value of the internuclear distance, the induced dipole moment, and the probability of electron ejection, we show that rotational, vibrational and electronic excitation as well as ionization can be simulated. We compare the results obtained using the time-dependent multiconfiguration method with the results obtained using the standard two-state Born-Oppenheimer approximation and the close-coupling expansion. We find that the multiconfiguration results for a wave function constructed using 21 time-dependent orbitals are in good agreement with the close-coupling results, but that the two-state Born-Oppenheimer approximation leads to an underestimation of the induced dipole moment by a factor of two and an overestimation the expectation value of the total angular momentum squared by a factor of 2.3.

Occurrence of Gravitational Collapse in the Accreting Neutron Stars of Binary-driven Hypernovae

The binary-driven hypernova (BdHN) model proposes long gamma-ray bursts (GRBs) originate in binaries composed of a carbon–oxygen (CO) star and a neutron star (NS) companion. The CO core collapse generates a newborn NS and a supernova that triggers the GRB by accreting onto the NSs, rapidly transferring mass and angular momentum to them. This article aims to determine the conditions under which a black hole (BH) forms from NS collapse induced by the accretion and the impact on the GRB’s observational properties and taxonomy. We perform three-dimensional, smoothed particle hydrodynamics simulations of BdHNe using up-to-date NS nuclear equations of state, with and without hyperons, and calculate the structure evolution in full general relativity. We assess the binary parameters leading either NS in the binary to the critical mass for gravitational collapse into a BH and its occurrence time, t col. We include a nonzero angular momentum of the NSs and find that t col ranges from a few tens of seconds to hours for decreasing NS initial angular momentum values. BdHNe I are the most compact (about 5 minute orbital period), promptly form a BH, and release ≳1052 erg of energy. They form NS–BH binaries with tens of kiloyears merger timescales by gravitational-wave emission. BdHNe II and III do not form BHs, and release ∼1050–1052 erg and ≲1050 erg of energy, respectively. They form NS–NS binaries with a range of merger timescales larger than for NS–BH binaries. In some compact BdHNe II, either NS can become supramassive, i.e., above the critical mass of a nonrotating NS. Magnetic braking by a 1013 G field can delay BH formation, leading to BH–BH or NS–BH with tens of kiloyears merger timescales.

Exact two-loop amplitudes for Higgs plus jet production with a cubic Higgs self-coupling

We compute the corrections to the two-loop amplitudes for gg → h, gg → hg, qg → hq, and qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} → hg due to a modified cubic Higgs self-coupling. The exact dependence on the Higgs and top-quark masses across the entire 2 → 2 phase space is determined by numerically solving a system of differential equations for the relevant master integrals. The calculated amplitudes are crucial for evaluating the impact of the considered corrections on exclusive pp → hj production at the hadronic event level. As an application, we calculate the non-universal, kinematic-dependent cubic Higgs self-coupling corrections to the Higgs-boson transverse momentum distribution in gluon-gluon fusion Higgs production for arbitrary values of the transverse momentum.

Tennis Player Momentum Analysis and Match Flow Prediction Model Based on PCA

Momentum is a fluctuating phenomenon that occurs during the course of a game when the seemingly dominant side scores consecutive points or influences the course of the entire game. And as tennis is a popular sport all over the world, exploring the effects and mechanisms of athletes' momentum on match changes and outcomes in tennis matches can provide reasonable match advice to athletes. To this end, this paper systematically establishes a prediction model based on tennis players' momentum analysis and match direction. In this paper, this text first cleaned the data for the 2023 Wimbledon tennis tournament obtained from the American Collegiate Mathematical Modeling Contest website and supplemented the missing values using cubic Hermite interpolation. The processed data is then analyzed using principal component analysis, where a linear combination of each principal component is defined as a momentum value, thus quantifying the momentum and creating a mathematical model between the indicator and the momentum. Finally, a momentum plot of the player is created to visualize the relationship between the player's momentum and the outcome of the race.

