Momentum Variables Research Articles

Neutrino quantum kinetics in two spatial dimensions

Our understanding of neutrino flavor conversion in the innermost regions of core-collapse supernovae and neutron star mergers is mostly limited to spherically symmetric configurations that facilitate the numerical solution of the quantum kinetic equations. In this paper, we simulate neutrino quantum kinetics within a (2+1+1) dimensional setup: we model the flavor evolution during neutrino decoupling from matter in two spatial dimensions, one neutrino momentum variable, and time; taking into account non-forward neutral current and charged current collisions of neutrinos with the matter background, as well as neutrino advection. In order to mimic fluctuations in the neutrino emission and matter background, and explore their effect on the flavor evolution, we introduce perturbations in the collision term as well as in the vacuum term of the Hamiltonian. Because of such perturbations, the initial symmetry of the neutrino field across the simulation annulus is broken and flavor conversion is qualitatively affected, with regions of larger flavor conversion alternating across the simulation annulus. In addition, neutrino advection is responsible for spreading flavor waves across neighboring spatial regions. Although based on a simplified setup, our findings highlight the importance of modeling neutrino quantum kinetics in multi-dimensions to assess the impact of neutrinos on the physics of compact astrophysical sources and nucleosynthesis.

Global Convergence of Natural Policy Gradient with Hessian-Aided Momentum Variance Reduction

Global Convergence of Natural Policy Gradient with Hessian-Aided Momentum Variance Reduction

Physics-informed neural networks coupled with flamelet/progress variable model for solving combustion physics considering detailed reaction mechanism

In recent years, physics-informed neural networks (PINNs) have shown potential as a method for solving combustion physics. However, current efforts using PINNs for the direct predictions of multi-dimensional flames only use global reaction mechanisms. Considering detailed chemistry is crucial for understanding detailed combustion physics, and how to accurately and efficiently consider detailed mechanisms under the framework of PINNs has not been explored yet and is still an open question. To this end, this paper proposes a PINN/flamelet/progress variable (FPV) approach to accurately and efficiently solve combustion physics, considering detailed chemistry. Specifically, the combustion thermophysical properties are tabulated using several control variables, with the FPV model considering detailed chemistry. Then, PINNs are used to solve the governing equations of continuity, momentum, and control variables with the thermophysical properties extracted from the FPV library. The performance of the proposed PINN/FPV approach is assessed for diffusion flames in a two-dimensional laminar mixing layer by comparing it with the computational fluid dynamics (CFD) results. It has been found that the PINN/FPV model can accurately reproduce the flow and combustion fields, regardless of the presence or absence of observation points. The quantitative statistics demonstrated that the mean relative error was less than 10%, and R2 values were all higher than 0.94. The applicability and stability of this model were further verified on other unseen cases with variable parameters. This study provides an efficient and accurate method to consider detailed reaction mechanisms in solving combustion physics using PINNs.

Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation

We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, instead of linear, bundle isomorphism between the tangent and cotangent bundles of the configuration space and some care is needed in the development of the geometric formalism. At the end of the day, the affine nature of the Legendre transform is reflected in the affine dependence of the brackets that we construct on the momentum variables. Our study is motivated by a wide class of nonholonomic systems involving rigid bodies with internal rotors which are of interest in control. Our construction provides a natural geometric framework for the (known) Hamiltonisations of the gyrostatic generalisations of the Suslov and Chaplygin sphere problems.

Intrinsic squeezing of mechanical motion of a harmonically trapped atom with spin-orbit coupling

In this paper we investigated one-dimensional harmonically trapped atom with Raman-induced spin-orbit coupling by mapping to quantum-like model. Using displacement Fock states in quantum optics and variational methods we found the odd-parity superposition state of left- and right-displaced oscillator state is a good approximate solution to the ground state, which captures the essential physics of the system. The ground state wave function owes nodes which is remarkably different from the conventional no-node theory in quantum mechanics. The results show the atomic motion of center of mass exhibits intrinsic squeezing properties with relation to the Raman and spin-orbit coupling strength characterized by the variance in position and momentum, information entropy, as well as the Wigner function of the ground state. The dynamics of center of mass are also studied which demonstrates intuitive Zitterbewegung oscillations in momentum space and real space. Our results could be used for observing Zitterbewegung oscillations in neutral atomic gases and engineering nonclassic states.

