Values Of Angular Momentum Research Articles

Particle acceleration of two general particles in the background of rotating Ayón-Beato-García black holes

The rotating Ay\'{o}n-Beato-Garc\'{i}a (ABG) black holes, apart from mass ($M$) and rotation parameter ($a$), has an additional charge $Q$ and encompassed the Kerr black hole as particular case when $Q=0$. We demonstrate the ergoregions of rotating ABG black holes depend on both rotation parameter $a$ and charge $Q$, and the area of the ergoregions increases with increase in the values of $Q$, when compared with the Kerr black hole and the extremal regular black hole changes with the value of $Q$. Ban{\~a}dos, Silk and West (BSW) demonstrated that an extremal Kerr black hole can act as a particle accelerator with arbitrarily high center-of-mass energy ($E_{CM}$) when the collision takes place at any point in the ergoregion and thus in turn provides a suitable framework for Plank-scale physics. We study the collision of two general particles with different masses falling freely from rest in the equatorial plane of a rotating ABG black hole near the event horizon and find that the $E_{CM}$ of two colliding particles is arbitrarily high when one of the particles take a critical value of angular momentum in the extremal case, whereas for nonextremal case $E_{CM}$ for a pair of colliding particles is generically divergent at the inner horizon, and explicitly studying the effect of charge $Q$ on the $E_{CM}$ for ABG black hole. In particular, our results in the limit $Q\rightarrow 0$ reduce exactly to \emph{vis-$\grave{a}$-vis} those of the Kerr black hole.

High-Performance and High-Capacity Ultraviolet Communication With Orbital Angular Momentum

In this paper, a high-performance and high-capacity ultraviolet (UV) communication system is presented using orbital angular momentum (OAM) of the Laguerre-Gaussian beam. It is well known that the Laguerre-Gaussian beams propagating along the same axis with different azimuthal states are mutually orthogonal. This orthogonality property allows OAM beams to be potentially useful in improving the performance of a UV communication system. In addition, an OAM beam with fixed angular momentum value could act as a data channel. We first derive a novel analytical expression for the UV channel impulse response considering the Laguerre-Gaussian beam with a fixed OAM mode value acting as a data channel. Based on this impulse response, novel expressions for average symbol error rate (ASER) and channel capacity are derived. It is shown via simulation that the proposed OAM based UV communication system achieves significantly higher error performance and higher channel capacity than conventional UV systems. It is also found that the received beam divergence is the main factor limiting the performance of the proposed system.

Vibronic states in conical intersections: manifestations of centrifugal energy and non-adiabaticity in optical spectra of Jahn-Teller systems

Quantum states in conical intersections of adiabatic potentials in Jahn-Teller systems, known as Slonczewski resonances, are considered. It is shown that centrifugal forces associated with the rotation of the Jahn-Teller deformation (pseudorotation) play an important role in these resonances causing appearance of gaps in the energy spectrum of these states. In addition, the decay of these states, caused by non-adiabaticity, decreases with increasing angular momentum of the pseudorotation. As a result, states with a large momentum acquire a long lifetime. The optical spectra of the A1→E electronic transition with different values of the pseudorotational angular momentum are presented. In these spectra, centrifugal energy gaps and the stabilization of levels with a large pseudorotation momentum are clearly identified.

Differentially rotating neutron stars in scalar-tensor theories of gravity

We present the first numerical models of differentially rotating stars in alternative theories of gravity. We chose a particular class of scalar-tensor theories of gravity that is indistinguishable from GR in the weak field regime but can lead to significant deviations when strong fields are considered. We show that the maximum mass that a differentially rotating neutron star can sustain increases significantly for scalarized solutions and such stars can reach larger angular momenta. In addition, the presence of a nontrivial scalar field has the effect of increasing the required axis ratio for reaching a given value of angular momentum, when compared to a corresponding model of same rest mass in general relativity. We find that the scalar field also makes rapidly rotating models less quasi-toroidal than their general-relativistic counterparts. For large values of the angular momentum and values of the coupling parameter that are in agreement with the observations, we find a second turning point for scalarized models along constant angular momentum sequences, which could have interesting implications for the stability of remnants created in a binary neutron star merger.

Orbit-induced localized spin angular momentum in the tight focusing of linearly polarized vortex beams.

