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At least 55 records · Page 3

Gravitational Wave Scattering via the Born Series: Scalar Tidal Matching to 𝒪⁡(𝐺 7 ) and Beyond

We introduce a novel method to compute gravitational wave amplitudes within the framework of effective field theory. By reinterpreting the Feynman diagram expansion as a Born series, our method offers several key advantages. It directly yields partial wave amplitudes, streamlining the matching with black hole perturbation theory. Long-distance gravitational interactions are unambiguously factorized from short-distance tidal effects, including dissipation, which are systematically incorporated via an in-in worldline effective action. Crucially, at every order in perturbation theory, integrals are expressed in terms of harmonic polylogarithms, enabling an end-to-end computation scalable to arbitrary orders. We illustrate the method with new predictions for scalar black hole Love numbers and their renormalization group equations to 𝒪⁡(𝐺 7 ).

effective field theory

Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U(1) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.

97 MATHEMATICS AND COMPUTING

A high frequency correction to the Kirchhoff approximation, with application to rough surface EM wave scattering

A high frequency correction to the Kirchhoff approximation is developed for application to rough surface scattering. An approximate solution to the magnetic field integral equation for perfect conductivity and plane wave excitation yields a perturbed surface current expressed as a linear function of the second derivatives of surface height. The corrected surface current vector is substituted into the far field Stratton-Chu integral and average backscattered powers for the four polarization combinations are computed on the assumption that the surface is describable as a stationary Gaussian random process. The strength of this scattering solution is that it can account for height curvature correlation without requiring small height and slope.

Jackson, F. C.

Attenuated direct and scattered wave propagation on simulated land mobile satellite service paths in the presence of trees

Measurements were made of direct path with no trees, attenuated direct, and tree scattered signal levels at 1.3 GHz. Signals were received in two small groves of mixed hardwood trees. In the groves studied, average total signal levels were about 13 dB below adjacent no-trees locations, with attenuated direct signal levels about 14.6 dB below the no-trees case and scattered signals about 17.3 dB below the no-trees case. A simple model for land mobile satellite service (LMSS) propagation in groves of trees is proposed. The model assumes a constant scattered signal contribution at 17 dB below no-trees levels added to an attenuated direct signal which varies, depending on the number and density of trees in the direct path. When total signal levels are strong, the attenuated direct signal dominates. When total signal levels are more than 15 dB below no-trees levels, the scattered signals dominate.

Campbell, Richard L.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang

Alfven wave scattering and the secondary to primary ratio

The cosmic ray abundances have traditionally been used to determine the elemental and isotopic nature of galactic ray sources and average measures of propagation conditions. Detailed studies of the physics of propagation are usually paired with relatively straightforward estimates of the secondary-to-primary (S/P) ratios. In the work reported here, calculations of elemental abundances are paired with a more careful treatment of the propagation process. It is shown that the physics of propagation does indeed leave specific traces of Galactic structure in cosmic ray abundances.

Bretthorst, G. L.

Variational divergence in wave scattering theory with Kirchhoffean trial functions

In a recent study of variational improvement of the Kirchhoff approximation for electromagnetic scattering by rough surfaces, a key ingredient in the variational principle was found to diverge for important configurations (e.g., backscatter) if the polarization had any vertical component. The cause and a cure of this divergence are discussed here. The divergence is demonstrated to occur for arbitrary perfectly conducting scatterers and its universal characterstics are determined, by means of a general divergence criterion that is derived. A variational cure for the divergence is prescribed, and it is tested successfully on a standard scattering model.

Bird, J. F.

Electromagnetic wave scattering at near-grazing incidence from a gently undulating, rough surface

Models to estimate the reflection coefficient of a statistically rough surface, for example the works of Beckmann, Smith, and Vesecky are discussed. Bistatic radar experiments carried out during the Apollo 16 mission provide a data set with which to compare theoretical models and experimental data. These bistatic S-band radar experiments provide experimental estimates of the Moon's bistatic, forward scatter, reflection coefficient for grazing angles of 2.5 to 78 deg. Theoretical expressions for the reflection coefficient are developed for comparison with these experimental data. At grazing angles below 10 deg the models of Smith and Vesecky compare favorably with the data. Beckmann's model falls significantly more rapidly with decreasing grazing angle than does the data.

Vesecky, J. F.

Leaf-shape effects in electromagnetic wave scattering from vegetation

A vegetation medium is modeled as a half-space of randomly distributed and oriented leaves of arbitrary shape. In accordance with the first-order radiative transfer theory, the backscattering coefficient for such a half-space is expressed in terms of the scattering amplitudes. For disc- or needle-shaped leaves, the generalized Rayleigh-Gans approximation is used to calculate the scattering amplitudes. This approach is valid for leaf dimensions up to the size of the incident wavelength. To examine the leaf-shape effect, elliptic discs are used to model deciduous leaves, and needles are used to model coniferous leaves. The differences between the scattering characteristics of leaves of different shapes are illustrated numerically for various orientations, frequencies, and incidence angles. It is found that the scattering characteristics of elliptic disc-shaped leaves are sensitive to the three angles of orientation and disc ellipticity. In general, both like and cross polarizations may be needed to differentiate the difference in scattering due to the shapes of the leaves.

Karam, Mostafa A.

A comparison of H-alpha intensity and radio wave scattering on eight low-latitude lines of sight

Radio scattering and H-alpha measurements for eight sources in Cygnus are compared. The diameter of the radio scattering disk at 1 GHz is found to be correlated with emission measure as determined from the H-alpha measurements, and that strong radio scattering characterized by a diameter of about 30 milliarcsec is produced in regions with emission measures of about 100/cm exp 6 pc or less. The slope of diameter-emission measure correlation is steeper than would be the case if all lines of sight were characterized by the same turbulent outer scale and modulation index. It is suggested that the lines of sight to unscattered or lightly scattered sources traverse only a diffuse medium which is revealed by H-alpha observations at high latitudes. Heavily scattered sources are viewed through an additional component of interstellar H II which has turbulence with different properties.

Spangler, Steven R.