Non-vanishing Angular Momentum Research Articles

Nonreciprocity and odd viscosity in chiral active fluids

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid [Formula: see text], quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse-graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a nonvanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other nondissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible nonreciprocal phase transition.

General relativity versus dark matter for rotating galaxies

A very general class of axially symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally supported galaxies. The exact vacuum solutions of the Einstein equations for this extended Weyl class of metrics allow us to rigorously deduce the following: (i) GR rotational velocity always exceeds the Newtonian velocity (thanks to Lenz’s law in GR). (ii) A non-vanishing intrinsic angular momentum (J) for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter (a)—a behaviour identical to that found for the Kerr metric. (iii) Asymptotic constancy of the same parameter a also demands a plateau in the rotational velocity. Unlike the Kerr metric, the extended Weyl metric can and has been continued within the galaxy, and it has been shown under what conditions Gauß and Ampére laws emerge along with Ludwig’s extended gravito-electromagnetism (GEM) theory with its attendant non-linear rate equations for the velocity field. Better estimates (than that from the Newtonian theory) for the escape velocity of the Sun have been presented.

Rashba effect: a chemical physicist's approach.

Understanding the mechanisms underlying the emergence of giant spin splitting (GSS) is fundamental in the pursuit of more robust strategies for designing materials with desired spin splitting. This drive for material innovation continues to captivate a burgeoning community of early-career researchers with backgrounds in chemistry and material science. However, new to the field, they are often equipped only with the insight provided by the original Bychkov-Rashba model. Furthermore, daunted by the tight-binding perspective on the non-vanishing orbital angular momentum (OAM), they struggle to accurately account for the atomic spin-orbit interaction (SOI) in the formation of GSS. To address these challenges and equip young chemists with better-suited tools, this review aims to provide a more intuitive perspective on atomic interactions (orbital hybridization), structure symmetry, and atomic SOI in the formation of GSS. In pursuit of this goal, the review explores the Bychkov-Rashba model, its advantages, and limitations. Subsequently, it introduces the orbital framework, wherein GSS is modulated by atomic SOI and the interplay of OAM with the surface electrostatic field. Given the explicit dependence of both these factors on OAM, the review examines why OAM is typically quenched in crystal structures and how chemical bonds involving different orbital types can lead to its non-zero values in the presence of inversion symmetry breaking. Finally, with this chemistry-focused perspective, the review examines the rise of GSS in selected examples.

Generation of ellipticity-tunable isolated attosecond pulses from diatomic molecules in intense laser fields

We theoretically investigate the high-order harmonic generation (HHG) and the isolated attosecond pulse (IAP) with tunable ellipticity from the aligned molecule. It is found that the ellipticity of harmonic depends on the internuclear distance R. Further analysis presents that the nonzero ellipticity of harmonic generated at R=6a.u. is attributed to the 2pσu state of H2+. The 2pσu state with nonvanishing angular momentum originates from a resonant transition from the 1sσg state induced by the fundamental pulse. With specific intensity of the orthogonally polarized two-color (OTC) laser fields, an IAP with high ellipticity can be obtained. To further illustrate the origin of the high ellipticity, we present the electron trajectories and electron currents induced by the electron wavepackets of H2+, which shows a clear picture of the dynamic process of HHG. Moreover, the polarization of the IAP varies from left to right elliptical polarization by synthesizing the harmonic spectrum with different orders. Such an IAP may serve as a potential tool for probing and manipulating the ultrafast magnetic and chiral dynamics.

QCD Effects in Non-QCD Theories

It is shown that, in some non-QCD theories, there are effects shared by QCD: (i)~in SU(2) Yang-Mills theory containing a nonlinear spinor field, there is a mass gap; (ii)~in SU(3) Proca-Higgs theory, there are flux tube solutions with a longitudinal electric field required for producing a force binding quarks; (iii)~in non-Abelian Proca-Higgs theories, there exist flux tube solutions with a momentum directed along the tube axis and particlelike solutions with a nonvanishing total angular momentum created by crossed color electric and magnetic fields; in QCD, such configurations may contribute to the proton spin. We discuss the conjecture that such non-QCD theories might be a consequence of approximate solution of an infinite set of Dyson-Schwinger equations describing the procedure of nonperturbative quantization. The phenomenon of dimensional transmutation for nonperturbative quantization and the analogy between nonperturbative quantization and turbulence modeling are also discussed.

