Wave Angular Momentum Research Articles

Dispersion interactions and reactive collisions of ultracold polar molecules

Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40K87Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.

Binary black hole merger in the extreme-mass-ratio limit: A multipolar analysis

Building up on previous work, we present a new calculation of the gravitational wave (GW) emission generated during the transition from quasi-circular inspiral to plunge, merger and ringdown by a binary system of nonspinning black holes, of masses $m_1$ and $m_2$, in the extreme mass ratio limit, $m_1 m_2\ll(m_1+m_2)^2$. The relative dynamics of the system is computed {\it without making any adiabatic approximation} by using an effective one body (EOB) description, namely by representing the binary by an effective particle of mass $\mu=m_1 m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M=m_1+m_2$ and submitted to an $\O(\nu)$ 5PN-resummed analytical radiation reaction force, with $\nu=\mu/M$. The gravitational wave emission is calculated via a multipolar Regge-Wheeler-Zerilli type perturbative approach (valid in the limit $\nu\ll 1$). We consider three mass ratios, $\nu={10^{-2},10^{-3},10^{-4}}$,and we compute the multipolar waveform up to $\ell=8$. We estimate energy and angular momentum losses during the quasi-universal and quasi-geodesic part of the plunge phase and we analyze the structure of the ringdown. We calculate the gravitational recoil, or "kick", imparted to the merger remnant by the gravitational wave emission and we emphasize the importance of higher multipoles to get a final value of the recoil $v/(c\nu^2)=0.0446$. We finally show that there is an {\it excellent fractional agreement} ($\sim 10^{-3}$) (even during the plunge) between the 5PN EOB analytically-resummed radiation reaction flux and the numerically computed gravitational wave angular momentum flux. This is a further confirmation of the aptitude of the EOB formalism to accurately model extreme-mass-ratio inspirals, as needed for the future space-based LISA gravitational wave detector.

Wave angular momentum and the evolution of planetary rings

A theory is proposed that provides angular momentum conservation through the acoustic drift mechanism for gap and ringlet formation in planetary rings. In this context, a new variant of drift mechanism is found, which is dominant if the collision frequency is of the order of the orbital frequency or less. An angular pseudo-momentum equation is derived for gravitational acoustic waves with dissipation. An explicit expression for angular pseudo-momentum, taking into account vertical wave structure, is obtained. The relation between Eulerian- and Lagrangian-averaged mass fluxes is also derived, and the advantages of the Lagrangian one are emphasized.

Quasinormal modes of black holes in anti-de Sitter space: A numerical study of the eikonal limit

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

Inertial frame rotation induced by rotating gravitational waves

We calculate the rotation of the inertial frame within an almost flat cylindrical region surrounded by a pulse of non-axially-symmetric gravitational waves that rotate about the axis of our cylindrical polar coordinates. Our spacetime has only one Killing vector. It is along the z-axis and hypersurface orthogonal. We solve the Einstein equations to first order in the wave amplitude and superpose such linearized solutions to form a wave pulse. We then solve the relevant Einstein equation to second order in the amplitude to find the rotation of inertial frames produced by the pulse. The rotation is without time delay. The influence of gravitational wave angular momentum on the inertial frame demonstrates that Mach's principle cannot be expressed in terms of the influence of the stress–energy–momentum tensor alone but must also involve influences of gravitational wave energy and angular momentum.

Dirac Particle in an Aharonov-Bohm Potential: The Structure of the First Order S-matrix

The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order \(S-$matrix into their $\frac{\Sigma_3}{2}-\)components (eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number.

The high partial wave phenomenon of spin changing atomic transitions

The collisional transition between two highly excited atomic states with different spin is investigated theoretically. Taking helium-like n1S–n3P as an example, it is found that the transition is driven in the highly ionized Fe ion purely by exchange, and the cross section becomes increasingly dominated by partial waves of high orbital angular momentum as the scattering energy increases. Whereas for the near-neutral Li ion the transition is dominated by channel coupling in low partial waves. Analytical benchmarks and numerical methods are developed for the accurate calculation of the exchange integral at high angular momentum. It is shown how the partial wave and energy dependence of the collision strength for high n spin changing transitions in the highly ionized ion is related to the overlap of the extended atomic orbitals.

Control of Diabatic versus Adiabatic Field Dissociation in a Heavy Rydberg System

A novel phenomenon is observed in the dynamics of laser-prepared coherent wave packets, bound by the Coulombic 1/r potential of an ion-pair system. After exciting weakly bound (approximately 3 meV) H(+)(-) wave packets in a Stark field, and permitting them to evolve in time, control of field dissociation via adiabatic and diabatic routes is demonstrated by applying delayed pulsed-electric fields, involving a zero-field crossing. Control manifests itself through the production of ions from each pathway at a different instant in time. This phenomenon is applied to map the oscillatory behavior of an angular momentum wave packet in a heavy Rydberg system. The characteristic frequencies of the observed Stark oscillations verify predicted mass-scaling laws for heavy Rydberg systems.

