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1. The scattering map determines the nonlinearity

   https://doi.org/10.1090/proc/16297  

   Killip, Rowan; Murphy, Jason; Visan, Monica (March 2023, Proceedings of the American Mathematical Society)

   Using the two-dimensional nonlinear Schrödinger equation as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under very mild assumptions on the nonlinearity, the wave operator uniquely determines the nonlinearity, as does the scattering map. Evaluating the scattering map on well-chosen initial data, we reduce the problem to an inverse convolution problem, which we solve by means of an application of the Beurling–Lax Theorem. 

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2. Estimating the impact of foregrounds on the future detection of Rayleigh scattering

   https://doi.org/10.1088/1475-7516/2022/09/048  

   Zhu, Yijie; Beringue, Benjamin; Choi, Steve K.; Battaglia, Nicholas; Meerburg, P. Daniel; Meyers, Joel (September 2022, Journal of Cosmology and Astroparticle Physics)

   Abstract Rayleigh scattering of the cosmic microwave background (CMB) by neutral hydrogen shortly after recombination leaves frequency-dependent imprints on intensity and polarization fluctuations. High signal-to-noise observations of CMB Rayleigh scattering would provide additional insight into the physics of recombination, including greater constraining power for parameters like the primordial helium fraction, the light relic density, and the sum of neutrino masses. However, such a measurement of CMB Rayleigh scattering is challenging due to the presence of astrophysical foregrounds, which are more intense at the high frequencies, where the effects of Rayleigh scattering are most prominent. Here we forecast the detectability of CMB Rayleigh scattering including foreground removal using blind internal linear combination methods for a set of near-future surveys. We show that atmospheric effects for ground-based observatories and astrophysical foregrounds pose a significant hindrance to detecting CMB Rayleigh scattering with experiments planned for this decade, though a high-significance measurement should be possible with a future CMB satellite. 

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3. The classical dynamics of gauge theories in the deep infrared

   https://doi.org/10.1007/JHEP05(2023)185  

   Flanagan, Éanna É.; Shehzad, Ibrahim (May 2023, Journal of High Energy Physics)

   A bstract Gauge and gravitational theories in asymptotically flat settings possess infinitely many conserved charges associated with large gauge transformations or diffeomorphisms that are nontrivial at infinity. To what extent do these charges constrain the scattering in these theories? It has been claimed in the literature that the constraints are trivial, due to a decoupling of hard and soft sectors for which the conserved charges constrain only the dynamics in the soft sector. We show that the argument for this decoupling fails due to the failure in infinite dimensions of a property of symplectic geometry which holds in finite dimensions. Specializing to electromagnetism coupled to a massless charged scalar field in four dimensional Minkowski spacetime, we show explicitly that the two sectors are always coupled using a perturbative classical computation of the scattering map. Specifically, while the two sectors are uncoupled at low orders, they are coupled at quartic order via the electromagnetic memory effect. This coupling cannot be removed by adjusting the definitions of the hard and soft sectors (which includes the classical analog of dressing the hard degrees of freedom). We conclude that the conserved charges yield nontrivial constraints on the scattering of hard degrees of freedom. This conclusion should also apply to gravitational scattering and to black hole formation and evaporation. In developing the classical scattering theory, we show that generic Lorenz gauge solutions fail to satisfy the matching condition on the vector potential at spatial infinity proposed by Strominger to define the field configuration space, and we suggest a way to remedy this. We also show that when soft degrees of freedom are present, the order at which nonlinearities first arise in the scattering map is second order in Lorenz gauge, but can be third order in other gauges. 

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4. Ballistic phonon lensing by the non-planar interfaces of embedded nanoparticles

   https://doi.org/10.1088/1367-2630/ad025a  

   Maranets, Theodore; Wang, Yan (October 2023, New Journal of Physics)

   Abstract In this work, we investigate the scattering behavior of a ballistic phonon wave incident on a dopant spherical nanoparticle embedded within a pure crystal through molecular dynamics simulations. Unique to this work, we also conduct conjugate simulations of ballistic phonon scattering on a dopant thin slab to compare and contrast scattering by non-planar heterogeneous interfaces (nanoparticle) and planar heterogeneous interfaces (thin slab). Analysis of the wave dynamics in real and reciprocal spaces reveal phonon mode-conversion in the nanoparticle scattering system is due to an unreported ‘phonon lensing’ effect where the phonon wave propagation is altered by refraction and reflection through the non-planar interfaces of the nanoparticle. The specific states of mode-conversion is shown to change with the character of the lensing that varies with nanoparticle size. Most significantly, the lensing phenomenon is absent in the phonon scattering by the thin slab and consequentially, results in differences in the scattering behaviors between the planar and non-planar interfaces. 

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5. Probing the Local Interstellar Medium with Scintillometry of the Bright Pulsar B1133 + 16

   https://doi.org/10.3847/1538-4357/ac460b  

   McKee, James W.; Zhu, Hengrui; Stinebring, Daniel R.; Cordes, James M. (March 2022, The Astrophysical Journal)

   Abstract The interstellar medium hosts a population of scattering screens, most of unknown origin. Scintillation studies of pulsars provide a sensitive tool for resolving these scattering screens and a means of measuring their properties. In this paper, we report our analysis of 34 yr of Arecibo observations of PSR B1133 + 16, from which we have obtained high-quality dynamic spectra and their associated scintillation arcs, arising from the scattering screens located along the line of sight to the pulsar. We have identified six individual scattering screens that are responsible for the observed scintillation arcs, which persist for decades. Using the assumption that the scattering screens have not changed significantly in this time, we have modeled the variations in arc curvature throughout the Earth’s orbit and extracted information about the placement, orientation, and velocity of five of the six screens, with the highest-precision distance measurement placing a screen at just ${5.46}_{-0.59}^{+0.54}$pc from the Earth. We associate the more distant of these screens with an underdense region of the Local Bubble. 

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