A hybrid trans-modal liquid crystal optical vortex generator

This work experimentally validates a large-aperture optical vortex generator using a novel hybrid structure, combining transmission electrode and modal techniques, in what we term the trans-modal technique. The continuous transmission electrode is designed to generate a linear voltage distribution between the contact electrodes, while the electrode stubs distribute the voltage across the active area. A high-resistivity layer of the conducting polymer PEDOT fills the gap between the electrodes, resulting in a completely continuous voltage distribution. A 1-cm aperture device is experimentally demonstrated, but the structure is completely scalable. Theoretical results validate the design, and experimental results demonstrate precise control over the topological charge for both positive and negative values of orbital angular momentum. Remarkably, the conversion efficiency for the first topological charges is almost 100%. The reduction in efficiency of the higher-order modes has been explained theoretically, and it is not caused by design but by the PEDOT characteristics. The fabrication process is straightforward, as the high-resistivity layer may also be inhomogeneous. This work contributes significantly to the field by introducing a novel method for optical vortex generation. The simplicity of the fabrication process, high conversion efficiency, and ability to control the topological charge make this technique a promising avenue for future research and applications.

Conditional Values in Quantum Mechanics.

We consider the local value of an operator for a given position or momentum and, more generally on the value of another arbitrary observable. We develop a general approach that is based on breaking up Aψ(x) as Aψ(x)ψ(x)=Aψ(x)ψ(x)R+iAψ(x)ψ(x)I where A is the operator whose local value we seek and ψ(x) is the position wave function. We show that the real part is related to the conditional value for a given position and the imaginary part is related to the standard deviation of the conditional value. We show that the uncertainty of an operator can be expressed in two parts that depend on the real and imaginary parts. In the case of the position representation, the expression for the uncertainty of an operator shows that there are two fundamental contributions, one due to the amplitude of the wave function and the other due to the phase. We obtain the equation of motion for the conditional values, and in particular, we generalize the Ehrenfest theorem by deriving a local version of the theorem. We give a number of examples, including the local value of momentum, kinetic energy, and Hamiltonian. We also discuss other approaches for obtaining a conditional value in quantum mechanics including using quasi-probability distributions and the characteristic function approach, among others.

Impact of medium anisotropy on quarkonium dissociation and regeneration

Quarkonium production in ultra-relativistic collisions plays a crucial role in probing the existence of hot QCD matter. This study explores quarkonia states dissociation and regeneration in the hot QCD medium while considering momentum anisotropy. The net quarkonia decay width (ΓD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _{D}$$\\end{document}) arises from two essential processes: collisional damping and gluonic dissociation. The quarkonia regeneration includes the transition from octet to singlet states within the anisotropic medium. Our study utilizes a medium-modified potential that incorporates anisotropy via particle distribution functions. This modified potential gives rise to collisional damping for quarkonia due to the surrounding medium, as well as the transition of quarkonia from singlet to octet states due to interactions with gluons. Furthermore, we employ the detailed balance approach to investigate the regeneration of quarkonia within this medium. Our comprehensive analysis spans various temperature settings, transverse momentum values, and anisotropic strengths. Notably, we find that, in addition to medium temperatures and heavy quark transverse momentum, anisotropy significantly influences the dissociation and regeneration of various quarkonia states.

Ab initio study of the interaction between the charged system (FH+) and the He atom

