Average Angular Momentum Research Articles

Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential.

In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.

Generation of discrete higher-order optical vortex lattice at focus.

Higher-order vortices (HOVs) extend the dimensions of optical vortex regulation, which is of great significance in optical communication and optical tweezers. Herein, we demonstrate an alternative scheme to produce a HOV in the focus plane using multiple Laguerre-Gaussian (LG) beam interference, termed a discrete higher-order optical vortex lattice (DHOVL). The modulation depth of the DHOVL exceeds 2π. In this case, the topological charge (TC) of the DHOVL is determined by the difference of the phase period between the innermost and the outermost interference beams. Compared with a conventional HOV (CHOV), the vortex exists in a form of multiple unit singularities sharing a dark core. In addition, the average orbital angular momentum per photon of the DHOVL increases with increasing TC, surpassing that of the CHOV. This work provides a novel, to the best of our knowledge, scheme to produce a HOV, which will facilitate several advanced applications, including optical micromanipulation, optical sensing and imaging, and optical fabrication.

Control of the vortex lattice formation in coupled atom-molecular Bose–Einstein condensate in a double well potential: role of atom-molecule coupling, trap rotation frequency and detuning parameter

We study the vortex formation in coupled atomic and molecular condensates in a rotating double well trap by numerically solving the coupled Gross–Pitaevskii like equations. Starting with the atomic condensate in the double well potential we considered two-photon Raman photo-association for coherent conversion of atoms to molecules. It is shown that the competition between atom-molecule coupling strength and repulsive atom-molecule interaction controls the spacings between atomic and molecular vortices and the rotation frequency of the trap is the key player for controlling the number of visible atomic and molecular vortices. Whereas the Raman detuning controls the spacing between atomic and molecular vortices as well as the number of atomic and molecular vortices in the trap. We have shown by considering the molecular lattices the distance between two molecular vortices can be controlled by varying the Raman detuning. In addition we have found that the Feynman rule relating the total number of vortices and average angular momentum both for atoms and molecules can be satisfied by considering the atomic and molecular vortices those are hidden in density distribution and seen as singularities in phase distribution of the coupled system except for the lattice structure where molecular vortices are overlapped with each other. It is found that although the number of visible/core vortices in atomic and molecular vortex lattices depends significantly on the system parameters the number of atomic and molecular hidden vortices remains constant in most of the cases.

Orientation of the spins of galaxies in the local volume

ABSTRACT We estimated the angular momentum, J, of 720 galaxies in the Local Volume with distances r < 12 Mpc. The distribution of the average angular momentum along the Hubble sequence has a maximum at the morphological type T = 4 (Sbc), while the dispersion of the J-values for galaxies is minimal. Among the Local Volume population, 27 elite spiral galaxies stand out, with an angular momentum > 0.15 of the Milky Way, J > 0.15JMW, making the main contribution ($\gt 90~{{\ \rm per\ cent}}$ ) to the total angular momentum of galaxies in the considered volume. Using observational data on the kinematics and structure of these galaxies, we determined the direction of their spins. We present the first map of the distribution of the spins of 27 nearby massive spiral galaxies in the sky and note that their pattern does not exhibit significant alignment with respect to the Local Sheet plane. The relationship between the magnitude of the angular momentum and stellar mass of the local galaxies is well represented by a power law with an exponent of (5/3) over an interval of six orders of magnitude of the mass of galaxies.

Asymptotic Quantization of a Particle on a Sphere

Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space T∗S2 in the limit of large average angular momentum. The cotangent bundle T∗S2 is also the classical manifold for systems with E(3) symmetry group with appropriately fixed Casimir operators. This allows us to employ the asymptotic form of the star-product proper for variable (integer) spin systems to develop a deformation quantization scheme for a particle moving on the two-dimensional sphere, whose observables are elements of e(3) algebra and the corresponding phase-space is T∗S2. We show that the standard commutation relations of the e(3) algebra are recovered from the corresponding classical Poisson brackets and the explicit expressions for the eigenvalues and eigenfunctions of some quantized classical observables (such as the angular momentum operators and their squares) are obtained.

