Conservation Of Total Angular Momentum Research Articles

Efficient multimode vectorial nonlinear propagation solver beyond the weak guidance approximation

In this paper, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular momentum of light upon propagation and takes into account the vectorial nature of the propagating modes, making it particularly relevant for studies in ring-core fibers. While conventional propagation solvers exhibit a computational complexity scaling as Nmode4, where Nmode is the number of considered modes, the present solver scales as Nmode3/2. As a first example, it is shown that orbital angular momentum modulation instability processes take place in ring-core fibers in realistic conditions. Finally, it is predicted that the modulation instability process is followed by the appearance of breather-like angular structures.

Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide

Planetary obliquity plays a significant role in determining the physical properties of planetary surfaces and climate. As direct detection is constrained due to the present observation accuracy, kinetic theories are helpful for predicting the evolution of planetary obliquity. Here the coupling effect between the eccentric Kozai–Lidov effect and the equilibrium tide is extensively investigated; the planetary obliquity is observed to follow two kinds of secular evolution paths, based on the conservation of total angular momentum. The equilibrium timescale of the planetary obliquity t eq varies along with r t , which is defined as the initial timescale ratio of the tidal dissipation and secular perturbation. We numerically derive the linear relationship between t eq and r t with the maximum likelihood method. The spin-axis orientation of S-type terrestrials orbiting M-dwarfs reverses over 90° when r t > 100, then enters the quasi-equilibrium state between 40° and 60°, while the maximum obliquity can reach 130° when r t > 104. Numerical simulations show that the maximum obliquity increases with the semimajor axis ratio a 1/a 2, but is not so sensitive to the eccentricity e 2. The likelihood of an obliquity flip for S-type terrestrials in general systems with a 2 < 45 au is closely related to m 1. The observed potentially oblique S-type planets HD 42936 b, GJ 86 Ab, and τ Boo Ab are explored and found to have a great possibility of rotating head-down over the secular evolution of spin.

Heavy-quark spin symmetry breaking in the Born-Oppenheimer approximation

Heavy-quark spin symmetry is explicitly broken by the mass splitting between a heavy-light pseudoscalar meson and its vector partner. This fact plays a pivotal role in the physics of states whose mass lies close to the threshold of an open-flavor meson pair, like X(3872). We show that this source of heavy-quark spin symmetry breaking can be systematically included within the diabatic representation of the Born-Oppenheimer approximation. We verify that including all the appropriate coupled channels guarantees conservation of total angular momentum, parity, and charge-conjugation parity. This marks a fundamental step towards a unified, first-principles study of quarkonia and meson molecules with hidden flavor.

Relativistic second-order dissipative spin hydrodynamics from the method of moments

We derive relativistic second-order dissipative fluid-dynamical equations of motion for massive spin-1/2 particles from kinetic theory using the method of moments. Besides the usual conservation laws for charge, energy, and momentum, such a theory of relativistic dissipative spin hydrodynamics features an equation of motion for the rank-3 spin tensor, which follows from the conservation of total angular momentum. Extending the conventional method of moments for spin-0 particles, we expand the spin-dependent distribution function near local equilibrium in terms of moments of the momentum and spin variables. We work to next-to-leading order in the Planck constant $\hbar$. As shown in previous work, at this order in $\hbar$ the Boltzmann equation for spin-1/2 particles features a nonlocal collision term. From the Boltzmann equation, we then obtain an infinite set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local equilibrium. In order to close this system of moment equations, a truncation procedure is needed. We employ the "14+24-moment approximation", where "14" corresponds to the components of the charge current and the energy-momentum tensor and "24" to the components of the spin tensor, which completes the derivation of the equations of motion of second-order dissipative spin hydrodynamics. For applications to heavy-ion phenomenology, we also determine dissipative corrections to the Pauli-Lubanski vector.