Thermodynamics of Kerr-AdS black holes in the restricted phase space

The thermodynamics for Kerr-AdS black hole in four dimensions is revisited using the recently proposed restricted phase space formalism, which includes the central charge C of the dual CFT and the chemical potential mu , but excludes the pressure and the conjugate volume, as thermodynamic variables. The Euler relation holds automatically, and the first order homogeneity of the mass and the zeroth order homogeneity of the intensive variables are made explicit. Thermodynamic processes involving each pair of conjugate variables are studied in some detail, with emphasis on the scaling properties of the equations of states. It turns out that the thermodynamic behavior of the Kerr-AdS black hole is very similar to that of the RN-AdS black hole studied earlier. In particular, it is found that, there is a first order supercritical phase equilibrium in the T-S processes at fixed nonvanishing angular momentum, while at vanishing angular momentum or at fixed angular velocities, there is always a non-equilibrium transition from a small unstable black hole state to a large stable black hole state. Moreover, there is a Hawking–Page phase transition in the mu -C processes. Due to the complicatedness of the Kerr metric, the exact critical point and the Hawking–Page temperature are worked out explicitly only in the slow rotating limit, however the characteristic thermodynamic properties do not rely on the slow rotating approximation.

A New Moving Frame for Trajectories with Non-Vanishing Angular Momentum

The theory of curves has a very long history. Moving frames defined on curves are important parts of this theory. They have never lost their importance. A point particle of constant mass moving along a trajectory in space may be seen as a point of the trajectory. Therefore, there is a very close relationship between the differential geometry of the trajectory and the kinematics of the particle moving on it. One of the most important elements of the particle kinematics is the jerk vector of the moving particle. Recently, a new resolution of the jerk vector, along the tangential direction and two special radial directions, has been presented by \"Ozen et al. (JTAM 57(2)(2019)). By means of these two special radial directions, we introduce a new moving frame for the trajectory of a moving particle with non vanishing angular momentum in this study. Then, according to this frame, some characterizations for the trajectory to be a rectifying curve, an osculating curve, a normal curve, a planar curve and a general helix are given. Also, slant helical trajectories are defined with respect to this frame. Afterwards, the necessary and sufficient conditions for the trajectory to be a slant helical trajectory (according to this frame) are obtained and some special cases of these trajectories are investigated. Moreover, we provide an illustrative numerical example to explain how this frame is constructed. This frame is a new contribution to the field and it may be useful in some specific applications of differential geometry, kinematics and robotics in the future.

Elliptical isolated attosecond-pulse generation from an atom in a linear laser field

We theoretically demonstrate a scheme to produce elliptically polarized isolated attosecond pulses, based on the high-order harmonic generation from the current-carrying state of an atom exposed in linearly polarized laser fields. It is shown that the nonzero ellipticity of the attosecond pulse generated at the single-atom level is attributed to the nonvanishing angular momentum of the state, which is further elucidated by the strong-field approximation model. With specific carrier envelope phases (CEPs), isolated attosecond pulses with large ellipticity can be obtained. Moreover, the ellipticity of high-order harmonics remains almost invariable versus the CEP of the few-cycle driving field. Hence, the temporal profile and ellipticity of the attosecond-pulse radiation can be manipulated separately, which is beneficial to shape the attosecond-pulse radiation without compromising the ellipticity. The obtained elliptical attosecond pulse may serve as a potential tool to explore and manipulate the ultrafast dynamics in magnetic materials and chiral media.

Synthetic magnetic fields for cold erbium atoms

The implementation of the fractional quantum Hall effect in ultracold atomic quantum gases remains, despite substantial advances in the field, a major challenge. Since atoms are electrically neutral, a key ingredient is the generation of sufficiently strong artificial gauge fields. Here we theoretically investigate the synthetization of such fields for bosonic erbium atoms by phase imprinting with two counterpropagating optical Raman beams. Given the nonvanishing orbital angular momentum of the rare-earth atomic species erbium in the electronic ground state and the availability of narrow-line transitions, heating from photon scattering is expected to be lower than in atomic alkali-metal species. We give a parameter regime for which strong synthetic magnetic fields with good spatial homogeneity are predicted. We also estimate the size of the Laughlin gap expected from the s-wave contribution of the interactions for typical experimental parameters of a two-dimensional atomic erbium microcloud. Our analysis shows that cold rare-earth atomic ensembles are highly attractive candidate systems for experimental explorations of the fractional quantum Hall regime.