Lasting effects of static magnetic field on classical Brownian motion.

The Bohr-Van Leeuwen theorem states that an external static magnetic field does not influence the state of a classical equilibrium system: There is no equilibrium classical magnetism, since the magnetic field does not do work. We revisit this famous no-go result and consider a classical charged Brownian particle interacting with an equilibrium bath. We confirm that the Bohr-Van Leeuwen theorem holds for the long-time (equilibrium) state of the particle. But the external static, homogeneous magnetic field does influence the long-time state of the thermal bath, which is described via the Caldeira-Leggett model. In particular, the magnetic field induces an average angular momentum for the (uncharged) bath, which separates into two sets rotating in opposite directions. The effect relates to the bath going slightly out of equilibrium under the influence of the Brownian particle and persists for arbitrarily long times. In this context we studied the behavior of the two other additive integrals of motion, energy, and linear momentum. The situation with linear momentum is different, because it is dissipated away by (and from) the bath modes. The average energy of the bath mode retains the magnetic field as a small correction. Thus, only the bath angular momentum really feels the magnetic field for long times.

Flux Eruption Events Drive Angular Momentum Transport in Magnetically Arrested Accretion Flows

We evolve two high-resolution general relativistic magnetohydrodynamic simulations of advection-dominated accretion flows around nonspinning black holes (BHs), each over a duration ∼3 × 105 GM BH/c 3. One model captures the evolution of a weakly magnetized (SANE) disk and the other that of a magnetically arrested disk (MAD). Magnetic flux eruptions in the MAD model push out gas from the disk and launch strong winds with outflow efficiencies at times reaching 10% of the incoming accretion power. Despite the substantial power in these winds, average mass outflow rates remain low out to a radius ∼100GM BH/c 2, only reaching ∼60%–80% of the horizon accretion rate. The average outward angular momentum transport is primarily radial in both modes of accretion, but with a clear distinction: magnetic flux eruption–driven disk winds cause a strong vertical flow of angular momentum in the MAD model, while for the SANE model, the magnetorotational instability (MRI) moves angular momentum mostly equatorially through the disk. Further, we find that the MAD state is highly transitory and nonaxisymmetric, with the accretion mode often changing to a SANE-like state following an eruption before reattaining magnetic flux saturation with time. The Reynolds stress changes directions during such transitions, with the MAD (SANE) state showing an inward (outward) stress, possibly pointing to intermittent MRI-driven accretion in MADs. Pinning down the nature of flux eruptions using next-generation telescopes will be crucial in understanding the flow of mass, magnetic flux, and angular momentum in sub-Eddington accreting BHs like M87* and Sagittarius A*.

The role of the turbulence driving mode for the initial mass function

ABSTRACT Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating, and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sink particle (protostellar) distribution for COMP is shifted to lower masses by a factor of ∼1.5 compared to SOL. Our simulation IMFs capture the important features of the observed IMF form. We find that turbulence-regulated theories of the IMF match our simulation IMFs reasonably well in the high-mass and low-mass range, but underestimate the number of very low-mass stars, which form towards the later stages of our simulations and stop accreting due to dynamical interactions. Our simulations show that for both COMP and SOL, the multiplicity fraction is an increasing function of the primary mass, although the multiplicity fraction in COMP is higher than that of SOL for any primary mass range. We find that binary mass ratio distribution is independent of the turbulence driving mode. The average specific angular momentum of the sink particles in SOL is a factor of 2 higher than that for COMP. Overall, we conclude that the turbulence driving mode plays a significant role in shaping the IMF.