Quantized Constrained Molecular Chains: Vibrations, Internal Rotations and Polymerization

The present work has a twofold purpose. a) It proposes a quantum-mechanical approach to constrained molecular chains and their small vibrations and rotations, by employing in a compact way vector variables and operators associated to the constituent units of the chain. The methods here differ from standard approaches based upon cartesian coordinates and normal modes and generalize previous quantum Hamiltonians describing only rotational degrees of freedom. Several models in D = 2, 3 spatial dimensions, with new Hermitean Hamiltonians, are formulated and analyzed. The chains studied successively display an increasing number of constraints: freely-jointed, freely-rotating and with constrained torsions. Conservation of total orbital angular momentum is analyzed. As a partial test, by using the present approach, the vibrational frequencies of certain triatomic molecules (water vapour, hydrogen sulfide, heavy water and sulfur dioxide) are computed and shown to be consistent with experimental data. b) A new (quantum-mechanical) analysis of polymerization, namely, the growth of a freely-jointed molecular chain (of the kind considered above) by binding an additional unit 1 to the chain, is presented. They move in a very dilute solution in a fluid at rest in thermal equilibrium about room temperature. The analysis is based upon a mixed (quantum-classical) distribution function in phase-space: a quantum Wigner-like one for unit 1 and a classical Liouville one for the chain. That leads to an approximate Schmolukowski equation for unit 1 alone and, through it, to compute the mean first passage time (MFPT) for unit 1 to become bound by the chain. The resulting MFPT displays a temperature dependence consistent with the Arrhenius formula for rate constants in chemical reactions.

Linear mode analysis from spin transport equation

We provide a linear analysis on normal modes of the spin Boltzmann equation proposed by Weickgenannt et al. [Phys. Rev. D 104, 016022 (2021)], where the nondiagonal or polarized part of the transition rate is neglected to ensure the Hermitian property of a linearized collision operator. As an instrumental element of spin kinetic theory, the conservation of total angular momentum is explicitly considered; thus, our analysis is relevant to the recent investigation on the issue of local spin polarization. By treating the linearized collision operator as an evolution operator, solving the normal modes turns out to be a degenerate perturbation problem in quantum mechanics. The dispersion relations of spinless modes are in accordance with well-known calculations, while the frequencies of spin modes are also determined up to second-order in wave vectors; the second-order expressions are only formal solutions to be further determined. Moreover, the relaxation of spin density is related to our linear mode analysis, which shall play a big role in investigating the issues of the local spin polarization in the relativistic heavy-ion collisions.

Experimental observation of the orbital Hall effect of light through pure orbit–orbit interaction for randomly and radially polarized vortex beams

The orbit–orbit interaction of light leads to fundamentally rich optical phenomena whose experimental exploration and theoretical understanding remain challenging. Here, we investigate polarization-independent vortex-induced beam shifts for light beams possessing random polarization and radial polarization. The experiments reveal an intriguing manifestation of the orbital Hall effect of light as a consequence of orbit–orbit interactions and resulting conservation of total angular momentum. An interferometric scheme is experimentally implemented to quantify the change in the phase structure of the orbital angular momentum carrying beam as signatures of the orbital Hall effect of light arising due to partial reflection at a dielectric interface. We also demonstrate, and thus corroborate, the conservation of total angular momentum for such vortex-induced beam shifts.

Some continuous and discontinuous Galerkin methods and structure preservation for incompressible flows

AbstractIn this paper, we present consistent and inconsistent discontinuous Galerkin (dG) methods for incompressible Euler and Navier–Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semi‐ and fully discrete energy stability of the proposed dG methods are proved in a unified fashion. Conservation of total energy, linear, and angular momentum is discussed with both central and upwind fluxes. Numerical experiments are presented to demonstrate our findings and compare our schemes with conventional schemes in the literature in both unsteady and steady problems. Numerical results show that global conservation of the physical quantities may not be enough to demonstrate the performance of the schemes, and our schemes are competitive and able to capture essential physical features in several benchmark problems.

