Terms Of Angular Momentum Research Articles

On discrete ground states of rotating Bose–Einstein condensates

The ground states of Bose–Einstein condensates in a rotating frame can be described as constrained minimizers of the Gross–Pitaevskii energy functional with an angular momentum term. In this paper we consider the corresponding discrete minimization problem in Lagrange finite element spaces of arbitrary polynomial order and we investigate the approximation properties of discrete ground states. In particular, we prove a priori error estimates of optimal order in the L 2 L^2 - and H 1 H^1 -norm, as well as for the ground state energy and the corresponding chemical potential. A central issue in the analysis of the problem is the missing uniqueness of ground states, which is mainly caused by the invariance of the energy functional under complex phase shifts. Our error analysis is therefore based on an Euler–Lagrange functional that we restrict to certain tangent spaces in which we have local uniqueness of ground states. This gives rise to an error decomposition that is ultimately used to derive the desired a priori error estimates. We also present numerical experiments to illustrate various aspects of the problem structure.

An empirical formula for the half-lives of one- and two-proton radioactivity

We have proposed an empirical formula for one- and two-proton decays, including the angular momentum term. While investigating the first term in the Viola–Seaborg formula, we found a linear relationship between the logarithmic half-life and the expression [Formula: see text] for each angular momentum state. Furthermore, we obtained a linear relationship between the slope and intercept as functions of the angular momentum (l). Using these relations, we proposed a generalized empirical formula for the half-lives of one- and two-proton radioactivity for all angular momentum states. We analyzed the accuracy of the formula predictions by computing the standard deviation between the predicted and experimental decay half-lives. For the decay of one proton, the standard deviation of the proposed formula is 0.389, while that of the generalized formula is 0.400. These values represent the lowest standard deviations compared to previous models and the empirical formula. In the case of two-proton decay, the standard deviation for the current formula is 1.31, and the generalized formula also exhibits a lower standard deviation of 1.32. This lowest standard deviation value indicates that the proposed formula is suitable for reproducing the experimental half-life. We extended the half-life predictions to another 207 nuclei for one-proton decay and 42 nuclei for two-proton decay cases, which are energetically possible. The estimated half-lives for both one- and two-proton decays agree well with other theoretical predictions.

Study of relativistic accretion flow in the [formula omitted] theory of gravity

We present the properties of relativistic, inviscid, low angular momentum, advective accretion flow in a f(R) gravity theory that satisfactorily mimics the asymptotically flat vacuum solutions of the Einstein’s equations. With this, we solve the governing equations describing the accretion flow and obtain the global transonic accretion solutions in terms of flow energy (E), angular momentum (λ) and gravity parameter (A) that determines the effect of f(R) gravity. We observe that depending on the model parameters, flow may contain either single or multiple critical points. We separate the effective domain of the parameter space in λ−E plane that admits accretion solutions possessing multiple critical points and observe that solution of this kind continues to form for wide range of the flow parameters. We examine the modification of the parameter space and reveal that it gradually shrinks with the decrease of A, and ultimately disappears for A=−2.34. Finally, we calculate the disk luminosity (L) considering bremsstrahlung emission process and find that global accretion solutions passing through the inner critical point are more luminous compared to the outer critical point solutions.

Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy and angular momentum in terms of the radius (r 0) of the timelike circular orbits. The existence and finiteness of energy and angular momentum constrain the possible range of PFDM parameter (χ) and r 0. In case of null geodesics, we calculate the radius rp of the unstable circular photon orbits. We then use the Lyapunov exponent to study the stability of the geodesics. Then we analyze the critical exponent useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinormal mode (QNM) frequencies and their dependence on χ and black hole charge Q. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on χ and Q. Finally, we evaluate the black hole shadow radius Rs and graphically observe the effect of χ and Q on it.

Partially coherent twisted vector vortex beam enabling manipulation of high-dimensional classical entanglement.

In this paper, we present a novel form of a partially coherent beam characterized by classical entanglement in higher dimensions. We coin the term "twisted vector vortex (TVV) beam" to describe this phenomenon. Similar to multi-partite quantum entangled states in higher dimensions, the partially coherent twisted vector vortex beam possesses distinct properties such as non-uniform polarization, vortex phase, and twist phase. Through experiments, we offer empirical evidence for these three degrees-of-freedom in the light field. The results demonstrate that the state of the light is inseparable in terms of polarization and orbital angular momentum (OAM) modes. Additionally, the twist phase introduces an additional dimension in controlling the vector vortex beam. This research reveals the possibility of new controlling dimensions in classical entanglement through the chirality of coherence within partially coherent light. Consequently, this opens up new avenues for the utilization of partially coherent light in both classical and quantum domains.