Toward the pole

We study the analytic structure of semiclassical conformal blocks, namely of the 1-point conformal block on the torus and of the 4-point conformal block on the sphere, as functions of the intermediate dimension. We interpret their discontinuities, which can be revealed with the use of a particular resummation procedure, holographically in terms of configurations of geodesics in AdS3. In other words, we study the behavior of the Ω-deformed mathcal{N} = 2 SYM theory in the Nekrasov-Shatashvili limit near those singular points, where naively the W-boson with non-vanishing angular momentum becomes massless. Upon a proper resummation of instanton contributions, these singularities disappear, which is similar to the Seiberg-Witten solution in the undeformed case where there is no massless W-boson. It is shown that the order parameter undergoes a non-analytic behavior near positions of the poles. The jump of the order parameter is interpreted holographically in terms of geodesic networks.

A guide to hunting periodic three-body orbits with non-vanishing angular momentum

A large number of periodic three-body orbits with vanishing angular momentum have been found in Newtonian gravity over the past 6 years due to a simple search method and to the contribution from practitioners outside the Celestial Mechanics community. Extension of such orbits to non-vanishing angular momentum has been lacking due to inter alia the absence of a sufficiently simple and widely known search method. We present a method, i.e., a general strategy plus detailed tactics (but not a specific algorithm, or a code), to numerically search for relative periodic orbits in the Newtonian three-body problem with three equal masses and non-vanishing angular momentum. We illustrate the method with an application to a specific, so-called Broucke–Hadjidemetriou–Hénon (BHH) family of periodic 3-body orbits: Our search yielded around 100 new “satellite” orbits, related to the original BHH orbits by a topological relation (defined in the text), with infinitely many orbits remaining to be discovered. We used the so-obtained orbits to test the period vs. topology relation that had previously been established, within a certain numerical accuracy, for orbits with vanishing angular momentum. Our method can be readily: (1) applied to families of periodic 3-body orbits other than the BHH one; (2) implemented using various standard algorithms for solving ordinary differential equations, such as the Bulirsch–Stoer and the Runge–Kutta–Fehlberg ones; (3) adapted to 3-body systems with distinct masses and/or coupling constants, including, but not limited to, Coulomb interaction. Our goal is to enable numerical searches for new orbits in as many families of orbits as possible, and thus to allow searches for other empirical relations, such as the aforementioned topology vs. period one.

Dynamical evolutions of -boson stars in spherical symmetry

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars (BSs) by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number . We call such solutions ‘-boson stars’. Here, we perform a series of fully non-linear dynamical simulations of perturbed -BSs in order to study their stability, and the final fate of unstable configurations. We show that for each value of , the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with BSs, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.

Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity

We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have non-vanishing angular momentum. As one tunes to more relativistic solutions (measured for example by an increasing redshift) there exists a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become conical in the sense that there is a deficit angle. Such solutions may provide self-consistent models for rotating circular cosmic strings.

Highly Efficient Broadband Multiplexed Millimeter-Wave Vortices from Metasurface-Enabled Transmit-Arrays of Subwavelength Thickness

The generation of ``structured'' light beams bearing nonvanishing orbital angular momentum is important for a wide range of microwave and optical applications. Unfortunately, current methods allow only narrow bandwidth, require an optically thick device, or are inefficient. This study leverages geometric phases due to spin-to-orbital interaction and tailored subwavelength transmit-arrays to enable highly efficient creation of broadband multiple vortex beams, free from normal-mode background interference. The design methodology and proposed structure can be further extended, for two-dimensional (de)multiplexing of vortex beams in momentum space.

Strong spin-orbit effects in transition metal oxides with tetrahedral coordination

To prove that spin-orbit coupling can play a relevant role in determining the magnetic structure of transition metal oxides with tetrahedral coordination, we investigate the d1 Mott insulator KOsO4, combining density functional theory calculations and the exact diagonalization approach. We find that the interplay between crystal field, strong spin-orbit coupling, electronic correlations and structural distortions brings the system towards an antiferromagnetic phase, characterized by a non-vanishing orbital angular momentum and anisotropy among the in-plane and the out-of-plane antiferromagnetic correlations. We also show that, due to the peculiar interplay between spin-orbit coupling, Hund's coupling and hopping connectivity the system is on the verge of developing short range ferromagnetic correlations marked by strong directionality.