Decoherence of a charged Brownian particle in a magnetic field: an analysis of the roles of coupling via position and momentum variables

Abstract The study of decoherence plays a key role in our understanding of the transition from the quantum to the classical world. Typically, one considers a system coupled to an external bath which forms a model for an open quantum system. While most of the studies pertain to a position coupling between the system and the environment, some involve a momentum coupling, giving rise to an anomalous diffusive model. Here we have gone beyond existing studies and analyzed the non-Markovian master equation, involving the quantum Langevin dynamics of a harmonically oscillating charged Brownian particle in the presence of a magnetic field and coupled to Ohmic (s = 1), sub-Ohmic (s < 1) and super-Ohmic (s > 1) heat baths via both position and momentum couplings. The presence of both position and momentum couplings leads to a stronger interaction with the environment, resulting in a faster loss of coherence compared to a situation where only position coupling is present. The rate of decoherence can be tuned by controlling the relative strengths of the position and momentum coupling parameters. In addition, the magnetic field results in the slowing down of the loss of information from the system, irrespective of the nature of coupling between the system and the bath. A faster decoherence rate is observed for higher values of the Ohmicity parameter ‘s’. Our results can be experimentally verified by designing a suitable ion trap setup.

Quantifying and analysing the angular momentum in volleyball jump serve during the aerial phase: relationship to arm swing speed.

In volleyball, the jump serve is a crucial and commonly used serving technique. Nonetheless, the angular momentum developed during the jump serve remains unexplored. The objectives of the current study were to determine the angular momentum manifesting during the airborne phase of the jump serve and to analyse the correlations between the angular momentum variables and arm swing speed. Three-dimensional coordinate data were obtained during the jump serves of 17 professional male volleyball players. Correlation and linear regression analyses were used to identify the angular momentum variables linked to the arm swing speed at ball impact (BI). The arm swing speed at BI exhibited significant correlations with the peak angular momentum of the attack arm (r = 0.551, p = 0.024), non-attack arm (r = 0.608, p = 0.011), non-attack leg (r = -0.516, p = 0.034), forearm (r = 0.527, p = 0.032), and hand (r = 0.824, p < 0.001). A stepwise regression model (R2 = 0.35, p = 0.043) predicted arm swing speed based on the peak angular momentum of the non-attack leg, forearm, and hand. The study results suggest that during the arm-acceleration phase, (1) increasing angular momentum with the non-attack leg helps maintain aerial body balance, thereby enhancing arm swing execution, and (2) controlling the magnitude and timing of the force exerted by the elbow and wrist is crucial for effectively transmitting angular momentum, contributing to an increase in arm swing speed.

The Climatology of Gravity Waves over the Low-Latitude Region Estimated by Multiple Meteor Radars

Atmospheric gravity waves (GWs) can strongly modulate middle atmospheric circulation and can be a significant factor for the coupling between the lower atmosphere and the middle atmosphere. GWs are difficult to resolve in global atmospheric models due to their small scale; thus, GW observations play an important role in middle atmospheric studies. The climatology of GW variance and momentum in the low-latitude mesosphere and lower thermosphere (MLT) region are revealed using multiple meteor radars, which are located at Kunming (25.6°N, 103.8°E), Sanya (18.4°N, 109.6°E), and Fuke (19.5°N, 109.1°E). The climatology and longitudinal variations in GW momentum fluxes and variance over the low-latitude region are reported. The GWs show strong seasonal variations and can greatly control the mesospheric horizontal winds via modulation of the quasi-geostrophic balance and momentum deposition. The different GW activities between Kunming and Sanya/Fuke are possibly consistent with the unique prevailing surface winds over Kunming and the convective system over the Tibetan Plateau according to the European Centre for Medium-Range Weather Forecasts (ECMWF), Reanalysis v5 (ERA5) data, and outgoing longwave radiation (OLR) data. These findings provide insight for better understanding the coupling between the troposphere and mesosphere.