Glow discharge excitation and ionization of chromium, comparison with iron

Cr I and Cr II emission spectra from a Grimm-type glow discharge (GD) in argon and neon were analyzed. Intensities of strong resonance Cr I lines were corrected for self-absorption and population functions (experimental Boltzmann plots) of the Cr I system were established. A prevailing excitation mechanism in Cr I is the electron impact (EI) excitation. Cr II spectra in both discharges were described by transition rate (TR) diagrams, under the model of radiatively-dominated deexcitation. The contribution of cascade excitation was subtracted and the resulting net-TR diagrams of Cr II were analyzed. Unlike ionic spectra of some other transition elements, asymmetric charge transfer (ACT) between the ions of the discharge gas and ground state Cr atoms does not play a role in the excitation of the Cr II spectrum, because of the absence of suitable states in Cr II that would allow simultaneous conservation of energy and total angular momentum. Cr II states below ≈17 eV are populated largely by EI excitation from long-lived low Cr II states. In a neon discharge, ACT reactions between neutral neon metastables and doubly charged Cr ions and between neutral chromium and neon molecular ions were identified. The findings reported here were compared with the excitation of Fe I and Fe II systems at similar conditions. A well-known ‘hydrogen effect’, an enhancement of the Cr II line at 267.7165 nm in the presence of hydrogen in a GD plasma, was explained by charge transfer reaction between H+ ions and neutral chromium.

Spin-to-orbital angular momentum conversion in harmonic generation driven by intense circularly polarized laser

Spin-to-orbital angular momentum conversion (STOC) is a very important fundamental phenomenon governed by the conservation of total angular momentum (TAM). In optics, this conversion is usually associated with the vortex light carrying the orbital angular momentum (OAM). In this paper we demonstrate a new mechanism to achieve STOC via the interaction of an intense circularly polarized (CP) laser pulse with a solid density plasma target. We find that when a laser pulse with relativistic intensity is tightly focused, a longitudinal electric field is induced owing to the finite transverse size and profile of the laser field. Therefore, even for the normally incident CP laser, the induced longitudinal electric field can drive an oscillating vortex plasma surface to emit the vortex harmonics when the laser interacts with the plasma target. Based on simulations and theoretical analysis, we verify this harmonic generation mechanism and reveal the STOC process in the harmonic generation. It is shown that the spin angular momenta of multiple fundamental-frequency photons are converted to the OAM of a single harmonic photon because of the TAM conservation. We also discuss the dynamical symmetries in the harmonic generation process, which physically constrains the harmonic orders, as well as the angular momenta. In addition, if a vortex laser beam or a spiral phase plate is used, the OAM of the harmonic photon becomes more tunable and controllable. This study provides a deep insight into the nature of the spin–orbital interaction in optics.

Relaxation of the Optical Anisotropy of Gas-Phase Molecular Complexes

The kinetics of optically induced anisotropy in molecular complexes with a nonequilibrium rotational distribution arising during their formation in the gas phase are calculated. It is shown that damped periodic oscillations, the period and amplitude of which depend on additional angular moments, appear in the anisotropy relaxation kinetics. The additional angular moments are determined by force moment vectors during translational-rotational exchange taking into account the law of conservation of total angular momentum of the molecules forming the complex. Anisotropy relaxation becomes significantly modulated as their magnitude increases. The estimated degree of optical anisotropy modulation and force moments during chemical bond formation can be used to clarify the stereodynamics of the complex-formation process.

Kinetic theory for massive spin−1/2 particles from the Wigner-function formalism

We calculate the Wigner function for massive spin-1/2 particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\hbar$. Going beyond leading order in $\hbar$ we then derive a generalized Boltzmann equation in which the force exerted by an inhomogeneous electromagnetic field on the particle dipole moment arises naturally. Carefully taking the massless limit we find agreement with previous results. The case of global equilibrium with rotation is also studied. Finally, we outline the derivation of fluid-dynamical equations from the components of the Wigner function. The conservation of total angular momentum is promoted as an additional fluid-dynamical equation of motion. Our framework can be used to study polarization effects induced by vorticity and magnetic field in relativistic heavy-ion collisions.