Simulations of idealised 3D atmospheric flows on terrestrial planets using LFRic-Atmosphere

Abstract. We demonstrate that LFRic-Atmosphere, a model built using the Met Office's GungHo dynamical core, is able to reproduce idealised large-scale atmospheric circulation patterns specified by several widely used benchmark recipes. This is motivated by the rapid rate of exoplanet discovery and the ever-growing need for numerical modelling and characterisation of their atmospheres. Here we present LFRic-Atmosphere's results for the idealised tests imitating circulation regimes commonly used in the exoplanet modelling community. The benchmarks include three analytic forcing cases: the standard Held–Suarez test, the Menou–Rauscher Earth-like test, and the Merlis–Schneider tidally locked Earth test. Qualitatively, LFRic-Atmosphere agrees well with other numerical models and shows excellent conservation properties in terms of total mass, angular momentum, and kinetic energy. We then use LFRic-Atmosphere with a more realistic representation of physical processes (radiation, subgrid-scale mixing, convection, clouds) by configuring it for the four TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) scenarios. This is the first application of LFRic-Atmosphere to a possible climate of a confirmed terrestrial exoplanet. LFRic-Atmosphere reproduces the THAI scenarios within the spread of the existing models across a range of key climatic variables. Our work shows that LFRic-Atmosphere performs well in the seven benchmark tests for terrestrial atmospheres, justifying its use in future exoplanet climate studies.

Convergence of the Laplace and the alternative multipole expansion approximation series for the Coulomb potential

Multipole expansion is a powerful technique used in many-body physics to solve dynamical problems involving correlated interactions between constituent particles. The Laplace multipole expansion series of the Coulomb potential is well established in literature. We compare its convergence with our recently developed perturbative and analytical alternative multipole expansion series of the Coulomb potential. In our working, we confirm that the Laplace and the analytical alternative multipole expansion series are equivalent as expected. In terms of performance, the perturbative alternative multipole expansion series underapproximate the expected results to some extent while the Laplace and the analytical alternative multipole expansion series yield results which are relatively accurate but oscillatory in nature even with a higher number of angular momentum terms employed. As a practical example, we have evaluated the Slater double integrals for two-electron systems using the multipole expansion techniques and a mean field approximation. The estimated results show that only spherical interactions are dominant while the higher-order interactions are negligible. To highlight the discrepancy in the application of each of the formulations of the multipole expansion series for the electron-electron interaction potential, an estimation of the non-relativistic groundstate energies of some helium-like systems, evaluated using the spherical approximation of the multipole potential, is provided. Our findings are likely to be useful in the treatment of the Coulomb potential in electronic structure calculations as well as in celestial mechanics.

Spin-1 quarkonia in a rotating frame and their spin contents

We propose a new way of studying the spin content of a hadron by looking at its response in a rotating frame. By collecting all responses of quarks and gluons in a rotating frame, we describe the spin-rotation coupling of spin-1 quarkonia and thereby reveal their spin contents in a relativistic formalism. We demonstrate that both the perturbative and non-perturbative contributions in the operator product expansion follow a universal formula that identifies the spin-rotation coupling with unit strength. This allows us to recognize the total spin-1 of the vector and axial vector quarkonia in terms of the total angular momentum of quarks and gluons. Specifically, we find the spin contents of J/ψ, χc1, ϒ(1S), and χb1 are slightly different from the naive quark model picture. For example, the J/ψ is traditionally considered as an S-wave particle, but we find quarks do not carry all of the total spin.

Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates

Using a quasispherical approximation of an affine-null metric adapted to an asymptotic Bondi inertial frame, we present high order approximations of the metric functions in terms of the specific angular momentum for a slowly rotating stationary and axisymmetric vacuum spacetime. The metric is obtained by following the procedure of integrating the hierarchy of Einstein equations in a characteristic formulation utilizing master functions for the perturbations. It further verified its equivalence with the Kerr metric in the slowly rotating approximation by carrying out an explicit transformation between the Boyer-Lindquist coordinates to the employed affine-null coordinates. A peculiar feature of the derivation is that in the solution of the perturbation equations for every order a new integration constant appears which cannot be set to zero using asymptotical flatness or regularity arguments. However, these additional integration constants can be absorbed into the overall Komar mass and Komar angular momentum of a slowly rotating black hole.