Search for a critical point of strongly-interacting matter in central 40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{40}$$\\end{document}Ar + 45\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{45}$$\\end{document}Sc collisions at 13 A–75 A GeV/c beam momentum

The critical point of strongly interacting matter is searched for at the CERN SPS by the NA61/SHINE experiment in central 40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{40}$$\\end{document}Ar + 45\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{45}$$\\end{document}Sc collisions at 13 A, 19 A, 30 A, 40 A, and 75 A GeV/c. The dependence of the second-order scaled factorial moments of proton multiplicity distributions on the number of subdivisions in transverse momentum space is measured. The intermittency analysis uses statistically independent data sets for every subdivision in transverse and cumulative-transverse momentum variables. The results obtained do not indicate the searched intermittent pattern. An upper limit on the fraction of correlated protons and the intermittency index is obtained based on a comparison with the Power-law Model.

Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, the so-called independent-oscillator model. This is followed by a discussion on the relevant ‘weak-coupling’ limit. In the steady state, we analyze the quantum counterpart of energy equipartition theorem which has generated a considerable amount of interest in recent literature. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion in a harmonic well. Following this, we explore some aspects of dissipative diamagnetism in the context of quantum Brownian oscillators, emphasizing upon the role of confining potentials and also upon the environment-induced classical-quantum crossover. We discuss situations where the system-bath coupling is via the momentum variables by focusing on a gauge-invariant model of momentum-momentum coupling in the presence of a vector potential; for this problem, we derive the quantum Langevin equation and discuss quantum thermodynamic functions. Finally, the topic of fluctuation theorems is discussed (albeit, briefly) in the context of classical and quantum cyclotron motion of a particle coupled to a heat bath.

Equivalence principle for quantum mechanics in the Heisenberg picture

We present an exact quantum observable analog of the weak equivalence principle for a ‘relativistic’ quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as p µ , rather than p µ . We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.

Higher order Galerkin finite element method for [formula omitted]-dimensional generalized Benjamin–Bona–Mahony–Burgers equation: A numerical investigation

In this article, we study solitary wave solutions of the generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equation using higher-order shape elements in the Galerkin finite element method (FEM). Higher-order elements in FEMs are known to produce better results in solution approximations; however, these elements have received fewer studies in the literature. As a result, for the finite element analysis of the gBBMB equation, we consider Lagrange quadratic shape functions. We employ the Galerkin finite element approximation to derive a priori error estimates for semi-discrete solutions. For fully discrete solutions, we adopt the Crank–Nicolson approach, and to handle nonlinearity, we utilize a predictor–corrector scheme with Crank–Nicolson extrapolation. Additionally, we perform a stability analysis for time using the energy method. In the space, O(h3) convergence in L2(Ω) norm and O(h2) convergence in H1(Ω) norm are observed. Furthermore, an optimal O(Δt2) convergence in the maximum norm for the temporal direction is also obtained. We test the theoretical results on a few numerical examples in one- and two-dimensional spaces, including the dispersion of a single solitary wave and the interaction of double and triple solitary waves. To demonstrate the efficiency and effectiveness of the present scheme, we compute L2 and L∞ normed errors, along with the mass, momentum, and energy invariants. The obtained results are compared with the existing literature findings both numerically and graphically. We find quadratic shape functions improve accuracy in mass, momentum, energy invariants and also give rise to a higher order of convergence for Galerkin approximations for the considered nonlinear problems.