Role of the absorption on the spin-orbit interactions of light with Si nano-particles

The conservation of the photon total angular momentum in the incident direction in an axially symmetric scattering process is a very well known fact. Nonetheless, the redistribution of this conserved magnitude into its spin and orbital components, an effect known as the spin-orbit interaction (SOI) of light, is still a matter of active research. Here, we discuss the effect of the absorption on the SOI in the scattering of a subwavelength silicon particle. Describing the scattering process of an electric and a magnetic dipole, we show via the asymmetry parameter that the SOI of light in the scattering of high refractive index nanoparticles endures in the presence of optical losses. This effect results in optical mirages whose maximum values surpass those of an electric dipolar scatterer.

All-optical spin switching under different spin configurations

All-optical spin switching represents a new frontier in femtomagnetism. However, its underlying principles are quite different from traditional thermal activated spin switching. Here, we employ an atomic spin model and present a systematic investigation from a single spin to a large system of over a million spins. We find that for a single spin without an external perturbation, the conservation of total angular momentum requires that the spin change, if any, exactly matches the orbital momentum change, but a laser pulse significantly alters this relation, where the spin change does not necessarily follow the orbital change. This is reflected in the strong dependence of switching on laser polarization. To have an efficient spin switching, the electron initial momentum direction must closely follow the spin’s orientation, so the orbital angular momentum is transverse to the spin and consequently the spin–orbit torque lies in the same direction as the spin. The module of the spin–orbit torque is , where is the angle between spin and position (momentum ) and is the angle between and . These findings are manifested in a much larger system. We find that the spin response depends on underlying spin structures. A linearly polarized laser pulse creates a dip in a uniform inplane-magnetized thin film, but has little effects on Néel and Bloch walls. Both right- and left- circularly polarized light ( and ) have stronger but different effects in both uniform spin domains and Néel walls. While light creates a basin of spins pointing down, light creates a mound of spins pointing up. In the vicinity of the structure spins are reversed, similar to the experimental observation. light has a dramatic effect, disrupting spins in Bloch walls. By contrast, light has a small effect on Bloch walls because only switches down spins up and once the spins already point up, there is no major effect. These findings are expected to have important implications in the future.

Plasmon‐Enhanced Spin–Orbit Interaction of Light in Graphene

AbstractA novel theoretical framework is developed describing polariton‐enhanced spin–orbit interaction (SOI) of light on the surface of 2D media. The reduced dimensionality of the system is exploited to introduce a quantum‐like formalism particularly suitable to fully take advantage of rotational invariance. Conservation of total angular momentum upon scattering enables the physical unveiling of the interaction between radiation and the 2D material along with the detailed exchange processes among orbital and spin components. In addition, the formalism is specialized to doped extended graphene, finding such an SOI to be dramatically enhanced by the excitation of plasmons propagating radially along the graphene sheet. Several examples of the enormous possibilities offered by plasmon‐enhanced SOI of light are provided including vortex generation, mixing, and engineering of tunable deep subwavelength arrays of optical traps in the near field.

Proton Spin Puzzle and Confinement of Quarks

It is shown that the confinement effect that is significant at great distances from the nucleon center is capable of inducing the appreciable quark helicity flip. A simultaneous change in projections of the orbital angular momentum of quarks on the direction of their motion, which follows from the Dirac equation, ensures the conservation of the total angular momentum of the system. Thus, a part of the proton spin, measured in experiments with deep inelastic scattering of leptons, may be hidden in the orbital angular momentum of quarks.