Optical spin-orbit interaction has gained much interest recently due to its universality and importance in modern photonics. In this Letter, we theoretically demonstrate that orbit-induced localized spin angular momentum (SAM) conversion can occur in the tight focusing of spin-free linearly polarized vortex beams (LPVBs). By analysis of the polarization states that are associated with the SAM density, we attribute the occurrence of such a conversion to the helical-phase-induced change of local polarization states in the focused field. In the local SAM, density can be further regulated by altering the sign and value of the orbital angular momentum in the incident LPVBs, as well as their polarization orientations. This Letter is expected to advance our understanding of optical spin-orbit coupling and benefit applications of optical microscopy and trapping.

Nuclear pairing fluctuations and angular momentum dependence of superconductivity in 94Mo nucleus

The effects of thermal fluctuations on pairing properties of nuclei with inclusion of angular momentum have been investigated. To treat nuclei at finite temperature and angular momentum, we have extended the formalism in which the mean value of the gap parameter is used to obtain thermal properties of nuclei based on the BCS scheme [Z. Kargar and V. Dehghani, J. Phys. G, Nucl. Part. Phys. 40 (2013) 045108] let us name it MEGBCS. The results obtained for [Formula: see text] nucleus show the appearance of thermally assisted pairing correlations with increasing angular momentum. Also, the [Formula: see text]-shaped heat capacity found experimentally [K. Kaneko et al., Phys. Rev. C 74 (2006) 024325] and theoretically, interpreted as the second phase transition in mesoscopic systems, disappears with increasing angular momentum above a critical value. The nuclear level density of [Formula: see text] is calculated versus excitation energy at various values of total angular momentum. The total level density matches the experimental data closely.

Thermal fluctuations and correlations among hairs of a stable quantum black hole: Some examples

We have already derived the criteria for thermal stability of charged rotating quantum black holes, for horizon areas that are large relative to the Planck area. The derivation is done by using results of loop quantum gravity and equilibrium statistical mechanics of the grand canonical ensemble. We have also showed that in four-dimensional spacetime, quantum AdS Kerr–Newman black hole and asymptotically AdS dyonic black hole with electric and magnetic charge are thermally stable within certain range of its parameters. In this paper, the expectation values of fluctuations and correlations among horizon area, electric charge and angular momentum (magnetic charge) of these black holes are calculated within their range of stability. Interestingly, it is found that leading order fluctuations of electric charge and angular momentum (magnetic charge), in large horizon area limit, are independent of the values of electric charge and angular momentum (magnetic charge) at equilibrium.

GCM Solver (Ver. 3.0): A Mathematica Notebook for Diagonalization of the Geometric Collective Model (Bohr Hamiltonian) with Generalized Gneuss–Greiner Potential

The program diagonalizes the Geometric Collective Model (Bohr Hamiltonian) with generalized Gneuss–Greiner potential with terms up to the sixth power in β . In nuclear physics, the Bohr–Mottelson model with later extensions into the rotovibrational Collective model is an important theoretical tool with predictive power and it represents a fundamental step in the education of a nuclear physicist. Nuclear spectroscopists might find it useful for fitting experimental data, reproducing spectra, EM transitions and moments and trying theoretical predictions, while students might find it useful for learning about connections between the nuclear shape and its quantum origin. Matrix elements for the kinetic energy operator and for scalar invariants as β 2 and β 3 cos ( 3 γ ) have been calculated in a truncated five-dimensional harmonic oscillator basis with a different program, checked with three different methods and stored in a matrix library for the lowest values of angular momentum. These matrices are called by the program that uses them to write generalized Hamiltonians as linear combinations of certain simple operators. Energy levels and eigenfunctions are obtained as outputs of the diagonalization of these Hamiltonian operators.

Formation of high-quality vortex laser beams with different orbital angular momenta in the laser resonator.

