Partial Wave Expansion Research Articles

Computation of acoustic scattered fields and derived radiation force and torque for axisymmetric objects at arbitrary orientations.

This study presents a theoretical framework for calculating acoustic scattering fields, as well as radiation force and torque resulting from the interaction between an incident wave and an axisymmetric object positioned at arbitrary orientations. Grounded in the partial-wave expansion method, it formulates scattering products using beam-shape and scalar scattering coefficients. The incorporation of geometric features into the scalar scattering coefficients is achieved through the conformal transformation approach. Notably, its applicability is restricted to scenarios where the object is positioned at its standard orientation, a limitation circumvented by employing rotational transformations to extend the model to non-standard orientations. A rotational transformation tunes the original frame (observation coordinate system) into a reference frame (computation coordinate system), for any deviated orientation and facilitating solution of scattering products. While the non-intuitive nature of rotational transformations disrupts the inheritability of the partial-wave expressions for the scattering products, an alternative approach is provided based on rotation addition theorem. This method directly incorporates object orientations into the beam-shape and scalar scattering coefficients, bypassing rotational transformations and preserving the partial-wave format. Comparative analysis with full three-dimensional numerical simulations shows theoretical methods are computationally more efficient while ensuring substantial consistency.

Basis Set Extrapolation from the Vanishing Counterpoise Correction Condition.

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters.

Learning S -matrix phases with neural operators

We use Fourier neural operators (FNOs) to study the relation between the modulus and phase of amplitudes in 2→2 elastic scattering at fixed energies. Unlike previous approaches, we do not employ the integral relation imposed by unitarity, but instead train FNOs to discover it from many samples of amplitudes with finite partial wave expansions. When trained only on true samples, the FNO correctly predicts (unique or ambiguous) phases of amplitudes with infinite partial wave expansions. When also trained on false samples, it can rate the quality of its prediction by producing a true/false classifying index. We observe that the value of this index is strongly correlated with the violation of the unitarity constraint for the predicted phase and present examples where it delineates the boundary between allowed and disallowed profiles of the modulus. Our application of FNOs is unconventional: it involves a simultaneous regression-classification task and emphasizes the role of statistics in ensembles of neural operators. We comment on the merits and limitations of the approach and its potential as a new methodology in theoretical physics. Published by the American Physical Society 2024

Spinning Q -ball superradiance in 3+1D

Recently, it was found that a Q-ball can amplify waves incident upon it, due to rotation in the internal space and the interaction of the two modes in the complex scalar field. While the spherically symmetric 3D case has been investigated previously, here we explore the 3D axisymmetric case, which is numerically much more challenging. The difficulty comes because a partial wave expansion is needed, and the different partial waves can not be separated, for either the background spinning Q-ball solution or the perturbative scattering on top of it. A relaxation method and a high dimensional shooting method are applied to compute the Q-ball solutions and the amplification factors respectively. We also classify the behavior of the amplification factors and we discuss their bounds and the superradiance criteria. Published by the American Physical Society 2024

Convergence-acceleration approach to partial-wave expansion of two-electron self-energy contributions to the Lamb shift

Convergence-acceleration approach to partial-wave expansion of two-electron self-energy contributions to the Lamb shift

De-projecting the EFThedron

The space of Wilson coefficients of EFT that can be UV completed into consistent theories was recently shown to be described analytically by a positive geometry, termed the EFThedron. However, this geometry, as well as complementary numerical methods of semi-definite programming, have so far focused on the positivity of the partial wave expansion, which allows bounding only ratios of couplings. In this paper we describe how the unitarity upper bound of the partial waves can be incorporated. This new problem can be formulated in terms of the well known L-moment problem, which we generalize and solve from a geometrical perspective. We find the non-projective generalization of the EFThedron has an infinite number of non-linear facets, which in some cases have remarkably simple descriptions. We use these results to derive bounds on single couplings, finding that the leading derivative operators are bounded by unity, when normalized by the cut-off scale and loop factors. For general operators of mass dimension 2k we find the upper bound is heavily suppressed at large k, with an 1/k fall-off.