Long-term changes in the Earth's climate: Milankovitch cycles as an exercise in classical mechanics

Long-term changes in the tilt of the Earth's axis, relative to the plane of its orbit, are of great significance to long-term climate change, because they control the size of the arctic and Antarctic circles. These “Milankovitch cycles” have hitherto been calculated by classical perturbation methods or by direct numerical integration of Newton's equations of motion. This paper presents an approximate calculation from simple considerations of angular momentum using similar methods to those used to study the precession of a spinning top. It is an instructive exercise in classical mechanics and gives a simple explanation of the phenomenon in terms of angular momentum. It is shown that the main component of “Milankovitch cycles” has a period of 41,000 yr and is due to one of the modes of precession of the Earth-Venus system. The other mode of this system produces a component of period 29,500 yr, and a third component of period 54,000 yr results from the influence of the precession of the orbits of Jupiter and Saturn. These results agree closely with several of the numerical simulations in the literature and strongly suggest that some other results in the literature are incorrect.

Properties of accretion flow in deformed Kerr spacetime

We study the properties of a low-angular momentum, inviscid, advective accretion flow in a deformed Kerr spacetime under the framework of general theory of relativity. We solve the governing equations that describe the flow motion in terms of input parameters, namely energy ($E$), angular momentum ($\lambda$), spin ($a_{\rm k}$) and deformation parameter ($\varepsilon$), respectively. We find that global transonic accretion solutions continue to exist in non-Kerr spacetime. Depending on the input parameters, accretion flow is seen to experience shock transition and we find that shocked induced accretion solutions are available for a wide range of the parameter space in $\lambda-E$ plane. We examine the modification of the shock parameter space with $\varepsilon$, and find that as $\varepsilon$ is increased, the effective region of the parameter space is reduced, and gradually shifted towards the higher $\lambda$ and lower $E$ domain. In addition, for the first time in the literature, we notice that accretion flow having zero angular momentum admits shock transition when spacetime deformation is significantly large. Interestingly, beyond a critical limit of $\varepsilon^{\rm max}$, the nature of the central object alters from black hole (BH) to naked singularity (NS) and we identify $\varepsilon^{\rm max}$ as function of $a_{\rm k}$. Further, we examine the accretion solutions and its properties around the naked singularity as well. Finally, we indicate the implications of the present formalism in the context of astrophysical applications.

Symmetry-dependent analytical all-electron potential for helium atom

Electron–electron interaction is the origin of the many-body problems usually encountered in physics and chemistry. Helium atom and other two-electron systems are the simplest many-body systems in nature. The Schrödinger equation even for such simple systems cannot be solved exactly without resorting to approximate methods. In this study, we have suggested a symmetry-dependent analytical all-electron potential for helium atom derived using an alternative multipole expansion, a variational technique, and a mean-field approximation. We have calculated the non-relativistic groundstate energy for helium atom to be −2.90422284. The suggested all-electron potential has a local Coulomb potential with embedded nuclear charge screening effect in the leading term of the multipole potential. A non-local component of the potential emanates from the higher-order angular momentum terms of the multipole series expansion. The higher-order multipole interactions are fully included through the exchange correlation processes where the interacting electrons exchange their angular momenta via the operator. With the derived potential, the effects of the local long-range and non-local short-range components, and the finite nuclear mass corrections are tested. Our results are in reasonable agreement with literature values. Indeed with the finite nuclear mass correction, we obtain the groundstate energy of helium atom to be −2.90382769.

Calculation of the singlet-triplet magnetic and electro-quadrupole transitions intensity for Ge2 molecule

Intensity of the parity-forbidden singlet-triplet (S-T) transitions of the Ge2 molecule in the near IR region has been studied by the multi-reference configuration interaction (MRCI) approach with spin-orbit coupling (SOC). Intensity of the sub-band is mainly dominated by the spin angular momentum term in the magnetic-dipole transition moment, which arises from the spin current inside the zero-field split sublevels of the ground state. The Einstein coefficients corresponding to vibronic bands 0–(2∼7), 1–(4∼7), 2–(6∼7), 3–7 of the transition are in the range of 0.304–0.463 s−1; these bands could be detected since they are not overlapped by the allowed rovibronic systems. The magnetic-dipole is only defined by the orbital angular momentum term and the band intensity is not sufficient for observation. The electric-quadrupole and transitions have also been calculated to be negligible. The triply forbidden electro-dipole transitions in the IR spectrum of the Ge2 throws new light on this little known domain of diatomic molecular spectroscopy. Highlights The parity-forbidden singlet–triplet transitions of the Ge2 has been studied. Intensity of the sub-band arises from the spin current inside the zero-field split sublevels of the ground state. Contributions of the a1Δg−1Πg and orbital transitions presented in the magnetic-dipole a 1Δg- transition are negligible.