AO/NAO response to climate change: 1. Respective influences of stratospheric and tropospheric climate changes

We utilize the GISS Global Climate Middle Atmosphere Model and eight different climate change experiments, many of them focused on stratospheric climate forcings, to assess the relative influence of tropospheric and stratospheric climate change on the extratropical circulation indices (Arctic Oscillation, AO; North Atlantic Oscillation, NAO). The experiments are run in two different ways: with variable sea surface temperatures (SSTs) to allow for a full tropospheric climate response, and with specified SSTs to minimize the tropospheric change. The results show that experiments with tropospheric warming or stratospheric cooling produce more positive AO/NAO indices. Experiments with tropospheric cooling or stratospheric warming produce a negative AO/NAO response. For the typical magnitudes of tropospheric and stratospheric climate changes, the tropospheric response dominates; results are strongest when the tropospheric and stratospheric influences are producing similar phase changes. Both regions produce their effect primarily by altering wave propagation and angular momentum transports, but planetary wave energy changes accompanying tropospheric climate change are also important. Stratospheric forcing has a larger impact on the NAO than on the AO, and the angular momentum transport changes associated with it peak in the upper troposphere, affecting all wavenumbers. Tropospheric climate changes influence both the AO and NAO with effects that extend throughout the troposphere. For both forcings there is often vertical consistency in the sign of the momentum transport changes, obscuring the difference between direct and indirect mechanisms for influencing the surface circulation.

Numerical Methods for the Evaluation of the Löwdin α-Function

The problem of expanding an angular momentum wave function centered at one point in terms of angular momentum wave functions centered at another point is analysed. The emphasis is on obtaining methods that can be applied to functions that are defined numerically, in contrast to analytic methods. Three numerical approaches are described, and it is found that one leads to extremely accurate results. The question of the rate of convergence of the resulting series is discussed, and results of the application of the expansion to the calculation of nuclear attraction three-center integrals, and electron-electron four-center integrals are presented.

Superrotation and equatorial waves in a T21 Venus‐like AGCM

Superrotation of more than 100 m s−1 is formed at the cloud top (65–70 km) in a T21 Venus‐like atmospheric general circulation model (Venus‐like AGCM) driven by a zonal‐mean thermal forcing. This is maintained by the Gierasch mechanism, in which meridional circulation efficiently pumps up angular momentum and various waves produce equatorward eddy momentum fluxes. In addition to the above mechanism, fast equatorial waves with a wide frequency range (including a famous 4‐day wave) enhance the cloud‐top superrotation, since the downward angular momentum flux of vertically propagating gravity waves is canceled by the upward flux of the fast equatorial waves.

Ballistic matter waves with angular momentum: Exact solutions and applications

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schr\odinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. We obtain results for ballistic scattering in an external uniform force field, where we provide analytical solutions for both the scattering waves and the integrated particle flux. Our theory directly applies to p-wave photodetachment in an electric field. Furthermore, illustrating the effects of extended sources, we predict some properties of vortex-bearing atom laser beams outcoupled from a rotating Bose-Einstein condensate under the influence of gravity.

Planet Migration and Gap Formation by Tidally Induced Shocks

Gap formation in a gas disk triggered by disk-planet tidal interaction is considered. Density waves launched by the planet are assumed to be damped as a result of their nonlinear evolution leading to shock formation and its subsequent dissipation. As a consequence wave angular momentum is transferred to the disk,leading to evolution of its surface density. Planetary migration is an important ingredient of the theory; effects of the planet-induced surface density perturbations on the migration speed are considered. A gap is assumed to form when a stationary solution for the surface density profile is no longer possible in the frame of reference migrating with the planet. An analytical limit on the planetary mass necessary to open a gap in an inviscid disk is derived. The critical mass turns out to be smaller than mass M_1 for which planetary Hill's radius equals disk scaleheight by a factor of at least Q^{5/7} (Q is the Toomre stability parameter) depending on the strength of the migration feedback. In viscous disks the critical planetary mass could vary from about 0.1M_1 to M_1, depending on the disk viscosity. This implies that a gap could be formed by a planet with mass 1-10 times bigger than the Earth mass depending on the disk aspect ratio, viscosity, and planet's location in the nebula.

The equatorial bulge, angular momentum and planetary wave motion

The equatorial bulge, angular momentum and planetary wave motion

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density N which travels at a relevant radial group speed Cg. The wave energy surface density ℰ and the wave angular momentum surface density J are related to N by ℰ=ωN and J=mN respectively, where ω is the angular frequency in an inertial frame of reference and the integer m, proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.

The equatorial bulge, angular momentum and planetary wave motion

The impact of the equatorial bulge on the equatorial angular momentum of planetary flows isinvestigated by considering both the situation on earth and on a spherical planet. First, arigorous proof of the suggestion of Bell is given that both the standard nonlinear and linearprimitive equations capture the impact of the bulge almost correctly, despite the fact that aspherical earth is assumed in these equations. Linear eigenmodes of shallow water flow withequivalent depth H are discussed both for the spheroid with a corresponding torque and aspherical planet without torque. Surprisingly, it is found that Rossby–Haurwitz waves as rotationalmodes for H→∞ are not affected by the bulge. For finite H, however, there are bothgravitational and rotational modes with equatorial angular momentum which are affected bythe bulge. In contrast, there is only one mode with equatorial angular momentum on thespherical planet. This mode is stationary.

