Three-dimensional Angular Momentum Research Articles

Kinematical coherence between satellite galaxies and host stellar discs for MaNGA and SAMI galaxies

ABSTRACT The effect of angular momentum on galaxy formation and evolution has been studied for several decades. Our recent two papers using IllustrisTNG-100 simulation have revealed the acquisition path of the angular momentum from large-scale environment (satellites within hundreds of kpc) through the circumgalactic medium (CGM) to the stellar discs, putting forward the co-rotation scenario across the three distance scales. In real observations, although the rotation signature for the CGM and environmental three-dimensional angular momentum are difficult to obtain, line-of-sight kinematics of group member galaxies and stellar disc kinematics of central galaxies are available utilizing existing group catalogue data and integral field unit (IFU) data. In this paper, we use (1) the group catalogue of SDSS DR7 and MaNGA IFU stellar kinematic maps and (2) the group catalogue of GAMA DR4 data and SAMI IFU stellar kinematic maps, to test if the prediction above can be seen in real data. We found the co-rotation pattern between stellar discs and satellites can be concluded with 99.7 per cent confidence level (∼3σ) when combining the two data sets. And the random tests show that the signal can be scarcely drawn from random distribution.

Dynamical and topological properties of the spin angular momenta in general electromagnetic fields

Spin angular momenta play important roles in light–matter interactions, leading to the emergence of the spin Hall effect and topological quasiparticles in modern optics. The typical approach is to decompose the spins of plane electromagnetic waves into longitudinal and transverse components, yet this description is not easily transferable to more structured electromagnetic environments. Here, we developed a field theory to reveal the physical origin and topological properties of longitudinal and transverse spins for arbitrary electromagnetic waves (including water waves and acoustic waves) in both near-field and free space. For electromagnetic waves carrying intrinsic helicity, we observed the emergence of helicity-dependent transverse spin possessing helicity-dependent spin-momentum locking. To verify that the number of spin-momentum locking states coincides with the spin Chern number, we experimentally measured the three-dimensional spin angular momentum densities of Bloch-type optical skyrmions. Our findings yield valuable insight for constructing spin-based field theory and exploiting optical topological quasiparticle-based applications.

Non-classical photonic spin texture of quantum structured light

Classical structured light with controlled polarization and orbital angular momentum (OAM) of electromagnetic waves has varied applications in optical trapping, bio-sensing, optical communications and quantum simulations. However, quantum noise and photon statistics of three-dimensional photonic angular momentum are relatively less explored. Here, we develop a quantum framework and put forth the concept of quantum structured light for space-time wavepackets at the single-photon level. Our work deals with three-dimensional angular momentum observables for twisted quantum pulses beyond scalar-field theory as well as the paraxial approximation. We show that the spin density generates modulated helical texture and exhibits distinct photon statistics for Fock-state vs. coherent-state twisted pulses. We introduce the quantum correlator of photon spin density to characterize nonlocal spin noise providing a rigorous parallel with electronic spin noise. Our work can lead to quantum spin-OAM physics in twisted single-photon pulses and opens explorations for phases of light with long-range spin order.

Differences in balance control between healthy younger and older adults during steady-state walking

Each year approximately one third of older adults fall and experience extensive musculoskeletal injuries and functional disabilities. An important element in maintaining dynamic balance is the regulation of whole-body angular momentum, which is achieved by proper foot placement with respect to the body center-of-mass as well as generation of appropriate ground reaction forces. Analyzing these quantities in younger and older adults may provide insight into differences in their underlying mechanics for maintaining dynamic balance. This study examined three-dimensional whole-body angular momentum in 13 healthy older (71.8 ± 8.3 years) and 9 younger (23.2 ± 2.8 years) adults walking at their self-selected and fastest-comfortable speeds. The older adults had a significantly higher range of frontal-plane angular momentum compared to the younger adults at both speeds, suggesting poorer mediolateral balance control. This difference was related to the older adults having a wider foot placement with respect to the body center-of-mass, which when combined with the vertical ground reaction force, created a higher destabilizing external moment during single-limb stance that acts to rotate the body towards the contralateral swing leg. To counteract this destabilizing moment, the older adults generated a higher hip abduction moment. There were no differences in the range of sagittal- and transverse-plane angular momentum between age groups at either speed. These results suggest that control of dynamic balance in the frontal-plane is more challenging than in the sagittal-plane for older adults and highlight the importance of proper weight transfer mechanisms and hip abductor force production for maintaining mediolateral balance during walking.

Optical needles with arbitrary three-dimensional spin angular momentum.