Finite series approach for the calculation of beam shape coefficients in ultrasonic and other acoustic scattering

Partial wave expansions with spherical wave functions are usually employed to describe complex velocity potentials or pressure fields in ultrasonic and acoustic scattering by spherical particles. The expansion coefficients – known as the beam shape coefficients (BSCs) – can be calculated using different approaches which have been largely unexplored in the acoustical literature. Here, we formally present the Finite Series method for the evaluation of BSCs of ultrasonic and acoustic arbitrary-shaped beams. Such a series, which relies on Neumann expansion theorem, is an alternative to quadratures whenever analytical solutions cannot be obtained from direct integration over polar and azimuthal spherical angles. As examples of application, we consider the calculation of BSCs of Bessel, Laguerre–Gauss and Gaussian beams under on-axis configuration, including a discussion on a modified version of the finite series method recently presented in the context of optical fields.

Absorption and unbounded superradiance in a static regular black hole spacetime

Regular black holes (RBHs)—geometries free from curvature singularities—arise naturally in theories of nonlinear electrodynamics. Here we study the absorption and superradiant amplification of a monochromatic planar wave in a charged, massive scalar field impinging on the electrically charged Ayón-Beato-García (ABG) RBH. Comparisons are drawn with absorption and superradiance for the Reissner-Nordström (RN) black hole in linear electrodynamics. We find that, in a certain parameter regime, the ABG absorption cross section is negative, due to superradiance, and moreover it is unbounded from below as the momentum of the wave approaches zero; this phenomenon of “unbounded superradiance” is absent in the RN case. We show how the parameter space can be divided into regions, using the bounded/unbounded and absorption/amplification boundaries. After introducing a high-frequency approximation based on particle trajectories, we calculate the absorption cross section numerically, via the partial-wave expansion, as a function of wave frequency, and we present a gallery of results. The cross section of the ABG RBH is found to be larger (smaller) than in the RN case when the field charge has the same (opposite) sign as the black hole charge. We show that it is possible to find “mimics”: situations in which the cross sections of both black holes are very similar. We conclude with a discussion of unbounded superradiance and superradiant instabilities. Published by the American Physical Society 2024

Optical radiation force and torque of light-sheets on a cylindrical particle near an infinite boundary

This work aims to extend the previous studies on the optical radiation force and torque for a cylindrical dielectric particle to the case near an infinite boundary. Without loss of generality, the two-dimensional cylindrical object is assumed to have an arbitrary shape and be immersed in any light-sheet beam of arbitrary wave front. The partial-wave series expansion method in cylindrical coordinates and the method of images are utilized to derive the exact expressions for the axial and transverse radiation force and torque functions, which are dependent on the beam shape coefficients of the incident light-sheet and the scattering coefficients characterized by the boundary conditions at the surface. Numerical computations are performed for a circular cylindrical particle illuminated by a two-dimensional plane wave and a two-dimensional Gauss beam, respectively, with particular emphases on the size parameter, the refractive index, the particle-boundary distance, the beam waist and the offset shifts. The radiation force will increase in magnitude and reverse its direction under selected conditions. When the absorptive cylindrical particle is shifted off-axially with respect to the beam axis, it will be rotated counterclockwise or clockwise by the radiation torque. The results obtained in this work have potential applications in non-contact particle manipulation and transportation using optical tweezers.

An approach without partial wave expansion to calculate scattering of spin-0 and spin- 1 2 $\frac{1}{2}$ particles in high energy regions and those governed by long range interactions

Abstract Scattering of spin-0 and spin- 1 2 $\frac{1}{2}$ particles is formulated in momentum space based on basis states being not expanded in partial waves. No sequential calculations with increasing angular momentum are performed to reach physical convergence, which depends on the scattering energy and the interaction range. Both nonrelativistic and relativistic cases are described. We put forward for consideration the utilization of this approach. By taking some simple interaction models we show some advantages in calculations representing those of high energy scattering as well as those of scattering governed by long range interactions.

Born approximation of trapping forces by acoustical Bessel and vortex fields.