Nonreciprocal photonic devices based onwhispering-gallery-modes microcavities

<p indent="0mm">Because the nonreciprocity has both theoretical and applicable prospects, it is desired to break through the restriction of the reciprocity principle for nonreciprocity optical transmission. Theoretically, the reciprocity principle is equivalent to the limited time reversal symmetry. To break the symmetry, the system should include nonlinearity, magneto-optical effects, or modulation in time. Some key components in the optical circuits, such as isolators, circulators, and phase shifters, are typical nonreciprocal devices. They are realized based on the Faraday effect of magneto-optical materials in traditional free-space optics. However, the magneto-optical materials are not naturally compatible with the integrated optics. Therefore, while pursuing the magneto-optical integration on a chip, people also devote to developing nonreciprocal theories and devices without magnetic materials. Whispering-gallery-modes (WGMs) optical microcavity has the advantages of small mode volume and high-quality factor. Therefore, many nonreciprocal strategies in photonic integration are based on optical microcavities. Similar to the nonreciprocal principle of the magneto-optical effect, the external bias fields (such as magnetic field, angular momentum, linear momentum, etc.) are necessary to break the time reversal symmetry. In this paper, we review the research on nonreciprocal optics in WGMs optical microcavities, and summarize recent research achievements in the following interaction categories: Magneto-optical effect, chiral coupling of atoms with energy level distribution bias, macroscopic Doppler effect with angular momentum bias, optomechanical driving, acousto-optic oscillation and nonlinear driving. Firstly, even on the chip, the magneto-optical effect is an important way to realize nonreciprocity. Nonreciprocity can be achieved by depositing/bonding magneto-optical materials on a silicon chip or using the spin-orbit interaction of WGMs in the YIG microsphere with the help of an external magnetic field. Secondly, preparing the atom to a specific Zeeman energy level can also lead to the polarization concerned interaction between the atoms and the photons, so that the nonreciprocity of the photon can be realized based on the control of the atomic ground state population. Thirdly, the Doppler effect can make the moving dielectric medium produce an additional refractive index related to the speed. Then the effective refractive index is different between the light propagating in the opposite directions. The reciprocity of the system is destroyed, thereby achieving nonreciprocity. Finally, the nonreciprocity of optomechanical systems, acousto-optic modulation, and nonlinear effects can be explained by the conservation of angular momentum of photon-phonon interactions. As a summary, some representative parameters of isolators obtained in related experiments are listed in the table. The existing solutions for nonreciprocity have also be classified in terms of angular momentum and interactions, which is beneficial to deeply understanding the existing solutions and to developing potential solutions. The research of nonreciprocity is also discussed by listing problems to be studied.

On the stability of shocks in isothermal black hole accretion discs

ABSTRACT Most black holes possess accretion discs. Models of such discs inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study shocks in a thin isothermal black hole accretion flow. Modelling infinitesimal viscosity allows the use of multiple-scales matched asymptotic methods. We thus derive the first explicit calculations of isothermal shock stability. We find that the inner shock is always unstable, and the outer shock is always stable. The growth/decay rates of perturbations depend only on an effective potential and the incoming–outgoing flow difference at the shock location. We give a prescription of accretion regimes in terms of angular momentum and black hole radius. Accounting for viscous angular momentum dissipation implies unstable outer shocks in much of parameter space, even for realistic viscous Reynolds numbers of the order ≈1020.

Approximate and Exact GR-Solutions for the Two-Body Problem

A binary gravitational rotator, also called the two-body problem, is a pair of masses m1, m2 moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) mr = m1m2/(m1+m2) orbiting around the total mass m = m1+m2 situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters gμν (m1, m2, R, a1, a2), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.