Based on our previous research on optical needles with arbitrary three-dimensional (3D) polarization, we investigate the relationship between the electric field and spin angular momentum (SAM). We have realized optical needles with arbitrary 3D spin-orientation and SAM per photon. To our best knowledge, it is the first time to obtain optical needles whose SAM can be customized on both direction and size. The relative error between the obtained spin and customized spin is always less than 5% even if SAM per photon is very small.

Spatial orientations of angular momentum vectors of galaxies in Supercluster S [173+014+0082

The spin vector orientation of 1302 SDSS (Sloan Digital Sky Survey) galaxies in Supercluster S[173+014+0082] having redshift 0.076 to 0.091 has been analysed. The positions, position angles and inclination angles of galaxies are used to convert two-dimensional observed parameters into three-dimensional angular momentum vectors of the galaxy using the `position angle-inclination' method. The expected isotropic distribution curves are determined performing numerical simulation by generating 107 virtual galaxies. The observed distribution is compared with the expected isotropic distribution curves using three statistical tools namely Chi-square test, auto-correlation test and Fourier test. Redshift map is studied and found that the distributions fit with the Gaussian. No preferred alignment of angular momentum vectors is noticed, supporting Hierarchy model of galaxy formation.
 BIBECHANA 18 (2021) 26-32

Distribution of high-dimensional orbital angular momentum entanglement over a 1 km few-mode fiber

High-dimensional entanglement has demonstrated its potential for increasing channel capacity and resistance to noise in quantum information processing. However, distributing it is a challenging task, imposing severe restrictions on its application. Here we report the first distribution of three-dimensional orbital angular momentum (OAM) entanglement via a 1-km-long few-mode optical fiber. Using an actively stabilizing phase precompensation technique, we successfully transport one photon of a three-dimensional OAM entangled photon pair through the fiber. The distributed OAM entangled state still shows a fidelity up to 71% with respect to the three-dimensional maximally entangled state (MES). In addition, we certify that the high-dimensional quantum entanglement survives the transportation by violating a generalized Bell inequality, obtaining a violation of ∼ 3 standard deviations from the classical limit with I 3 = 2.12 ± 0.04 . The method we developed can be extended to a higher OAM dimension and larger distances in principle. Our results make a significant step towards future OAM-based high-dimensional long-distance quantum communication.

Three-Dimensional Simultaneous Arbitrary-Way Orbital Angular Momentum Generator Based on Transformation Optics.

In wireless communications, people utilize the technology of diversity against multipath fading, so as to improve the reliability of communication equipment. One of the long-standing problems in diversity antennas is the limited number of diversity in a certain space. In this paper, we provide a solution to this issue by a three-dimensional (3D) simultaneous arbitrary-way orbital angular momentum (OAM) generator (3D SAWOG) based on transformation optics. The proposed 3D SAWOG consists of a metamaterial block and a group of transformation cylinders, by which arbitrary-way planar wavefronts can be converted to helical wavefronts with various topological charges simultaneously. The 2D four-way OAM generator and the 3D SAWOG are analyzed, designed, and simulated. The simulation results validate the performance of a 3D SAWOG successfully, indicating that the proposed model possess a high mode purity and expansibility. The SAWOG can be used as a novel diversity antenna array due to the orthogonal property among different modes, which could provide more degrees of freedom than traditional dual-polarization antennas, further improving the reliability of the communication systems.

Microscopic benchmark study of triaxiality in low-lying states of76Kr

We report on a seven-dimensional generator coordinate calculation in the two deformation parameters $\beta$ and $\gamma$ together with projection on three-dimensional angular momentum and two particle numbers for the low-lying states in $^{76}$Kr. These calculations are based on covariant density functional theory. Excellent agreement is found with the data for the spectrum and the electric multipole transition strengths. This answers the important question of dynamic correlations and triaxiality in a fully microscopic way. We find that triaxial configurations dominate both the ground state and the quasi $\gamma$-band. This yields a different picture from the simple interpretation in terms of "coexistence of a prolate ground state with an oblate low-lying excited state", which is based on the measured sign of spectroscopic quadrupole moments. This study also provides for the first time a benchmark for the collective Hamiltonian in five dimensions. Moreover, we point out that the staggering phase of the $\gamma$-band is not a safe signature for rigid triaxiality of the low-energy structure.