Analysis of Atmosphere Momentum, Price Perception and Brand Image on Sales Customer Satisfaction Batik in Central Lombok

This study aims to explore the influence of atmosphere momentum analysis, price perception, and brand image on customer satisfaction with batik in Central Lombok. This research involved 200 respondents selected through a purposive sampling procedure. The analytical method used is descriptive qualitative. The population of this study were visitors to Kisaran batik in the last 5 months. The research results show that the analysis variables of atmosphere momentum, price perception, and brand image have a significant impact on customer satisfaction with the batik range as a whole. These findings are consistent with the models and colors offered by Kisaran batik. This research provides a deeper understanding of the factors that influence customer satisfaction in the context of batik in Central Lombok. Thus, this research provides an important contribution to the understanding of the relationship between atmosphere momentum, price perception, brand image, and customer satisfaction in the context of batik. The practical implications of these findings can help stakeholders in developing more effective marketing strategies to increase customer satisfaction in the batik industry in Central Lombok. Additionally, this research also highlights the importance of considering these factors in designing satisfying customer experiences and strengthening brand image.

Relativistic spin dynamics for vector mesons

We propose a relativistic theory for spin density matrices of vector mesons based on Kadanoff-Baym equations in the closed-time-path formalism. The theory puts the calculation of spin observables such as the spin density matrix element ρ00 for vector mesons on a solid ground. Within the theory we formulate ρ00 for ϕ mesons into a factorization form in separation of momentum and spacetime variables. We argue that the main contribution to ρ00 at lower energies should be from the ϕ fields that can polarize the strange quark and antiquark in the same way as electromagnetic fields. The key observation is that there is correlation inside the ϕ meson wave function between the ϕ field that polarizes the strange quark and that polarizes the strange antiquark. This is reflected by the fact that the contributions to ρ00 are all in squares of fields that are nonvanishing even if the fields may strongly fluctuate in spacetime. The fluctuation of strong force fields can be extracted from ρ00 of unflavored vector mesons as links to fundamental properties of quantum chromodynamics. Published by the American Physical Society 2024

Tangent functor on microformal morphisms, and non-linear pullbacks for forms and cohomology

We show how the tangent functor extends from ordinary smooth maps to “microformal morphisms” (also called “thick morphisms”) of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations between the cotangent bundles specified by generating functions depending on position variables on the source manifold and momentum variables on the target manifold (as formal power expansions), regarded as part of the structure. Microformal morphisms act on functions by non-linear (in general) pullbacks. We obtain here non-linear pullbacks of (pseudo)differential forms and show that they respect the de Rham differentials as “non-linear chain maps” that can induce non-linear transformations of cohomology.

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

In this work, we compute the Lewis and Berry phases for a gravitational wave interacting with a two dimensional quantum harmonic oscillator in the transverse-traceless gauge. We have considered a gravitational wave consisting of the plus polarization term only. Considering the cross polarization term to be absent makes the Hamiltonian separable in terms of the first and the second spatial coordinates. We then compute the Lewis phase by assuming a suitable form of the Lewis invariant considering only quadratic order contributions from both position and momentum variables. Next, we obtain two Lewis invariants corresponding to each separable part of the full Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase. Then making an adiabatic approximation enables us to isolate the Berry phase for the full system. After this we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency. Finally, we consider a gravitational wave with cross polarization only interacting with an isotropic two dimensional harmonic oscillator. For this we obtain the Lewis phase and the total Berry phase of the system, which is found to be dependent upon the cross polarization part of the gravitational wave.

Photoproduction of P-wave doubly charmed baryon at future e+e− collider

The photoproduction of P-wave doubly charmed baryon (Ξcc) is investigated in the context of future high-energy and high-luminosity e+e− colliders. The direct photoproduction via the sub-process γ+γ→Ξcc+c¯+c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\gamma +\\gamma \ o {\\Xi}_{cc}+\\overline{c}+\\overline{c} $$\\end{document} and the resolved channel γ+g→Ξcc+c¯+c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\gamma +g\ o {\\Xi}_{cc}+\\overline{c}+\\overline{c} $$\\end{document} are considered. Within the framework of non-relativistic QCD, the calculation encompasses four P-wave (cc)-diquark configurations: cc3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {(cc)}_{\\overline{\ extbf{3}}} $$\\end{document}[1P1], (cc)6[3P0], (cc)6[3P1] and (cc)6[3P2]. The two S-wave states, cc3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {(cc)}_{\\overline{\ extbf{3}}} $$\\end{document}[3S1] and (cc)6[1S0], are also included for comparison. The cross sections, as well as the differential distributions involving transverse momentum, rapidity, and angular variables, have been computed. Numerical results reveal that the resolved photoproduction process plays a significant role and can provide dominant contributions. The photoproduction rate of the P-wave Ξcc is approximately one order of magnitude lower than that of the S-wave.