대학 여자 멀리뛰기 엘리트 선수와 아마추어 선수의 각운동량 비교분석

The purpose of this study was to compare and analyze the angular momentum of the lower extremities and upper extremities and the resultant velocity of the COM(center of mass) in the long jump motions of elite female long jump athletes and amateur athletes. This study obtained the following results. First, the average angular momentum of the right arm of the elite female long jump athlete and amateur athlete during the long jump action was high in all events except Event 4, Event 5, and Event 6, and there was a significant difference in Event 8. Second, the average angular momentum of the left arm during the long jump of elite female long jump athletes and amateur athletes was high in all events except Event 3, Event 4, and Event 5, and there was a significant difference in Event 8. Third, the average angular momentum of the right leg of the elite female long jump athlete and amateur athlete during the long jump was high in all events except for Event 3 and Event 4. There was a significant difference between Event 3 and Event 8. Fourth, the average angular momentum of the left leg of the elite female long jump athlete and amateur athlete during the long jump operation was high in all Events except Event 1 and Event 5, and there was a significant difference in Event 8. Fifth, the average COM resultant velocity of the elite female long jump athlete and amateur athlete during the long jump action showed that the average COM resultant velocity of all Event elite athlete was high, showing a significant difference.

Investigation of empirical heat capacity in hot-rotating A ∼ 200 nuclei

The empirical heat capacities of some hot-rotating A ∼ 200 nuclei (184Re, 200Tl, 211Po, and 212At) have been investigated by combining the angular-momentum dependent back-shifted Fermi gas (BSFG) model of nuclear level density (NLD) with the experimental NLD data extracted from the neutron-evaporation spectra at the average total angular momentum ⟨J⟩ = 12 ℏ. The parameters of the BSFG are obtained by fitting its NLD to the corresponding measured data using an advanced package of program modeling (CPM) provided by Python feature of IBM decision optimization CPLEX. The results obtained show that the shell correction plays an important role in the formation of empirical S-shaped heat capacity, which serves as a fingerprint for the pairing phase transition in finite nuclear systems. The 184Re nucleus, which is deformed and has small shell correction, exhibits a weaker S-shaped heat capacity than the remaining three spherical 200Tl, 211Po, and 212At nuclei that have large shell effects. This result contrasts with that recently predicted by the microscopic exact pairing plus independent-particle model at finite temperature (EP + IPM), in which the S-shaped heat capacity was predicted in 184Re only. This discrepancy between the heat capacities obtained within the BSFG and EP + IPM models suggests that an NLD model capable of well describing the experimental data while also having intrinsic and as complete as possible physical interpretations is still required in order to provide the exact description of nuclear thermodynamic quantities. In addition, more experimental NLD data in other mass and higher energy regions are also demanded.

Control of orbital angular momentum of optical vortex beams with complex wandering perturbations.

This work investigates how independent perturbations and cross-correlation perturbations affect optical vortex beams. Theoretical and experimental results show that both perturbations cause the intensity, average orbital angular momentum (OAM), and the OAM spectrum of the vortex beam to vary periodically with the perturbation direction, but with different periods. When the beam is subjected to independent perturbations, the average OAM changes periodically with θ in every π/2; when the beam is subjected to cross-correlation perturbations, the average OAM varies with θ in every π. The results of this work provide a method to control the OAM and regulate low-coherence vortex beams in turbulent environments.

Ultra-intense vortex laser generation from a seed laser illuminated axial line-focused spiral zone plate.

Relativistic vortex laser has drawn increasing attention in the laser-plasma community owing to its potential applications in various domains, e.g., generation of energetic charged particles with orbital angular momentum (OAM), high OAM X/γ-ray emission, high harmonics generation, and strong axial magnetic-field production. However, the generation of such relativistic vortex laser is still a challenge to the current laser technology. Using micro-structure targets named axial line-focused spiral zone plate (ALFSZP), we propose a novel scheme for ultra-intense vortex laser generation. In the scheme, a relativistic Gaussian laser pulse irradiates an ALFSZP, and diffracts as it passes through the ALFSZP. Due to the focusing and radial Hilbert transform capabilities of the ALFSZP, the seed laser is converted efficiently to a vortex one which is then well focused in a tunable focal volume. Three-dimensional particle-in-cell simulations indicate that using a seed laser pulse with intensity of 1.3 × 1020 W/cm2, the vortex laser intensity achieved is as high as 1.3 × 1021 W/cm2 with the averaged angular momentum per photon up to 0.73ℏ, promising diverse applications in various fields aforementioned.

