Terms Of Angular Momentum Research Articles

Deformations of Axially Symmetric Initial Data and the Mass-Angular Momentum Inequality

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which preserves the relevant geometry, while achieving the maximal condition and its implied inequality (in a weak sense) for the scalar curvature; this answers a question posed by R. Schoen. The primary equation involved, bears a strong resemblance to the Jang-type equations studied in the context of the positive mass theorem and the Penrose inequality. Each equation in the system is analyzed in detail individually, and it is shown that appropriate existence/uniqueness results hold with the solution satisfying desired asymptotics. Lastly, it is shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass and angular momentum.

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the inertial and the rotating frame, using three tetrad fields: one for each of two frameworks proposed to select the tetrad field so as to solve this non-uniqueness problem, and one proposed by Ryder. We find that Mashhoon's term is there if the tetrad rotates as does the reference frame --- but then it is also there in the energy operator for the inertial frame. In fact, the Dirac Hamiltonian operators in two reference frames in relative rotation, but corresponding to the same tetrad field, differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.

On extremal limits and duality orbits of stationary black holes

With reference to the effective three-dimensional description of stationary, single center solutions to (ungauged) symmetric supergravities, we complete a previous analysis on the definition of a general geometrical mechanism for connecting global symmetry orbits (duality orbits) of non-extremal solutions to those of extremal black holes. We focus our attention on a generic representative of these orbits, providing its explicit description in terms of D=4 fields. As a byproduct, using a new characterization of the angular momentum in terms of quantities intrinsic to the geometry of the D=3 effective model, we are able to prove on general grounds its invariance, as a function of the boundary data, under the D=4 global symmetry. In the extremal under-rotating limit it becomes moduli-independent. We also discuss the issue of the fifth parameter characterizing the four-dimensional seed solution, showing that it can be generated by a transformation in the global symmetry group which is manifest in the D=3 effective description.

Green's function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments

We develop a nonlocal-response generalization to the Green-function surface-integral method (GSIM), also known as the boundary-element method (BEM). This numerically light method can accurately describe the linear hydrodynamic nonlocal response of arbitrarily shaped plasmonic nanowires in arbitrary dielectric backgrounds. All previous general-purpose methods for nonlocal response are bulk methods. We also expand the possible geometries to which the usual local-response GSIM can be applied, by showing how to regularize singularities that occur in the surface integrals when the nanoparticles touch a dielectric substrate. The same regularization works for nonlocal response. Furthermore, an effective theory is developed to explain the numerically observed nonlocal effects. The nonlocal frequency blueshift of a cylindrical nanowire in an inhomogeneous background generally increases as the nanowire radius and the longitudinal wavenumber become smaller, or when the effective background permittivity or the mode inhomogeneity increase. The inhomogeneity can be expressed in terms of an effective angular momentum of the surface-plasmon mode. We compare local and nonlocal response of free-standing nanowires, and of nanowires close to and on top of planar dielectric substrates. Especially for the latter geometry, considerable differences in extinction cross sections are found for local as compared to nonlocal response, similar to what is found for plasmonic dimer structures.

Entropy-product rules for charged rotating black holes

We study the universal nature of the product of the entropies of all horizons of charged rotating black holes. We argue, by examining further explicit examples, that when the maximum number of rotations and/or charges are turned on, the entropy product is expressed in terms of angular momentum and/or charges only, which are quantized. (In the case of gauged supergravities, the entropy product depends on the gauge-coupling constant also.) In two-derivative gravities, the notion of the "maximum number" of charges can be defined as being sufficiently many non-zero charges that the Reissner-Nordstrom black hole arises under an appropriate specialisation of the charges. (The definition can be relaxed somewhat in charged AdS black holes in $D\ge 6$.) In higher-derivative gravity, we use the charged rotating black hole in Weyl-Maxwell gravity as an example for which the entropy product is still quantized, but it is expressed in terms of the angular momentum only, with no dependence on the charge. This suggests that the notion of maximum charges in higher-derivative gravities requires further understanding.