Rotating hairy black holes in arbitrary dimensions

A class of exact rotating black hole solutions of gravity nonminimally coupled to a self-interacting scalar field in arbitrary dimensions is presented. These spacetimes are asymptotically locally anti-de Sitter manifolds and have a Ricci-flat event horizon hiding a curvature singularity at the origin. The scalar field is real and regular everywhere and its effective mass, coming from the nonminimal coupling with the scalar curvature, saturates the Breitenlohner-Freedman bound for the corresponding spacetime dimension. The rotating black hole is obtained by applying an improper coordinate transformation to the static one. Although both spacetimes are locally equivalent, they are globally different, as it is confirmed by the nonvanishing angular momentum of the rotating black hole. It is found that the mass is bounded from below by the angular momentum in agreement with the existence of an event horizon. The thermodynamical analysis is carried out in the grand canonical ensemble. The first law is satisfied and a Smarr formula is exhibited. The thermodynamical local stability of the rotating hairy black holes is established from their Gibbs free energy. However, the global stability analysis establishes that the vacuum spacetime is always preferred over the hairy black hole. Thus, the hairy black hole is likely to decay into the vacuum one for any temperature.

Quasinormal modes of scale dependent black holes in (1+2)-dimensional Einstein-power-Maxwell theory

We study for the first time the stability against scalar perturbations, and we compute the spectrum of quasinormal modes of three-dimensional charged black holes in Einstein-power-Maxwell non-linear electrodynamics assuming running couplings. Adopting the 6th order WKB approximation we investigate how the running of the couplings change the spectrum of the classical theory. Our results show that all modes corresponding to non-vanishing angular momentum are unstable both in the classical theory and with the running of the couplings, while the fundamental mode can be stable or unstable depending on the running parameter and the electric charge.

Spinning of particles in optical double-vortex beams

Optical spin angular momentum, an intrinsic part of optical angular momemtum, can induce a spinning motion of a trapped particle around its own axis in optical manipulation. Focusing of a type of double-vortex (DV) input field obtained by linearly superposing two optical vortex beams with equal but opposite topological charges, yields a multi-lobe focal field, each of which has non-vanishing optical spin angular momentum, and is capable of trapping particle while spinning the particle around a certain axis. Significantly, both the focusing properties and the spinning dynamics are strongly polarization dependent. For instance, the focused field of a circularly polarized double-vortex (CPDV) beam carries transverse and longitudinal spin angular momenta, inducing axial spinning of the trapped particles, whereas the focused field of a radially polarized double-vortex (RPDV) beam possesses purely transverse spin angular momentum and can drive the particles to spin transversely to the optical axis. These results may find potential applications in light beam shaping and optical manipulations.

Bose-Einstein condensation of erbium atoms in a quasielectrostatic optical dipole trap

Quantum gases of rare-earth elements are of interest due to the large magnetic moment of many of those elements, leading to strong dipole-dipole interactions, as well as an often nonvanishing orbital angular momentum in the electronic ground state, with prospects for long coherence time Raman manipulation, and state-dependent lattice potentials. We report on the realization of a Bose-Einstein condensate of erbium atoms in a quasielectrostatic optical dipole trap generated by a tightly focused midinfrared optical beam derived from a $\textrm{CO}_2$ laser near 10.6$\mu$m in wavelength. The quasistatic dipole trap is loaded from a magneto-optic trap operating on a narrow-line erbium laser cooling transition near 583nm in wavelength. Evaporative cooling within the dipole trap takes place in the presence of a magnetic field gradient to enhance the evaporative speed, and we produce spin-polarized erbium Bose-Einstein condensates with $3\times10^4$ atoms.

Rotating solutions in critical Lovelock gravities

For appropriate choices of the coupling constants, the equations of motion of Lovelock gravities up to order n in the Riemann tensor can be factorized such that the theories admits a single (A)dS vacuum. In this paper we construct two classes of exact rotating metrics in such critical Lovelock gravities of order n in d=2n+1 dimensions. In one class, the n angular momenta in the n orthogonal spatial 2-planes are equal, and hence the metric is of cohomogeneity one. We construct these metrics in a Kerr-Schild form, but they can then be recast in terms of Boyer-Lindquist coordinates. The other class involves metrics with only a single non-vanishing angular momentum. Again we construct them in a Kerr-Schild form, but in this case it does not seem to be possible to recast them in Boyer-Lindquist form. Both classes of solutions have naked curvature singularities, arising because of the over rotation of the configurations.