We investigated the molecular structure and spectroscopic properties of the charged system (FH+) in interaction with a helium atom using an ab initio quantum chemistry approach in Jacobi coordinates. Our study focused on the ground state X2Π of (FH+) with various theoretical methods including UCCSD, UCCSD(T) and UCCSD(T)-F12, alongside basis sets like aug-cc-pVnZ (n = T, Q, 5, and 6) and cc-pVQZ-F12. We evaluated how these methods and basis sets affect the minimum energies We assessed the impact of the methods, basis sets, and extrapolation approaches on the minimum energies. Potential energy surfaces (PES) were generated using the correlated UCCSD(T)-F12 method with cc-pVQZ-F12 for hydrogen and fluorine, and cc-pVQZ-F12/optri for helium. These surfaces, considering spin-orbit coupling, are degenerate for linear geometries (θ=0° and θ=180°) of the (FH+)-He complex and correlate with the doubly degenerate X2Π state of (FH+). Our results reveal a strong anisotropic character at short and intermediate distances and a quasi-isotropic character upon dissociation into FH+ and He. We compared the spectroscopic parameters of the (FH+)-He complex with existing theoretical data, finding that the linear arrangement exhibits the highest stability, consistent with previous results for similar complexes. This conclusion is supported by the Milliken atomic charge distribution and a three-dimensional map of the Molecular Electrostatic Potential. Additionally, we used the LEVEL program, to calculate the bound rovibronic levels of the (FH+)-He complex for angular momentum values Ω=1/2 and Ω=3/2. Utilizing our ab initio results and a general interpolation approach based on the Reproducing Kernel Hilbert Space method, we generated contour maps illustrating the analytical potential for the (FH+)-He system. These findings will be employed to study the stabilities, geometries, energetics, and structures of the FH+ charged system within helium clusters.

Three-dimensional solitons supported by the spin–orbit coupling and Rydberg–Rydberg interactions in [formula omitted]-symmetric potentials

Excited states (ESs) of two- and three-dimensional (2D and 3D) solitons of the semivortex (SV) and mixed-mode (MM) types, supported by the interplay of the spin–orbit coupling (SOC) and local nonlinearity in binary Bose–Einstein condensates, are unstable, on the contrary to the stability of the SV and MM solitons in their fundamental states. We propose a stabilization strategy for these states in 3D, combining SOC and long-range Rydberg–Rydberg interactions (RRI), in the presence of a spatially-periodic potential, that may include a parity-time (PT)-symmetric component. ESs of the SV solitons, which carry integer vorticities S and S+1 in their two components, exhibit robustness up to S=4. ESs of MM solitons feature an interwoven necklace-like structure, with the components carrying opposite fractional values of the orbital angular momentum. Regions of the effective stability of the 3D solitons of the SV and MM types (both fundamental ones and ESs), are identified as functions of the imaginary component of the PT-symmetric potential and strengths of the SOC and RRI terms.

Electron tail suppression and effective collisionality due to synchrotron emission and absorption in mildly relativistic plasmas

Synchrotron radiation losses are a significant cause of concern for high-temperature aneutronic fusion reactions such as proton–Boron 11. The fact that radiation losses occur primarily in the high-energy tail, where the radiation itself has a substantial impact on the electron distribution, necessitates a self-consistent approach to modeling the diffusion and drag induced by synchrotron absorption and emission. Furthermore, an accurate model must account for the fact that the radiation emission spectrum is momentum-dependent, and the plasma opacity is frequency-dependent. Here, we present a simple Fokker–Planck operator, built on a newly solved-for blackbody synchrotron diffusion operator, which captures all relevant features of the synchrotron radiation. Focusing on magnetic mirror fusion plasmas, we show that significant suppression of the electron distribution occurs for relativistic values of the perpendicular electron momentum, which therefore emit much less radiation than predicted under the assumption of a Maxwell–Jüttner distribution.

Circular motion and collisions of charged spinning particles near Kerr Newman black holes