Vortex formation and quench dynamics of rotating quantum droplets

We investigate vortex formation and quench dynamics in rotating quantum droplets. We use the variational method to analytically show that vortex formation requires the breakdown of the rotational symmetry of the system via shape deformations and calculate the bifurcation point and lowest energy surface mode of the system. In our numerical simulations, we first demonstrate the systematic stationary vortex states and their critical points with the imaginary time propagation method, in which the average angular momentum acts as the convergence condition of the final state, we also show that the critical points for vortex formation via simulation are consistent with variational results. Then, we present two methods for generating vortex states via the real-time quench dynamics with symmetric and asymmetric rotating quantum droplet traps, by choosing different quench times and rotation strengths, one obtains the final states with arbitrary vortices. Our study provides a dynamic method for experimentally investigating vortex formation in rotating quantum droplets.

New avenue for accurate analytical waveforms and fluxes for eccentric compact binaries

We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by $40\%$ with respect to previous work, with $4.5\%$ fractional difference for eccentricity $e=0.9$ and black hole dimensionless spin $-0.9\leq \hat{a}\leq +0.9$. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.

Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation

Gravitational radiation can be decomposed as an infinite sum of radiative multipole moments, which parametrize the waveform at infinity. The multipolar-post-Minkowskian formalism provides a connection between these multipoles and the source multipole moments, known as explicit integrals over the matter source. The gravitational wave energy, angular momentum and linear momentum fluxes are then expressed as multipolar expansions containing certain combinations of the source moments. We compute several gauge-invariant quantities as "building blocks" entering the multipolar expansion of both radiated energy and angular momentum at the 2.5 post-Newtonian (PN) level of accuracy in the case of hyperboliclike motion, by completing previous studies through the calculation of tail effects up to the fractional 1PN order. We express such multipolar invariants in terms of certain eccentricity enhancement factor functions, which are the counterpart of the well known enhancement functions already introduced in the literature for ellipticlike motion. Finally, we use the complete 2.5PN-accurate averaged energy and angular momentum fluxes to study the associated adiabatic evolution of orbital elements under gravitational radiation reaction.

Directional dependence of the event-by-event neutron- γ multiplicity correlations in Cf252(sf)

We differentiate the event-by-event n-$\gamma$ multiplicity data from \ce{^{252}Cf}(sf) with respect to the energies of the emitted particles as well as their relative angles of emission. We determine that neutron emission enhances $\gamma$-ray emission around $0.7$ and $1.2$ MeV, but the only directional alignment was observed for $E_\gamma \leq 0.7$ MeV and tended to be parallel and antiparallel to neutrons emitted in the same event. The emission of $\gamma$ rays at other energies was determined to be nearly isotropic. The presence of the emission and alignment enhancements is explained by positive correlations between neutron emission and quadrupole $\gamma$-ray emission along rotational bands in the de-exciting fragments. This observation corroborates the hypothesis of positive correlations between the angular momentum of a fragment and its intrinsic excitation energy. The results of this work are especially relevant in view of the recent theoretical and experimental interest in the generation of angular momentum in fission. Specifically, we have determined an alignment of the fragments angular momenta in a direction perpendicular to the direction of motion. We interpret the lack of $n$-$\gamma$ angular correlations for fission fragments near closed shells as a weakening of the alignment process for spherical nuclei. Lastly, we have observed that statistical $\gamma$ rays are emitted isotropically, indicating that the average angular momentum removed by this radiation is small. These results, and the analysis tools presented in this work, represent a stepping stone for future analysis of $n$-$\gamma$ emission correlations and their connection to angular momentum properties.