Toroidal modeling of plasma response to RMP fields for HL-2M

The plasma response to the n = 1, 2, 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, and the consequences on the fast ion confinement, are numerically investigated for a reference high-pressure plasma in HL-2M, by utilizing the linear resistive magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). The best coil current configurations, in terms of the coil phasing between the upper and lower rows of coils for controlling type-I edge localized modes (ELMs) in HL-2M, are identified as −130, −30, 180 degrees for the n = 1, 2, 4 fields, respectively, based on the edge peeling-tearing plasma response criterion. The plasma is found to substantially amplify the applied vacuum RMP field with the best coil phasing for the reference HL-2M equilibrium. The overall field amplification factor, defined as the peak-to-peak ratio of the poloidal spectra for the total field perturbation including the plasma response and the vacuum field alone, is about five for all n’s. The amplification, however, does not occur with the worst coil phasing for ELM control. This field amplification due to the high-pressure plasma response, together with the plasma screening of the resonant radial field components in the core region, have several consequences on the fast ion confinement in HL-2M during ELM control with RMP. (i) Three-dimensional fields including the plasma response, and with the best coil phasing, substantially enhance the distortion of fast ion orbits compared to the vacuum field approximation. With the n = 1 RMP, the plasma-response-induced enhancement of the orbit distortion reaches a factor of four when measured in terms of the canonical toroidal angular momentum. (ii) With the best coil phasing, the plasma response widens the stochastic region for the particle orbits on the Poincaré plane. (iii) The orbit islands, including the plasma response, remain as large as the vacuum counterparts in the plasma core where strong screening of the resonant field components occur. All these effects lead to enhanced fast ion transport (and loss) in the high-pressure HL-2M plasma, when the best RMP spectrum is applied to control ELMs.

Advances in vibrational configuration interaction theory ‐ part 1: Efficient calculation of vibrational angular momentum terms

Finite basis vibrational configuration interaction theory (VCI) is a highly accurate method for the variational calculation of state energies and related properties, but suffers from fast growing computational costs in dependence of the size of the correlation space. In this series of papers, concepts and techniques will be presented, which diminish the computational demands and thus broaden the applicability of this method to larger molecules or more complex situations. This first part focuses on a highly efficient implementation of the vibrational angular momentum (VAM) terms as occurring in the Watson Hamiltonian and the prediagonalization of initial subspaces within an iterative configuration selective VCI implementation. Working equations and benchmark calculations are provided, the latter demonstrating the increased performance of the new algorithm.

Coexistence of vortex arrays and surface capillary waves in spinning prolate superfluid He4 nanodroplets

Within Density Functional Theory, we have studied the interplay between vortex arrays and capillary waves in spinning prolate He-4 droplets made of several thousands of helium atoms. Surface capillary waves are ubiquitous in prolate superfluid He-4 droplets and, depending on the size and angular momentum of the droplet, they may coexist with vortex arrays. We have found that the equilibrium configuration of small prolate droplets is vortex-free, evolving towards vortex-hosting as the droplet size increases. This result is in agreement with a recent experiment [S.M. O'Connell et al., Phys. Rev. Lett. 124, 215301 (2020)], where it has been disclosed that vortex arrays and capillary waves coexist in the equilibrium configuration of very large drops. Contrarily to viscous droplets executing rigid body rotation, the stability phase diagram of spinning He-4 droplets cannot be universally described in terms of dimensionless angular momentum and angular velocity variables: instead, the rotational properties of superfluid helium droplets display a clear dependence on the droplet size and the number of vortices they host.

Free-space realization of tunable pin-like optical vortex beams

We demonstrate, both analytically and experimentally, free-space pin-like optical vortex beams (POVBs). Such angular-momentum-carrying beams feature tunable peak intensity and undergo robust antidiffracting propagation, realized by judiciously modulating both the amplitude and the phase profile of a standard laser beam. Specifically, they are generated by superimposing a radially symmetric power-law phase on a helical phase structure, which allows the inclusion of an orbital angular momentum term to the POVBs. During propagation in free space, these POVBs initially exhibit autofocusing dynamics, and subsequently their amplitude patterns morph into a high-order Bessel-like profile characterized by a hollow core and an annular main lobe with a constant or tunable width during propagation. In contrast with numerous previous endeavors on Bessel beams, our work represents the first demonstration of long-distance free-space generation of optical vortex “pins” with their peak intensity evolution controlled by the impressed amplitude structure. Both the Poynting vectors and the optical radiation forces associated with these beams are also numerically analyzed, revealing novel properties that may be useful for a wide range of applications.