Recent estimates of Earth‐atmosphere interaction torques and their use in studying polar motion variability

The use of Earth‐atmosphere interaction torques is a potential but generally less addressed alternative to the classical angular momentum approach for modeling variations in Earth rotation. We present an update on this subject for the purpose of explaining seasonal and intraseasonal polar motion variability based on the output of the most recent meteorological reanalysis systems of the ECMWF (European Centre for Medium‐Range Weather Forecasts) and NASA's Global Modeling and Assimilation Office. The agreement of both models in terms of the three prime torque constituents is shown to be far superior to that of the conventionally deployed wind term of atmospheric angular momentum (AAM). A sufficiently good closure of the equatorial AAM budget equation within the ECMWF reanalysis provides additional endorsement for the use of atmospheric torques as excitation measures. When used as such, polar motion residuals after reduction of the AAM pressure term, as well as oceanic and hydrological excitation, are considerably better modeled by the torque‐based quantities than by the standard wind term of AAM, in particular at intraseasonal periodicities. This finding is obtained by means of a newly proposed, hybrid excitation formalism, which derives the AAM counterparts of torque terms from inversion of the AAM budget equation in the frequency domain.

Lower bounds for the area of black holes in terms of mass, charge, and angular momentum

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a single black hole in the setting of axisymmetric maximal initial data sets for the Einstein-Maxwell equations, when the non-electromagnetic matter fields are not charged and satisfy the dominant energy condition. It is shown that the inequality is saturated if and only if the initial data arise from the extreme Kerr-Newman spacetime. Further refinements are given when either charge or angular momentum vanish. Lastly, we discuss the validity of the lower bound in the presence of multiple black holes.

First observations of quasi 120 day oscillation in Mesospheric winds and temperature: Observations inferred from Meteor Radar

AbstractFor the first time, the presence of quasi 120 day oscillation in the neutral winds and temperature at mesosphere and lower thermosphere (MLT) region, measured using meteor wind radar over an equatorial station Thumba (8.5°N, 76.5°E) is discussed. The amplitudes of quasi 120 day oscillation as a function of height have been established over Thumba. The origin of the quasi 120 day oscillation in geophysical parameters at MLT heights are discussed in terms of the atmospheric angular momentum, F10.7, and Lyman‐alpha solar flux and nonlinear interactions between annual and semiannual oscillations. The significance of the present study lies in providing the observational evidence for quasi 120 day oscillation in the MLT region and in discussing the possible source mechanisms for the observed oscillation.

Vibrational Configuration Interaction Using a Tiered Multimode Scheme and Tests of Approximate Treatments of Vibrational Angular Momentum Coupling: A Case Study for Methane

We present vibrational configuration interaction calculations employing the Watson Hamiltonian and a multimode expansion. Results for the lowest 36 eigenvalues of the zero total angular momentum rovibrational spectrum of methane agree with the accurate benchmarks of Wang and Carrington to within a mean unsigned deviation of 0.68, 0.033, and 0.014 cm(-1) for 4-mode, 5-mode, and 6-mode representations, respectively. We note that in the case of the 5-mode results, this is a factor of 10 better agreement than for 5-mode calculations reported earlier by Wu, Huang, Carter, and Bowman for the same set of eigenvalues, which indicates that the multimode expansion is even more rapidly convergent than previously demonstrated. Our largest calculations employ a tiered approach with matrix elements treated using a variable-order multimode expansion with orders ranging from 4-mode to 7-mode; strategies for assigning matrix elements to particular multimode tiers are discussed. Improvements of 7-mode coupling over 6-mode coupling are small (averaging 0.002 cm(-1) for the first 36 eigenvalues) suggesting that 7-mode coupling is sufficient to fully converge the results. A number of approximate treatments of the computationally expensive vibrational angular momentum terms are explored. The use of optimized vibrational quadratures allows rapid integration of the matrix elements, especially the vibrational angular momentum terms, which require significantly fewer quadrature points than are required to integrate the potential. We assign the lowest 243 states and compare our results to those of Wang and Carrington, who provided assignments for the same set of states. Excellent agreement is observed for most states, but our results are lower for some of the higher-energy states by as much as 20 cm(-1), with the largest deviations being for the states with six quanta of excitation in the F2 bends, suggesting that the earlier results were not fully converged with respect to the basis set. We also provide corrections to several of the state assignments published previously.