We investigate the dynamics of spinning particles with an electric charge orbiting electrically charged Kerr–Newman black holes. First, we derive the equations of motion for the test particles using the Mathisson-Papapetrou-Dixon (MPD) equations, taking into account electromagnetic interaction and the interaction between the particle spin and the spacetime curvature known as the Lorentz coupling term in the MPD equation. We analyze the related effective potential in various scenarios of particle spin, angular momentum, and black hole spin orientation. In addition, we provide graphical analyses of the radius of innermost stable circular orbits (ISCOs) of the particles, their angular momentum, and energy at ISCOs and superluminal bounds. The ISCOs for positive and negatively charged particles are almost the same. The combined effects of the black hole and particle spins enhance the Coulomb interaction effect on the ISCO radius. The ISCO energy and angular momentum decrease with the increase in particle spin. In the Reissner–Nordström (RN) black hole limit, the decreasing rate is faster at positive values of the particle spin, and the spin limit changes in the Kerr–Newman black hole case. Finally, we study collisions between spinning charged particles near Kerr–Newman black holes. The critical values of the angular momentum of spinning charged particles are explored, and the particles can collide in various cases of particle and black hole spin, as well as the particle angular momentum. We also analyze electromagnetic and spin effects on the center-of-mass energy of the colliding particles.

Thermometry with a dissipative heavy impurity

Improving the measurement precision of low temperature is significant in fundamental science and advanced quantum technology application. However, the measurement precision of temperature T usually diverges as T tends to zero. Here, by utilizing a heavy impurity to measure the temperature of a Bose gas, we obtain the Landau bound to precision δ2T∝T2 to avoid the divergence. When the initial momentum of the heavy impurity is close to be fixed and nonzero, the measurement precision can be δ2T∝T3 to break the Landau bound. We derive the momentum distribution of the heavy impurity at any moment and obtain the optimal measurement precision of the temperature by calculating the Fisher information. As a result, we find that increasing the expectation value P0 and reducing the variance Δ/2 of the initial momentum can help to improve the measurement precision. Moreover, under certain conditions, Δ/P0 is a relevant parameter, the smallness of which helps improve the thermometric precision of the probe. In addition, the momentum measurement is the optimal measurement of the temperature in the case that the initial momentum is close to be fixed and not equal to zero. The kinetic energy measurement is the optimal measurement in the case that the expectation value of the initial momentum is close to zero. Finally, we obtain that the temperatures of two Bose gases can be measured simultaneously. The simultaneous measurement precision is proportional to T2 when two temperatures are close to T. Published by the American Physical Society 2024

Universal scaling in far-from-equilibrium quantum systems: An equivalent differential approach

Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution toward thermalization. Notably, the concept of nonthermal fixed points (NTFPs)-responsible for the emergence of spatiotemporal universal scaling in far-from-equilibrium systems-has played a crucial role in both theoretical and experimental investigations. In this work, we introduce a differential equation that has the universal scaling associated with NTFPs as a solution. The advantage of working with a differential equation, rather than only with its solution, is that we can extract several insightful properties not necessarily present in the solution alone. How the differential equation is derived allows physical interpretation of the universal exponents in terms of the time dependence of the amplitude of the distributions and their momentum scaling. Employing two limiting cases of the equation, we determined the universal exponents related to the scaling using the distributions near just two momentum values. We established a solid agreement with previous investigations by validating this approach with three distinct physical systems. This consistency highlights the universal nature of scaling due to NTFPs and emphasizes the predictive capabilities of the proposed differential equation. Moreover, under specific conditions, the equation predicts a power-law related to the ratio of the two universal exponents, leading to implications concerning particle and energy transport. This suggests that the observed power-laws in far-from-equilibrium turbulent fluids could be related to the universal scaling due to NTFPs, potentially offering insights into the study of turbulence.

Hydrogen-iodine scattering. II. Rovibronic analysis and collisional dynamics.

Our recently published [Weike et al., J. Chem. Phys. 159, 244119 (2023)] spin-orbit coupled diabatic potential energy model for HI is used in a thorough analysis of bound and quasi-bound states as well as elastic and inelastic processes in H + I collisions. The potential energy model, designed explicitly for studying scattering, accurately describes the various couplings in the system, which lead to complex dynamics. Ro-vibronic bound and quasi-bound states related to the adiabatic electronic ground state and an excited electronic state are analyzed. Calculations using the full 104 × 104 diabatic matrix model or a single adiabatic state are compared in order to investigate approximations in the latter. Elastic and inelastic scattering cross sections as well as thermal rates between the ground and first excited fine structure levels of iodine are computed for collision energies up to 12 500 cm-1. Resonances related to the quasi-bound states are analyzed in terms of their energy, width, lifetime, and decay probabilities. The effect of different resonances on the thermal rates is discussed. Resonances between 30 000 and 40 000 cm-1 are also studied for selected values of the total angular momentum, in particular their decay probabilities into different final states of iodine and hence their potential effect on branching ratios in photodissociation of HI.