Pressure Gradient, Power, and Energy of Vortices

We consider small vortices, such as tornadoes, dust devils, waterspouts, small hurricanes at low latitudes, and whirlpools, for which the Coriolis force can be neglected, and hence within which the flow is cyclostrophic. Such vortices are (at least approximately) cylindrically symmetrical about a vertical axis through the center of a calm central region or eye of radius reye. In the region reye≤r≤rmax fluid (gas or liquid) circulates about the eye with speed v∝rn(n<0). We take rmax to be the outer periphery of the vortex, where the fluid speed is reduced to that of the surrounding wind field (in the cases of tornadoes, dust devils, water-spouts, and small hurricanes at low latitudes) or deemed negligible (in the case of whirlpools). If n=-1, angular momentum is conserved within the fluid itself; if n≠-1, angular momentum must be exchanged with the surroundings to ensure conservation of total angular momentum. We derive the steepness and upper limit of the pressure gradients in vortices. We then discuss the power and energy of vortices. We compare the kinetic energy of atmospheric vortices and the power required to maintain them against frictional dissipation with the same quantities for Earth’s atmosphere as a whole. We explain why the kinetic energy of atmospheric vortices must be replaced on much shorter timescales than is the case for Earth’s atmosphere as a whole. Comparisons of cyclostrophic flow with geostrophic and friction-balanced flows are then provided. We then consider an analogy that might be drawn, at least to some extent, with gravitational systems, considering mainly spherically-symmetrical and cylindrically-symmetrical ones. Generation of kinetic energy at the expense of potential energy in fluid vortices, in geostrophic and friction-balanced flows, and in gravitational systems is then discussed. We explain the variations of pressure and gravitational gradients corresponding to generation of kinetic energy equaling, exceeding, and falling short of frictional dissipation. In the Appendix, we describe a simple method for maximizing power extraction from environmental fluid (water or air) flows, which is also applicable to artificial (e.g., internal combustion) engines. In summary, we provide an overview of features and energetics of Earth’s environmental fluid flows (focusing largely on vortices) and of gravitational analogies thereto that, even though mainly semiquantitative, hopefully may be helpful.

Imbert-Fedorov shift in Weyl semimetals: Dependence on monopole charge and intervalley scattering

The Imbert-Fedorov (IF) shift in optics describes the transverse shift of light beams at the reflection interface. Recently, the IF shift of Weyl fermions at the interface between Weyl semimetals (WSMs) with single monopole charge has been studied. Here, we study the IF shift at the interface between two WSMs, each of which is carrying an arbitrary integer monopole charge. We find a general relation between the monopole charges of the two WSMs and the IF shift. In particular, the IF shift is proportional to the monopole charge if both WSMs have the same one. Our results can be used to infer the topology of the materials by experimentally measuring their IF shift. Furthermore, we consider the possibility that the Weyl fermions are scattered to other Weyl cones during the reflection, which results in qualitatively different behavior of the IF shift. While we use a quantum mechanical approach to solve the problem, semiclassical equations of motion and the conservation of total angular momentum can help us intuitively interpret our results in special cases.

The fate of pancake vortices

Nonlinear evolution of pancake-like vortices in a uniformly rotating and stratified fluid is studied using a 3D Boussinesq numerical model at large Rossby numbers. After the initial stage of viscous decay, the simulations reveal exponential growth of toroidal circulation cells (aka Taylor vortices) at the peripheral annulus with a negative Rayleigh discriminant. At the nonlinear stage, these thin cells redistribute the angular momentum and density differently at the levels of radial outflow and inflow. Resulting layering, with a vertical stacking of sharp variations in velocity and density, enhances small-scale mixing and energy decay. Characteristic detectable stretching patterns are produced in the density field. The circulation patterns, induced by centrifugal instability, tend to homogenize the angular momentum in the vicinity of the unstable region. We demonstrate that the peak intensity of the cells and the vortex energy decay are dramatically reduced by the earth’s rotation due to conservation of total absolute angular momentum. The results have important implications for better understanding the fate of pancake vortices and physical mechanisms of energy transfer in stratified fluids.

Compton Scattering of a Vortex Light Beam

Energy-momentum conservation laws in Compton scattering are analyzed. The conservation of total angular momentum is applied to a general formula that describes the variation of the light angular momentum. The Compton scattering model of a vortex beam is generalized to describe the momentum exchange beyond the well-known photon wave number shift. The illustrated analysis indicates that the light angular momentum may vary due to Compton scattering.