A scheme for forming high-quality vortex laser beams by employing spiral phase elements inside a laser resonator is presented theoretically. The calculated results show that the purity of the generated mode will decrease slightly as the mode order increases. However, the purity can achieve higher than 0.97 even for the high-order mode. More important, the value of the orbital angular momentum is controllable. Then, the influence of production and alignment errors, including the number of phase levels of the spiral phase elements, the surface roughness of the reflective mirrors, and the decenter of the reflective mirrors, is discussed in detail. The results show that the diffraction loss of the proposed system is more sensitive to production errors, and the purity of the generated mode is more sensitive to alignment errors. Thus, we estimate that the height of one step of the spiral structure should be less than one-fifteenth of the wavelength, the maximum surface fluctuation should be less than one-twentieth of the wavelength, and the vertical distance between the centers of the two reflective mirrors should be less than 20 μm if one wants to obtain high-quality vortex laser beams with high efficiency. The requirements for precision are acceptable for existing microfabrication and operation technologies.

Geodesics around oscillatons made of exponential scalar field potential

Oscillatons are spherically symmetric solutions to the Einstein Klein Gordon (EKG) equations for soliton stars made of real time dependent scalar fields. These equations are non singular and satisfy flatness conditions asymptotically with periodic time dependency. In this paper, we investigate the geodesic motion of particles moving around an oscillaton related to a time dependent scalar field. Bound orbital is found for these particles under the condition of particular values of angular momentum L and initial radial position. We discuss this topic for an exponential scalar field potential which could be of the exponential form with a scalar field and investigate whether the radial coordinates of such particles oscillate in time or not and thereby we could predict the corresponding oscillating period as well as amplitude. It is necessary to recall, in general relativity, a geodesic generalizes the notion of a straight line to curved space time. Importantly, the world line of a particle free from all external, non gravitational forces, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved space time geometry where the source of curvature is the stress energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4D space time geometry around the star onto 3D space.

Calculations of Differential Cross Sections Using Mixed Quantum/Classical Theory of Inelastic Scattering.

It is shown that the mixed quantum/classical theory (MQCT) for the description of molecular scattering is considerably improved by using integer values of orbital angular momentum l, just like in quantum theory, instead of treating it as a continuous classical variable related to the impact parameter. This conclusion is justified by the excellent accuracy of the modified theory for prediction of the differential cross sections, at various values of collision energy and in both forward and backward scattering regimes. This approach requires fewer trajectories, compared to the random Monte Carlo sampling, and the only convergence parameter is lmax (maximum orbital angular momentum) similar to Jmax in the full quantum theory (maximum total angular momentum). Calculations of differential and integral cross sections for elastic and inelastic channels are presented, and the role of the scattering phase is discussed. The low-energy range is analyzed in detail to obtain insight into how the mixed quantum/classical treatment works in the scattering regime dominated by resonances. The differential cross section for rotationally inelastic scattering, computed by MQCT approach, is presented for the first time.

Semiclassical description of chiral geometry in triaxial nuclei

A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors corresponding to two high-$j$ quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational principle. The resulting classical energy function is used to investigate the rotational dynamics of the system. It is found that the classical energy function exhibits two minima starting from a critical angular momentum value which depends on the single-particle configuration and the asymmetry measure $\gamma$. The emergence of the two minima is attributed to the breaking of the chiral symmetry. Quantizing the energy function for a given angular momentum, one obtains a Schr\"{o}dinger equation with a coordinate dependent mass term for a symmetrical potential which changes from a single to a double well shape as the angular momentum pass the critical value. The energies of the chiral partner bands for a given angular momentum are then given by the lowest two eigenvalues. The procedure is exemplified for maximal triaxiality and two $h_{11/2}$ quasiparticles, with the results used for the description of the chiral doublet bands in $^{134}$Pr.

Scattering of CO with H2O: Statistical and classical alternatives to close-coupling calculations.

Energy transfer in inelastic atom-molecule and molecule-molecule collisions can be described theoretically using the quantum-mechanical close-coupling method. Unfortunately, for bimolecular collisions implying heavy colliders and/or for which the potential energy surface has a deep well, the resulting coupled equations become numerically intractable and approximate methods have to be employed. H2O-CO collisions provide an important example for which close-coupling calculations are not feasible. In this paper, we investigate the accuracy of three approximate methods (the coupled states method, the quasi-classical trajectory method, and the statistical adiabatic channel model) to describe inelastic collisions of H2O with CO. We perform scattering calculations on a recent 5D potential energy surface, and we compare the results of the three approximate methods to fully converged close-coupling calculations at energies below 300 cm-1 and at low values of the total angular momentum. We show that the statistical method provides an attractive alternative to fully quantum mechanical close-coupling calculations at low collision energies, while the quasi-classical method is more advantageous at high energies.