Acoustic radiation forces have been used to trap various objects for fundamental studies and practical applications. Born approximation method, originally introduced to solve quantum scattering problems, is herein extended to analyze trapping forces exerted by two- and three-dimensional acoustic Bessel and vortex fields on spherical and nonspherical objects of arbitrary size. The results are compared with the conventional models like the partial wave expansion and Gorkov force potential. It is shown that for weakly scattering objects (such as common soft biological particles surrounded by fluids), the Born approximation can make predictions for the trapping forces on objects whose characteristic lengths are even up to multiple wavelengths of the sound beams. With the aid of the approximation, the Gorkov force potential is applied to analyze and gain insights into trapping forces on large objects far beyond the original Rayleigh scattering regime. The effects caused by the beam parameters, object shape, and orientation on the trapping behaviors are revealed. This work is useful for the further study of acoustic radiation forces and will guide the experiment of simplified acoustic tweezers on arbitrary-shaped particles.

On unitarity of the Coon amplitude

The Coon amplitude is a one-parameter deformation of the Veneziano amplitude. We explore the unitarity of the Coon amplitude through its partial wave expansion using tools from q-calculus. Our analysis establishes manifest positivity on the leading and sub-leading Regge trajectories in arbitrary spacetime dimensions D, while revealing a violation of unitarity in a certain region of (q, D) parameter space starting at the sub-sub-leading Regge order. A combination of numerical studies and analytic arguments allows us to argue for the manifest positivity of the partial wave coefficients in fixed spin and Regge asymptotics.

Partial-wave expansion of the Uehling potential

Partial-wave expansion of the Uehling potential

Classical observables from partial wave amplitudes

We study the formalism of Kosower-Maybee-O’Connell (KMOC) to extract classical impulse from quantum amplitude in the context of the partial wave expansion of a 2-to-2 elastic scattering. We take two complementary approaches to establish the connection. The first one takes advantage of Clebsch-Gordan relations for the base amplitudes of the partial wave expansion. The second one is a novel adaptation of the traditional saddle point approximation in the semi-classical limit. In the former, an interference between the S-matrix and its conjugate leads to a large degree of cancellation such that the saddle point approximation to handle a rapidly oscillating integral is no longer needed. As an example with a non-orbital angular momentum, we apply our methods to the charge-monopole scattering problem in the probe limit and reproduce both of the two angles characterizing the classical scattering. A spinor basis for the partial wave expansion, a non-relativistic avatar of the spinor-helicity variables, plays a crucial role throughout our computations.

From celestial correlators to AdS, and back

We present a general relation between celestial correlation functions in d-dimensions and Witten diagrams in (d + 1)-dimensional Euclidean anti-de Sitter (EAdS) space, to all orders in perturbation theory. Contact diagram processes are proportional to contact Witten diagrams and particle exchanges can be recast as a continuum of particle exchanges in EAdS where the exchanged particles carrying unitary Principal Series representations of SO(d + 1, 1). One can then try to import familiar EAdS techniques to study the properties of celestial correlators. In this work we use this relation to infer the analytic structure of the spectral density in the conformal partial wave expansion of celestial correlators which, at least perturbatively, should be a meromorphic function of the spectral parameter. We also discuss non-perturbative constraints from unitarity in Euclidean Conformal Field Theory, which requires positivity of the spectral density. This extends similar relations recently uncovered between boundary correlation functions in de Sitter space and Witten diagrams in EAdS, suggesting that EAdS could play a central role in efforts towards holography for all lambdas.

Rigorous full-wave calculation of optical forces on microparticles immersed in vector Pearcey beams.

We present the electromagnetic fields of vector Pearcey beams by employing the vector angular spectrum representation. The beams maintain the inherent properties of autofocusing performance and inversion effect. Based on the generalized Lorenz-Mie theory and Maxwell stress tensor approach, we derive the partial-wave expansion coefficients of arbitrary beams with different polarization and the rigorous solution to evaluate the optical forces. Furthermore, we investigate the optical forces experienced by a microsphere placed in vector Pearcey beams. We study the effects on the longitudinal optical force arising from the particle size, permittivity and permeability. This exotic curved trajectory transport of particles by vector Pearcey beams may find applications in the case where the transport path is partly blocked.