Absorption of angular momentum by black holes and D-branes

We consider the absorption of higher angular momentum modes of scalars into black holes, at low energies, and ask if the resulting cross sections are reproduced by a D-brane model. To get the correct dependence on the volume of the compactified dimensions, we must let the absorbing element in the brane model have a tension that is the geometric mean of the tensions of the D-string and an effective stringlike tension obtained from the D5-brane; this choice is also motivated by T-duality. In a dual model we note that the correct dependence on the volume of the compact dimensions and the coupling arise if the absorbing string is allowed to split into many strings in the process of absorbing a higher angular momentum wave. We obtain the required energy dependence of the cross section by carrying out the integrals resulting from partitioning the energy of the incoming quantum into vibrations of the string.

Radiatively Damped Density Waves in Optically Thick Protostellar Disks

The redistribution of angular momentum and mass in circumstellar disks by spiral density waves is governed by processes that dissipate the waves. Dissipation is usually attributed to unspecified nonlinear processes or an ad hoc viscosity. In this paper, we examine dissipation by radiative losses associated with the cyclic compression and expansion of disk material by the density waves. We consider linear, discrete modes in optically thick disks and use a simplified treatment of the radiative losses in order to assess the parameter dependences and importance of radiative damping. Wave action conservation principles are generalized to describe the effect of dissipation (by any means) and the consequent coupling of wave and disk energy and momenta. A relation is derived (in the WKBJ limit) between radial mass transport of disk material and the azimuthally averaged dissipation rate. A wave amplitude equation is similarly derived, which describes the radial evolution of wave angular momentum, and therefore the radial deposition of angular momentum in the disk. Associated with the equation is a characteristic damping length, proportional to the cooling time from the base state temperature times the radial wave speed, and a factor that depends weakly on optical depth. The damping length is used to define, in terms of the disk base state temperature and surface density, regimes of strong and weak radiative damping. Waves in warm disks may be damped close to the resonances at which they are excited, while waves in cold disks can propagate to distances at which other dissipative mechanisms may dominate. It is found that the boundary between these regimes cuts across values that are thought to have characterized the primitive solar nebula. Thus both strong and weak radiative damping may be encountered in circumstellar disks in general.

Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid

We derive a hierarchy of approximate models of wave mean-flow interaction (WMFI) by using asymptotic expansions and phase averages either in Euler's equations for a stratified rotating inviscid incompressible fluid, or in Hamilton's principle for these equations. Two small dimensionless parameters are used in these expansions. The first parameter is the ratio of time scales between internal waves at most wave numbers and the mesoscale mean flow of the fluid. This “adiabatic ratio” is small and is comparable to the corresponding ratio of space scales for the class of initial conditions that support internal waves. The other small parameter used in these expansions is the ratio of the amplitude of the internal wave to its wavelength. An application of Noether's theorem to the phase-averaged Hamilton's principle shows that the resulting equations conserve the wave action, convect a potentional vorticity and can, depending on the order of approximation, convect wave angular momentum. Passage from the phase-averaged Hamilton's principle to the Hamiltonian formulation brings the WMFI theory into the Lie-Poisson framework in which formal and nonlinear stability analysis may be applied. This framework also suggests a two-fluid model of the interaction of waves and mean flow similar to that for the superfluid and normal fluid components of liquid He 4 without vortices. We also discuss the relations of these results to the Charney-Drazin nonacceleration theorem, Whitham averaging, WKB stability theory, and Lagrangian-mean fluid equations for prescribed wave displacements.

A spherical mass shell as a `total reflector' for gravitational waves

For normal bulk material the reflection coefficient for gravitational waves is usually much smaller than 1. Therefore, a spherical mass shell (mass M, radius R) can serve as a `container' for gravitational radiation at most in the extreme case R = 2M. If, however, the shell material is especially adapted to the properties of the wave, total reflection can occur due to interference effects, i.e. suitable mass shells can totally reflect weak gravitational waves of arbitrary frequency and angular momentum l coming from the outside; for waves inside the shell total reflection is only possible for a series of discrete -values, dependent on R and l. This is proven by first-order perturbation theory on the basis of the Schwarzschild mass shell. Perturbation of the exterior Schwarzschild metric is treated in Regge - Wheeler gauge. Connection of this exterior metric to a (suitably transformed) flat interior metric at r = R according to Israel's method leads to a unique relation between the amplitudes of the ingoing and outgoing wave (total reflection!). For , the shell material fulfils the dominant energy condition. The logarithmic phase of the asymptotic gravitational wave (in radiation gauge) compares nicely with the phase in relativistic Coulomb scattering: different sign of the logarithmic term due to gravitational attraction, and a factor 2 due to the spin of the `graviton'.