Expanding wave packets and the quantum to classical transition

The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.

SU(N) symmetry of coherent photons controlled by rotated waveplates

The coherent state from a laser source has spin and orbital degrees of freedom, which allow an arbitrary superposition state among orthogonal states with varying amplitudes and phases. Here, we theoretically show coherent photons with SU(N) symmetry are characterised by expectation values of angular momentum shown on a hypersphere in SO(N2−1) space. To demonstrate expected unitary transformations in experiments, we have constructed generators of transformations in the Lie group simply by combining widely available optical components such as waveplates and vortex lenses. We show a superposition state between twisted and Gaussian states is characterised by the dynamics of the topological charge upon the transformation in SU(3) states. We also realised photonic singlet and triplet states corresponding to SU(4) states, which were projected to SU(2)×SU(2) states upon passing through a rotated polariser.

Predicting Student Academic Performance Using Neural Networks: Analyzing the Impact of Transfer Functions, Momentum and Learning Rate

Artificial Neural Networks (ANN) demonstrate a compelling application of AI in predicting student performance, a critical aspect for both students and educators. Accurate forecasting of student achievements enables educators to monitor progress effectively, allowing educational institutions to optimize outcomes and improve student results. This study focuses on leveraging ANN for predictive analytics in student performance. Through a detailed evaluation of transfer functions, optimizers, learning rates, and momentum values, the model achieves an impressive 98% accuracy with specific configurations: a learning rate of 0.005, momentum of 0.7, Sigmoid transfer function, and SGD optimizer. Additionally, the study performs a comparative analysis of various Machine Learning Algorithms, including ANN, Support Vector Machines (SVM), K-Nearest Neighbors (KNN), Decision Trees (DT), Naive Bayes (NB), and Logistic Regression (LR). Using data from 689 B.Tech students at IP University, the analysis reveals that ANN outperforms other algorithms with an accuracy of 97%. This high accuracy demonstrates the potential of ANN in educational settings, providing a valuable tool for educators to enhance student performance and outcomes.

Метод дослідження ізомерів з великим значенням енергії і моменту

The technique for investigating isomeric states of nuclei with a large values of energy and total momentum created in the neutron capture reaction has been developed. The technique is based on the spectrometry of multiplicity, energy, and time of registration of instantaneous and delayed gamma cascades of isomer occupancy and decay, respectively. The technique was tested in measurements of the isomeric ratio of the 183W level with energy Eiz = 1.285 MeV with total moment Jπiz = 4-, 5- and lifetime Tiz = 8.2 μs in the neutron absorption reaction, which is equal to αiz = (4.7 ± 0.9)⋅10-3. At large values of the efficiency of registration of acts of settlement and decay of the isomer (0.6 - 0.8), the level of the corresponding background of the spectrometer is only 3.5⋅10-4 s-1. At the countable load at the spectrometer input ∼1.5⋅103 s-1, the expected sensitivity of determining the isomeric ratio in measurements with the mono isotope of the sample is αiz ∼(0.3 ± 1.0)⋅10-4.

Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center-of-mass energy, Penrose-process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value aE. Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter γ. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter γ and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and γ the ISCO becomes larger than that for the Kerr spacetime. For the center-of-mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose-process is more efficient for smaller values of the string cloud parameter b and the parameter γ has no significant impact on this process. Moreover we see that an increase in the parameters b, γ and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, γ and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.