Structure of geodesics in the regular Hayward black hole space-time

The regular Hayward model describes a non-singular black hole space-time. By analyzing the behaviors of effective potential and solving the equation of orbital motion, we investigate the time-like and null geodesics in the regular Hayward black hole space-time. Through detailed analyses of corresponding effective potentials for massive particles and photons, all possible orbits are numerically simulated. The results show that there may exist four orbital types in the time-like geodesics structure: planetary orbits, circular orbits, escape orbits and absorbing orbits. In addition, when $\ell$, a convenient encoding of the central energy density $3/8\pi\ell^{2}$, is $0.6M$, and $b$ is $3.9512M$ as a specific value of angular momentum, escape orbits exist only under $b>3.9512M$. The precession direction is also associated with values of $b$. With $b=3.70M$ the bound orbits shift clockwise but counter-clockwise with $b=5.00M$ in the regular Hayward black hole space-time. We also find that the structure of null geodesics is simpler than that of time-like geodesics. There only exist three kinds of orbits (unstable circle orbits, escape orbits and absorbing orbits).

Role of input angular momentum and target deformation on the incomplete-fusion dynamics in the O16+Sm154 system at ELab=6.1 MeV/nucleon

Spin distributions of nine evaporation residues $^{164}\mathrm{Yb}(xn)$, $^{163}\mathrm{Tm}(pxn)$, $^{168,167}\mathrm{Er}(2pxn)$, $^{163\ensuremath{-}161}\mathrm{Ho}(\ensuremath{\alpha}pxn)$, $^{164}\mathrm{Dy}\phantom{\rule{0.16em}{0ex}}(\ensuremath{\alpha}2pxn)$, and $^{160}\mathrm{Dy}(2\ensuremath{\alpha}xn)$ produced through complete- and incomplete-fusion reactions have been measured in the system $^{16}\mathrm{O}+^{154}\mathrm{Sm}$ at projectile energy $=6.1\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ using the in-beam charged-particle ($Z=1,2$)--\ensuremath{\gamma}-ray coincidence technique. The results indicate the occurrence of incomplete fusion involving the breakup of $^{16}\mathrm{O}$ into $^{4}\mathrm{He}+^{12}\mathrm{C}$ and/or $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ followed by fusion of one of the fragments with target nucleus $^{154}\mathrm{Sm}$. The pattern of measured spin distributions of the evaporation residues produced through complete and incomplete fusion are found to be entirely different from each other. It has been observed from these present results that the mean input angular momentum for the evaporation residues produced through complete fusion is relatively lower than that of evaporation residues produced through incomplete-fusion reactions. The pattern of feeding intensity of evaporation residues populated through complete- and incomplete-fusion reactions has also been studied. The evaporation residues populated through complete-fusion channels are strongly fed over a broad spin range and widely populated, while evaporation residues populated through incomplete-fusion reactions are found to have narrow range feeding only for high spin states. Comparison of present results with earlier data suggests that the value of mean input angular momentum is relatively higher for a deformed target and more mass asymmetric system than that of a spherical target and less mass asymmetric system by using the same projectile and the same energy. Thus, present results indicate that the incomplete-fusion reactions not only depend on the mass asymmetry of the system, but also depend on the deformation of the target.

High-resolution observations of IRAS 08544-4431: Detection of a disk orbiting a post-AGB star and of a slow disk wind.