MAMPOSSt: Modelling Anisotropy and Mass Profiles of Observed Spherical Systems – I. Gaussian 3D velocities

Mass modelling of spherical systems through internal kinematics is hampered by the mass–velocity anisotropy degeneracy inherent in the Jeans equation, as well as the lack of techniques that are both fast and adaptable to realistic systems. A new fast method, called Modelling Anisotropy and Mass Profiles of Observed Spherical Systems (MAMPOSSt), is developed and thoroughly tested. MAMPOSSt performs a maximum-likelihood fit of the distribution of observed tracers in projected phase space (projected radius and line-of-sight velocity). As in other methods, MAMPOSSt assumes a shape for the gravitational potential (or equivalently the total mass profile). However, instead of postulating a shape for the distribution function in terms of energy and angular momentum, or supposing Gaussian line-of-sight velocity distributions, MAMPOSSt assumes a velocity anisotropy profile and a shape for the 3D velocity distribution. The formalism is presented for the case of a Gaussian 3D velocity distribution. In contrast to most methods based on moments, MAMPOSSt requires no binning, differentiation, nor extrapolation of the observables. Tests on cluster-mass haloes from ΛCDM dissipationless cosmological simulations indicate that, with 500 tracers, MAMPOSSt is able to jointly recover the virial radius, tracer scale radius, dark matter scale radius and outer or constant velocity anisotropy with small bias (<10 per cent on scale radii and <2 per cent on the two other quantities) and inefficiencies of 10, 27, 48 and 20 per cent, respectively. MAMPOSSt does not perform better when some parameters are frozen, and even particularly worse when the virial radius is set to its true value, which appears to be the consequence of halo triaxiality. The accuracy of MAMPOSSt depends weakly on the adopted interloper removal scheme, including an efficient iterative Bayesian scheme that we introduce here, which can directly obtain the virial radius with as good precision as MAMPOSSt. Additional tests are made on the number of tracers, the stacking of haloes, the chosen aperture, and the density and velocity anisotropy models. Our tests show that MAMPOSSt with Gaussian 3D velocities is very competitive with other methods that are either currently restricted to constant velocity anisotropy or 3 orders of magnitude slower. These tests suggest that MAMPOSSt can be a very powerful and rapid method for the mass and anisotropy modelling of systems such as clusters and groups of galaxies, elliptical and dwarf spheroidal galaxies.

Study of Wheel Activated Gyroscopic-like Motion in Spacecraft Rotational Dynamics

This research investigates the applications of a gyroscopic-like motion embedded in the attitude dynamics of a rigid-body that can be induced with an onboard torque wheel. The motion may be utilized by a rigid spacecraft to regain its attitude stability from a tumbling or a flat-spin situation to rotate about a designated principal axis, which parallels to the spin axis of the torque wheel. Also, the total angular momentum of the spacecraft remains conserved during the process as disturbance torques around the system in space are considered relatively very small and are ignored. To start the motion, the wheel is manipulated to rotate the spacecraft platform with reaction torque such that the projection of the total angular momentum falls in a proper quadrant on the plane perpendicular to the designated principal axis. Then, the projection is able to activate a self-induced, gyroscopic- like motion, which in effect transfers angular momentum to the wheel and the platform along the designated principal axis, aligning the designated principal axis with the total angular momentum and reducing the nutation angle between the two to zero. The phenomenon can be derived from the attitude model in terms of angular momentum. The control law of the wheel torque is formulated with the method of feedback linearization following the results from the Lyapunov stability analysis. Without any direct control effort, simulation results indicate that efficient time and energy can be achieved with effective attitude recovery of a spacecraft to any of the principal axis compared to the existing methods, and the wheel momentum accumulated during the motion can be predicted after the alignment maneuver.