Whole-body angular momentum during stair ascent and descent

The generation of whole-body angular momentum is essential in many locomotor tasks and must be regulated in order to maintain dynamic balance. However, angular momentum has not been investigated during stair walking, which is an activity that presents a biomechanical challenge for balance-impaired populations. We investigated three-dimensional whole-body angular momentum during stair ascent and descent and compared it to level walking. Three-dimensional body-segment kinematic and ground reaction force (GRF) data were collected from 30 healthy subjects. Angular momentum was calculated using a 13-segment whole-body model. GRFs, external moment arms and net joint moments were used to interpret the angular momentum results. The range of frontal plane angular momentum was greater for stair ascent relative to level walking. In the transverse and sagittal planes, the range of angular momentum was smaller in stair ascent and descent relative to level walking. Significant differences were also found in the ground reaction forces, external moment arms and net joint moments. The sagittal plane angular momentum results suggest that individuals alter angular momentum to effectively counteract potential trips during stair ascent, and reduce the range of angular momentum to avoid falling forward during stair descent. Further, significant differences in joint moments suggest potential neuromuscular mechanisms that account for the differences in angular momentum between walking conditions. These results provide a baseline for comparison to impaired populations that have difficulty maintaining dynamic balance, particularly during stair ascent and descent.

Whole-body angular momentum in incline and decline walking

Angular momentum is highly regulated over the gait cycle and is important for maintaining dynamic stability and control of movement. However, little is known regarding how angular momentum is regulated on irregular surfaces, such as slopes, when the risk of falling is higher. This study examined the three-dimensional whole-body angular momentum patterns of 30 healthy subjects walking over a range of incline and decline angles. The range of angular momentum was either similar or reduced on decline surfaces and increased on incline surfaces relative to level ground, with the greatest differences occurring in the frontal and sagittal planes. These results suggest that angular momentum is more tightly controlled during decline walking when the risk of falling is greater. In the frontal plane, the range of angular momentum was strongly correlated with the peak hip and knee abduction moments in early stance. In the transverse plane, the strongest correlation occurred with the knee external rotation peak in late stance. In the sagittal plane, all external moment peaks were correlated with the range of angular momentum. The peak ankle plantarflexion, knee flexion and hip extension moments were also strongly correlated with the sagittal-plane angular momentum. These results highlight how able-bodied subjects control angular momentum differently on sloped surfaces relative to level walking and provide a baseline for comparison with pathological populations that are more susceptible to falling.

Spatial orientation of angular momentum vector of galaxies in three merging binary clusters

We present spatial orientations of angular momentum vectors of galaxies in three merging binary clusters A1750, A3395 and A3528. The axial ratio and intrinsic flatness of galaxy are used to convert two-dimensional given parameters into three-dimensional angular momentum vector of the galaxy. We have performed K-S, Kuiper and Fourier tests in order to examine non-random effects. The merging binary cluster A3395 that exhibits strongly distorted feature in its maps of temperature and surface brightness showed a random orientation in the spatial orientation of angular momentum vectors of galaxies. A weak anisotropic distribution in the angular momentum vectors of galaxies is noticed in the sub-structures of A3528. We suspect a relation between the stages of merging and the non-random alignments of galaxies in the sub-structures of the binary clusters. Possible explanation of the results will be discussed.

LOW-LYING STATES IN 30Mg: A BEYOND RELATIVISTIC MEAN-FIELD INVESTIGATION

The recently developed model of three-dimensional angular momentum projection plus generator coordinate method on top of triaxial relativistic mean-field states has been applied to study the low-lying states of 30 Mg . The effects of triaxiality on the low-energy spectra and E 0 and E 2 transitions are examined.

Three-dimensional angular momentum projection in relativistic mean-field theory

Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero-range \ensuremath{\delta} forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes $^{24}\mathrm{Mg}$, $^{30}\mathrm{Mg}$, and $^{32}\mathrm{Mg}$.

Restoration of rotational symmetry in deformed relativistic mean-field theory

We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei. Collective states with good quantum angular momentum are built projecting out the intrinsic deformed mean-field states. Results for 24Mg are shown as an illustrative application.

Three-Dimensional Angular Momentum Projected Relativistic Point-Coupling Approach for Low-Lying Excited States in 24Mg

A full three-dimensional angular momentum projection on top of a triaxial relativistic mean-Geld calculation is implemented for the first time. The underlying Lagrangian is a point coupling model and pairing correlations are taken into account by a monopole force. This method is applied for the low-lying excited states in 24Mg. Good agreement with the experimental data is found for the ground state properties. A minimum in the potential energy surface for the 2+1 state, with β ≃ 0.55,γ ≃ 10°, is used as the basis to investigate the rotational energy spectrum as well as the corresponding B(E2) transition probabilities as compared to the available data.