Constructing the general partial wave and renormalization in effective field theory

We construct the general partial wave amplitude basis for the $N\ensuremath{\rightarrow}M$ scattering, which consists of Poincar\'e Clebsch-Gordan coefficients, in a Lorentz invariant form given in terms of the spinor-helicity variables. The inner product of the Clebsch-Gordan coefficients is defined, which converts on-shell phase space integration into an algebraic problem. We also develop the technique of partial wave expansions of arbitrary amplitudes, including those with infrared divergence. These are applied to the computation of anomalous dimension matrix for general effective operators, where unitarity cuts for the loop amplitudes, with an arbitrary number of external particles, are obtained via partial wave expansion.

Scattering and conversion of electromagnetic and gravitational waves by Reissner-Nordström black holes: The Regge pole description

We investigate the problem of scattering and conversion of monochromatic planar gravitational and electromagnetic waves impinging upon a Reissner-Nordstr\"om black hole using a Regge pole description, i.e., a complex angular momentum approach. For this purpose, we first compute numerically the Regge pole spectrum for various charge-to-mass ratio configurations. We then derive an asymptotic expressions for the lowest Regge poles, and by considering Bohr-Sommerfeld-type quantization conditions, obtain the spectrum of weakly damped quasinormal frequencies from the Regge trajectories. Next, we construct the scattering and conversion amplitudes as well as the total differential cross sections for different processes using both a complex angular momentum representation and a partial wave expansion method. Finally, we provide an analytical approximation of the scattering and conversion cross sections of different processes from asymptotic expressions for the lowest Regge poles and the associated residues based on the correspondence Regge poles, ``surface waves'' propagating close to the photon (graviton) sphere. This allows us to extract the physical interpretation encoded in the partial wave expansions in the high-frequency regime (i.e., in the short-wavelength regime), and to describe semiclassically with very good agreement both black hole glory and a large part of the orbiting oscillations, thus unifying these two phenomena from a purely wave point of view.

Nuclear-level effective theory of μ→e conversion: Formalism and applications

New mu-to-e conversion searches aim to advance limits on charged lepton flavor violation (CLFV) by four orders of magnitude. By considering P and CP selection rules and the structure of possible charge and current densities, we show that rates are governed by six nuclear responses. To generate a microscopic formulation of these responses, we construct in non-relativistic effective theory (NRET) the CLFV nucleon-level interaction, then embed it in a nucleus. We discuss previous work, noting the lack of a systematic treatment of the various small parameters. Because the momentum transfer is comparable to the inverse nuclear size, a full multipole expansion of the response functions is necessary, a daunting task with Coulomb-distorted electron partial waves. We perform such an expansion to high precision by introducing a simplifying local electron momentum, treating the full set of 16 NRET operators. Previous work has been limited to the simplest charge/spin operators, ignored Coulomb distortion (or alternatively truncated the partial wave expansion) and the nucleon velocity operator, which is responsible for three of the response functions. This generates inconsistencies in the treatment of small parameters. We obtain a "master formula" for mu-to-e conversion that properly treats all such effects and those of the muon velocity. We compute muon-to-electron conversion rates for a series of experimental targets, deriving bounds on the coefficients of the CLFV operators. We discuss the nuclear physics: two types of coherence enhance certain CLFV operators and selection rules blind elastic mu-to-e conversion to others. We discuss the matching of the NRET onto higher level EFTs, and the relation to mu-to-e conversion to other CLFV tests. Finally we describe a publicly available script that can be used to compute mu-to-e conversion rates in nuclear targets.

Curved photonic nanojet generated by a rotating cylinder.

The curved photonic nanojet (CPNJ) produced due to the interaction between a dielectric circular cylinder rotating at a stable angular velocity and a plane wave is investigated. Based on this model, the optical Magnus effect of a dielectric circular cylinder is verified. And the analytical expression of both internal and external electric field are given based on the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates. The influence of the size parameter, the relative refractive index, and the rotating dimensionless parameter on the CPNJ are analyzed and discussed in numerical results. The "photonic nanojet curved" effect is highlighted, which can be used to generate the off-axis photonic nanojet (PNJ) controlling particles by adjusting the angular velocity of the dielectric cylinder. The results of this manuscript have promising application prospects in optical tweezers, particle manipulation, and optical trapping. Moreover, it also provides theoretical support for the particle spinning and generation of the off-axis CPNJ.