In order to study the effects of rotating disks in the post-asymptotic giant branch (post-AGB) evolution, we observe a class of binary post-AGB stars that seem to be systematically surrounded by equatorial disks and slow outflows. Although the rotating dynamics had only been well identified in three cases, the study of such structures is thought to be fundamental to the understanding of the formation of disks in various phases of the late evolution of binary stars and the ejection of planetary nebulae from evolved stars. We present ALMA maps of 12CO and 13CO J=3-2 lines in the source IRAS 08544-4431, which belongs to the above mentioned class of objects. We analyzed the data by means of nebula models, which account for the expectedly composite source and can reproduce the data. From our modeling, we estimated the main nebula parameters, including the structure and dynamics and the density and temperature distributions. We discuss the uncertainties of the derived values and, in particular, their dependence on the distance. Our observations reveal the presence of an equatorial disk in rotation; a low-velocity outflow is also found, probably formed of gas expelled from the disk. The main characteristics of our observations and modeling of IRAS 08544-4431 are similar to those of better studied objects, confirming our interpretation. The disk rotation indicates a total central mass of about 1.8 M⊙, for a distance of 1100 pc. The disk is found to be relatively extended and has a typical diameter of ~ 4 1016 cm. The total nebular mass is ~ 2 10-2M⊙, of which ~ 90% corresponds to the disk. Assuming that the outflow is due to mass loss from the disk, we derive a disk lifetime of ~ 10000 yr. The disk angular momentum is found to be comparable to that of the binary system at present. Assuming that the disk angular momentum was transferred from the binary system, as expected, the high values of the disk angular momentum in this and other similar disks suggest that the size of the stellar orbits has significantly decreased as a consequence of disk formation.

The GALAH survey: stellar streams and how stellar velocity distributions vary with Galactic longitude, hemisphere, and metallicity

Using GALAH survey data of nearby stars, we look at how structure in the planar (u,v) velocity distribution depends on metallicity and on viewing direction within the Galaxy. In nearby stars, with distance d < 1 kpc, the Hercules stream is most strongly seen in higher metallicity stars [Fe/H] > 0.2. The Hercules stream peak v value depends on viewed galactic longitude, which we interpret as due to the gap between the stellar stream and more circular orbits being associated with a specific angular momentum value of about 1640 km/s kpc. The association of the gap with a particular angular momentum value supports a bar resonant model for the Hercules stream. Moving groups previously identified in Hipparcos observations are easiest to see in stars nearer than 250 pc, and their visibility and peak velocities in the velocity distributions depends on both viewing direction (galactic longitude and hemisphere) and metallicity. We infer that there is fine structure in local velocity distributions that varies over distances of a few hundred pc in the Galaxy.

Mixture of two ultra cold bosonic atoms confined in a ring: stability and persistent currents

In this article we investigate the stability of quantized yrast states in a mixture of two distinguishable equal mass bosonic atoms confined in a ring. We focus in the study of energetic stability since the Bloch analysis and the Bogoliubov theory establishes that only energetically stable quantized yrast states are capable of sustain a persistent current. In the framework of the Bogoliubov theory we study the stability in two different cases chosen by physical considerations. In one case we analyze how the inter and intraspecies interaction strengths affect the stability of a selected quantized yrast state specified by the angular momentum per particle and the population imbalance. In the other case, for a fixed dynamics specified by given values of interaction strengths, we determine the stability of quantized yrast states as function of the angular momentum per particle and the population imbalance. We also examined the stability of the mixture in the rarefied limit and we found a critical value of the population imbalance which gives the size of the window of energetic stability and a critical value of angular momentum per particle which is an upper bound of the possible values of angular momentum per particle carried by energetically stable quantized yrast states.

Analysis of minimal length effect on the non-relativistic energy and wave function for the exponential type potential using Supersymmetric Quantum Mechanics

In this research, the minimal length effect was analysed on the energy and wave functions of the non-relativistic mechanical quantum system by studying the Schrodinger equation. The three dimensional Schrodinger equation with minimal length for the exponential type potential was solved by using supersymmetric quantum mechanics. To get the solution, the exponential type potential was reduced to the Morse potential. The non-relativistic energy was calculated numerically for diatomic molecules, LiH and HCl by using the Matlab software. From the results were shown that the presence of minimal length gives effect to the non-relativistic energy, it was seen clearly in the higher value of angular momentum l and quantum number n.

Half theory fractional angular momentum and the application of fractional derivatives to quantum mechanics

In this paper, we review the fractional derivative and apply it to various problems in quantum mechanics. Among other things, we find fractional angular momentum, with “fractional spherical harmonics” as solutions to the squared quantum mechanical angular momentum operator, but with non-integer eigenvalues. These fractional functions might be interpreted as intermediary states visited by an orbiting electron as it jumps between the more stable, integer angular momentum values in an atom. Alternatively, these fractional states may be of interest in the mechanisms of chemical bonding. The justification for these new states, which are normalizable solutions to Hermitian operators, depends of course on experiment. We remember Feynmann’s statement about quantum mechanics, “Everything that is not expressly forbidden, is mandatory.”