Spin-orbital state induced by strong spin-orbit coupling

To clarify a crucial role of a spin-orbit coupling in the emergence of novel spin-orbital states in 5d-electron compounds such as Sr2IrO4, we investigate ground state properties of a t2g-orbital Hubbard model on a square lattice by Lanczos diagonalization. In the absence of the spin-orbit coupling, the ground state is spin singlet. When the spin-orbit coupling is strong enough, the ground state turns into a weak ferromagnetic state. The weak ferromagnetic state is a singlet state in terms of an effective total angular momentum. Regarding the orbital state, we find the so-called complex orbital state, in which real xy, yz, and zx orbital states are mixed with complex coefficients.

Outstanding features of reactions with halo nuclei

Recent results for total reaction and fusion excitation functions for halo systems are compiled. The striking similarity in the behavior of total cross sections for proton-halo (8B) and neutron-halo (6He) systems is pointed out. Static and dynamic halo effects are elucidated by comparing data for a neutron-halo nucleus and its core. Fusion cross sections are discussed in terms of a maximum angular momentum for fusion, Lf. A linear energy dependence for Lf is consistent with the data for all the existing measurements so this might actually be a characteristic feature of true halo systems. A qualitative difference between the fusion of neutro-halo and proton-halo systems also is pointed out.

Hot subdwarf stars in close-up view

Subluminous B stars (sdBs) form the extremely hot end of the horizontal branch and are therefore related to the blue horizontal branch (BHB) stars. While the rotational properties of BHB stars have been investigated extensively, studies of sdB stars have concentrated on close binaries that are influenced by tidal interactions between their components. Here we present a study of 105 sdB stars, which are either single stars or in wide binaries where tidal effects become negligible. The projected rotational velocities have been determined by measuring the broadening of metal lines using high-resolution optical spectra. All stars in our sample are slow rotators (${v_{\rm rot}\sin{i}}<10\,{\rm km\,s^{-1}}$). Furthermore, the $v_{\rm rot}\sin{i}$-distributions of single sdBs are similar to those of hot subdwarfs in wide binaries with main-sequence companions as well as close binary systems with unseen companions and periods exceeding $\simeq1.2\,{\rm d}$. We show that blue horizontal and extreme horizontal branch stars are also related in terms of surface rotation and angular momentum. Hot blue horizontal branch stars ($T_{\rm eff}>11\,500\,{\rm K}$) with diffusion-dominated atmospheres are slow rotators like the hot subdwarf stars located on the extreme horizontal branch, which lost more envelope and therefore angular momentum in the red-giant phase. The uniform rotation distributions of single and wide binary sdBs pose a challenge to our understanding of hot subdwarf formation. Especially the high fraction of helium white dwarf mergers predicted by theory seems to be inconsistent with the results presented here.

Implementation of gravitational shocks in two-dimensional Fokker-Planck models

We derive analytical formulae for drift and dispersion terms of energy and angular momentum (� ΔE� , � (ΔE) 2 � , � ΔJ� ,a nd� (ΔJ) 2 � )a s well as their cross term (� ΔEΔJ� ) for stellar systems under an impulsive perturbation. These terms are expressed as functions of E, J, and orbit averages of powers of radius (r) and the product of radius and velocity (rv), and we confirm our formulae with a numerical simulation. Then with another numerical simulation for a time-varying (Gaussian) perturbation, we find that the adiabatic corrections suggeted by Gnedin and Ostriker can be applied not only to the energy changes (drift and dispersion) but also tothe angular momentum changes, if the changes are expressed as functions of energy only. The corrections do not describe the changes accurately when the changes are considered as functions of both energy and angular momentum. The deviations between the numerical simulation and analytical expectations are consierable only in the cluster core though, where the effect of perturbation is relatively weaker. These results are to be implemented in two-dimensional (E − J) Fokker-Planck models of the evolution of globular clusters.