Further Simplification of the Manifold Correction Method for Orbit Integration

By introducing some quantities defined on the moving orbital plane, we have developed three ways to further reduce the number of variables in our two simplified methods of manifold correction, from nine to seven or six per celestial body. Among these, the simplest option uses a set of six variables consisting of the three-dimensional orbital angular momentum vector, the two independent components of the Laplace integral vector on the moving orbital plane, and a true orbital longitude measured from an origin solely determined from the orbital angular momentum vector. This scheme no longer requires any manifold correction, as does the standard method to integrate the Cartesian coordinates and velocity. However, the new method is much more precise than the standard method. For example, the longitude error of Mercury in a simultaneous integration of the Sun and nine major planets with a step size of 1.4 days exceeds 360° after a few thousand years when using the standard method but remains at the milliarcsecond level if the new method is used. In addition, the new method achieves better performance than any of the manifold correction methods we have developed, as long as round-off errors are negligible.

Singularity Analysis of Variable Speed Control Moment Gyros

Single-gimbal control moment gyros (CMGs) have many advantages over other actuators for attitude control of spacecraft. For instance, they act as torque amplifiers and, thus, are suitable for slew maneuvers. However, their use as torque actuators is hindered by the presence of singularities, that, when encountered, do not allow a CMG cluster to generate torques about arbitrary directions. One method to overcome this drawback is to use variable-speed single-gimbal control moment gyros (VSCMGs). Whereas the wheel speed of a conventional CMG is constant, VSCMGs are allowed to have variable wheel speed. Therefore, VSCMGs have extra degrees of freedom that can be used to achieve additional objectives, such as singularity avoidance and/or power tracking, as well as attitude control. The singularity problem of a VSCMGs cluster is studied in detail for the cases of attitude tracking, with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. This criterion can be used to size the wheels and develop appropriate momentum damping strategies tailored to the specific mission requirements. I. Introduction A CONTROL moment gyro (CMG) is a device used as an actuator for attitude control of spacecraft. It generates torques through angular momentum transfer to and from the main spacecraft body. This is achieved by changing the direction of the angular momentum vector of a gimballed flywheel. Because a CMG operates in a continuous manner, contrary to the gas jet’s on/off operation, it can achieve precise attitude control. Moreover, as with other momentum exchange devices, for example, reaction wheels, it does not consume any propellant, thus prolonging the operational life of the spacecraft. Single-gimbal CMGs essentially act as torque amplifiers. 1 This torque amplification property makes them especially advantageous as attitude control actuators for large space spacecraft and space structures, for example, a space station. In fact, single-gimbal and double-gimbal CMGs have been used for attitude control of the Skylab, the MIR and the International Space Station (ISS). An obstacle when using a CMG system in practice is the existence of singular gimbal angle states for which the CMGs cannot generate a torque along arbitrary directions. At each singular state, all admissible torque directions lie on a two-dimensional surface in the three-dimensional angular momentum space; therefore, the CMG system cannot generate a torque normal to this surface. The CMG singularities can be classified into two categories: 1) external or saturated singularities in which the total angular momentum sum of the CMGs lies on the maximum momentum envelope and 2) internal singularities in which the total momentum lies inside this envelope. The external singularities can be easily anticipated from the given CMG configuration and mission profile; therefore, they can be taken into account at the design step. A properly designed momentum management scheme can also relieve the external singularity problem. The internal CMG singularities, on the other hand, are in general difficult to anticipate. Avoiding such internal singularities has, thus, been a long-standing problem in the CMG

Bound states in one and two spatial dimensions

In this article we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive potential has a bound state, it is easy to construct examples where weak potentials have an infinite number of bound states. These examples have potentials which decrease at infinity faster than expected. Using somewhat stronger conditions, we derive explicit bounds on the number of bound states in one dimension, using known results for the three-dimensional zero angular momentum. A change of variables which allows us to go from the one-dimensional case to that of two dimensions results in a bound for the zero angular momentum case. Finally, we obtain a bound on the total number of bound states in two dimensions, first for the radial case and then, under stronger conditions, for the noncentral case.

Quantum kicked top: Lie algebraic approach

Dynamical system describing nonlinear dynamics of a three-dimensional angular momentum J is analysed. It is shown that the dynamics can be linearised by suitable embedding in a larger linear space of μ(2 j + 1) Lie algebra. Consequences of the linearisation are analysed and, especially, possibility of defining dual classical dynamics is considered.