Angular momentum transfer in multinucleon transfer channels of O18+Np237

The angular momentum of a primary excited compound nucleus produced in multinucleon transfer reaction is an important quantity to evaluate cross sections to synthesize neutron-rich heavy-element nuclei as well as for surrogate reaction studies. The mechanism is, however, not enough understood due to the lack of detailed experimental data. In the present study, we determined the angular momentum of primary excited nuclei, $^{237,238,239}\mathrm{Np}, ^{238,239,240}\mathrm{Pu}$, and $^{239,240,241}\mathrm{Am}$, produced in the multinucleon transfer channels of the $^{18}\mathrm{O}+^{237}\mathrm{Np}$ reaction. With this aim, angular distributions of fission fragments with respect to the axis perpendicular to the reaction plane were measured for each compound nucleus. The distributions show an anisotropy exhibiting an enhanced yield on the reaction plane. They are well reproduced by a saddle-point model, from which the average angular momentum is derived in the model framework. The angular momentum increases with the compound-nucleus mass, thus the number of nucleons exchanged, but shows a saturating trend toward heavier compound nuclei. These results are the first ones to point to the dependence of the angular momentum on the transfer channels.

The quantum vortex states in extended Bose–Hubbard model: effects of lattice geometries, inter-particle interactions and spatial inhomogeneity

We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square, rectangular and triangular. Using numerical exact diagonalization method we show how the rotation introduces vortex states of different ground-state symmetries and the transition between these states at discrete rotation frequencies. We show how the geometry of the lattice plays crucial role in determining the maximum number of vortex states as well as the general characteristics of these states such as, the average angular momentum $<L_z>$, the current at the perimeter of the lattice, phase winding, the relation between the maximum phase difference, the maximum current and also the saturation of the current between the two neighboring lattice points. The effect of the two- and three-body interactions between the particles, both attractive and repulsive, also depends on the geometry of the lattice as the current flow or the lattice current depends on the interactions. We also consider the effect of the spatial inhomogeneity introduced by the presence of an additional confining harmonic trap potential. It is shown that the curvature of the trap potential and the position of the minimum of the trap potential with respect to the axis of rotation or the center of the lattice have a significant effect on the general characteristics these vortex states.

Fusion Reaction Study of some Selected Halo Systems

The challenge in studying fusion reaction when the projectile is neutron or proton rich halo nuclei is the coupling mechanism between the elastic and the breakup channel, therefore the motivation from the present calculations is to estimate the best coupling parameter to introduce the effect of coupled-channels for the calculations of the total cross section of the fusion , the barrier distribution of the fusion and the average angular momentum 〈L〉 for the systems 6He+206Pb, 8B+28Si, 11Be+209Bi, 17F+208Pb, 6He+238U, 8He+197Au and 15C+232Th using quantum mechanical approach. A quantum Coupled-Channel Calculations are performed using CC code. The predictions of quantum mechanical approach are comparable with the measured data that is available. Above and below the Coulomb barrier, comparison of theoretical calculations of quantum mechanical with the relevant measured data demonstrates good agreement.

Spontaneous symmetry breaking in persistent currents of spinor polaritons

We predict the spontaneous symmetry breaking in a spinor Bose–Einstein condensate of exciton-polaritons (polaritons) caused by the coupling of its spin and orbital degrees of freedom. We study a polariton condensate trapped in a ring-shaped effective potential with a broken rotational symmetry. We propose a realistic scheme of generating controllable spinor azimuthal persistent currents of polaritons in the trap under the continuous wave optical pump. We propose a new type of half-quantum circulating states in a spinor system characterized by azimuthal currents in both circular polarizations and a vortex in only one of the polarizations. The spontaneous symmetry breaking in the spinor polariton condensate that consists in the switching from co-winding to opposite-winding currents in opposite spin states is revealed. It is characterized by the change of the average orbital angular momentum of the condensate from zero to non-zero values. The radial displacement of the pump spot and the polarization of the pump act as the control parameters. The considered system exhibits a fundamental similarity to a superconducting flux qubit, which makes it highly promising for applications in quantum computing.