Angular momentum limit for fusion of halo and weakly bound systems

Recent experimental results for the fusion of the proton-halo system ${}^{8}\text{B}\phantom{\rule{-0.16em}{0ex}}+\phantom{\rule{-0.16em}{0ex}}{}^{58}\text{Ni}$ are discussed. A strong enhancement is observed both below and above the barrier. This is qualitatively different from the usual sub-barrier enhancement observed for many heavy-ion systems. Arguments are given that relate the enhancement to a static halo effect directly associated to the extended size of the proton-halo state. A simple single-barrier model is proposed which describes the fusion cross sections in terms of a maximum angular momentum for fusion, ${L}_{f}$. It is shown that a linear energy dependence for ${L}_{f}$ gives a surprisingly good description of the experimental fusion excitation function not only for ${}^{8}\text{B}\phantom{\rule{-0.16em}{0ex}}+\phantom{\rule{-0.16em}{0ex}}{}^{58}\text{Ni}$ but also for the neutron-halo systems ${}^{6}\text{He}\phantom{\rule{-0.16em}{0ex}}+\phantom{\rule{-0.16em}{0ex}}{(}^{209}\text{Bi},{}^{64}\text{Zn})$. The model is also applied to several weakly bound systems.

GPDs AND TMDs

For transversely polarized nucleons the distribution of quarks in the transverse plane is transversely shifted and that shift can be described in terms of Generalized Parton Distributions (GPDs). This observation provides a 'partonic' derivation of the Ji-relation for the quark angular momentum in terms of GPDs. Wigner distributions are used to show that the difference between the Jaffe-Manohar definiton of quark orbital angular momentum and that of Ji is equal to the change of orbital angular momentum due to the final state interactions as the struck quark leaves the target in a DIS experiment.

Delta and Omega masses in a three-quark covariant Faddeev approach

We present the solution of the Poincare-covariant Faddeev equation for the Delta(1232) and Omega(1672) baryons. The covariant structure of the corresponding baryon amplitudes and their decomposition in terms of internal spin and orbital angular momentum is explicitly derived. The interaction kernel is truncated to a rainbow-ladder dressed-gluon exchange such that chiral symmetry and its dynamical breaking are correctly implemented. The resulting physical masses agree reasonably with experiment and their evolution with the pion mass compares favorably with lattice calculations. Evidence for the non-sphericity of the Delta-resonance is discussed as well.

Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in a supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. We then define an operator whose continuum limit corresponds to an angular momentum in terms of the creation–annihilation operators of our model. Coherent states with the correct continuum limit are also constructed. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.

Nonclassical effects in a highly nonlinear generalized homogeneous Dicke model

An intensity dependent nonlinear coupling model of N two-level atoms (generalized Dicke model) interacting dispersively with a bimodal cavity field via two-photon transitions is investigated in a scenario where the rotating wave approximation is assumed. The model becomes homogeneous in the sense that the spin transition frequency is the same for all atoms and the coupling constants emerging from the collective interactions of the atomic system with the cavity field depend only on the particular radiation field mode. This allows us to represent the Dicke Hamiltonian entirely in terms of the total angular momentum J . It is assumed that, initially, the atomic system and the field are in a disentangled state where the field modes are in Glauber coherent states and the atomic system is a superposition of states | J M 〉 (Dicke states). The model is numerically tested against simulations of normal squeezing variance of the field, squeezing factors based on the Heisenberg uncertainty principle, along with the statistical properties of the light leading to the possible production of nonclassical effects, such as degree of second-order coherence in the modes, degree of intermode correlation, as well as violation of the Cauchy–Schwartz inequality. Analytical expression of the total density operator matrix elements at t > 0 shows the present nonlinear model to be strongly entangled, which is reflected in the time evolution of the linear entropy, where the superposition states are reduced to statistical mixtures. Thus, the present generalized Dicke model does not preserve the modulus of the Bloch vector. The computations, performed in the weak coupling and strong field limits, were conducted via second-order Dyson perturbative expansion of the time evolution operator matrix elements for the totality of the angular momentum states of the atomic system.