SARAH-M: A fast stochastic recursive gradient descent algorithm via momentum

As a simple but effective way, the momentum method has been widely adopted in stochastic optimization algorithms for large-scale machine learning problems and the success of stochastic optimization with the momentum term for many applications in machine learning and other related areas has been reported everywhere. However, the understanding of how the momentum improves the performance of modern variance reduced stochastic gradient algorithms, e.g., the stochastic dual coordinate ascent average gradient (SDCA) method, the stochastically controlled stochastic gradient (SCSG) method, the stochastic recursive gradient algorithm (SARAH), etc., is still limited. To tackle this issue, this work studies the performance of SARAH with the momentum term theoretically and empirically, and develops a novel variance reduced stochastic gradient algorithm, termed as SARAH-M. We rigorously prove that SARAH-M attains a linear rate of convergence for minimizing the strongly convex function. We further propose an adaptive SARAH-M method (abbreviated as AdaSARAH-M) by incorporating the random Barzilai–Borwein (RBB) technique into SARAH-M, which provides an easy way to determine the step size for the original SARAH-M algorithm. The theoretical analysis that shows AdaSARAH-M with a linear convergence speed is also provided. Moreover, we show that the complexity of the proposed algorithms can outperform modern stochastic optimization algorithms. Finally, the numerical results, compared with state-of-the-art algorithms on benchmarking machine learning problems, verify the efficacy of the momentum in variance reduced stochastic gradient algorithms.

Epidemiology and Time-Loss Shoulder Injuries in Professional South African Rugby Players: A Prospective Study That Focuses on Real-Time Collision Data during a Tackle

Background: In rugby, the shoulder contributes to attack/defence during collisions, tackling, falling, scrummaging, and mauling. We investigated the frequency, tissue, and pathology type of shoulder injuries per player position among professional South African rugby players, and compared injury severity in the context of momentum, intensity, and collision variables. Methods: A prospective study collecting shoulder injury data of 80 male Super Rugby players (&gt;18 years) over 4 seasons (2018–2021). Players wore a Catapult Evo GPS unit during training and match-play, recording performance variables and collision forces during injury. We collected tissue and pathology types of injury from players’ medical files, clinical examinations, and special investigations. Results: Shoulder injuries contributed to 17% of all injuries, ranging from 2 to 34% per year. Forwards (63%) sustained most shoulder injuries, specifically locks (30%). Acromioclavicular (AC) joint (47%) was mostly involved, and ligament/joint capsule (65%) was the most common tissue type injured. Injuries with the highest average momentum resulted in players suffering minimal to mild severity injuries (1–7 days time-loss). Backs (631.15 kg·m/s) required less momentum than forwards (816.00 kg·m/s) to suffer injuries resulting in &gt;28 days time-loss (p = 0.008). Backs encountered higher match intensity (67.76 m/min, p = 0.031) and highest average collisions (0.28/min) without suffering more severe (&gt;28 days time-loss) injuries. Match intensity of &gt;60 m/min resulted in more than 55% of shoulder injuries. Conclusion: One in six injuries in this cohort was shoulder-related. Forwards, specifically locks, sustained most shoulder injuries. The AC joint was the tissue type that mainly contributed. Backline players were involved in higher velocity contact, game intensity, and collision frequency but suffered fewer injuries. However, they required less momentum to sustain more severe injuries.

Large-step neural network for learning the symplectic evolution from partitioned data

ABSTRACT In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate ($\boldsymbol q$) and momentum ($\boldsymbol p$) variables generated by a symplectic mapping. Based on Chen &amp; Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series ($\boldsymbol q_i$, $\boldsymbol p_i$) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25 000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work: (1) the conservation of the Jacobi integral and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.