Abstract This paper presents a method for characterizing a beam incident on a quadrant photodetector (QPD). The approach is straightforward to implement, as it relies on hardware typically already available for the alignment control of optical cavities in gravitational-wave detectors. It enables measurement of the beam size at the detector plane, allowing for remote adjustment of telescope systems to restore optimal Gouy phase separation. The method has been experimentally validated for beam sizes ranging from 0.05 to 0.5 times the QPD active area, with measurement uncertainties below 12% for small beams and decreasing for larger beams. The novelty of this method relies on the fact that it can also be used to identify stray beams impinging on the QPD, as their presence can significantly degrade the sensor performance. In particular, stray beams may introduce spurious offsets and excess noise in the angular control signals. Consequently, the ability to detect and characterize these beams constitutes a valuable diagnostic capability, facilitating the identification of their origin and the implementation of effective mitigation measures.
Abstract We introduce the notion of moving Cartan geometries described by quotients of Lie groups and Lie algebras with spacetime dependant structure constants and construct associated deformed topological gauge action functionals for Lorentzian (including dS and AdS) and Lorentz × Weyl moving geometries. The actions feature a generalization of the Nieh-Yan topological term for a varying coupling constant. We compute the equations of motion of the gauge + matter actions and show that they dictate at each spacetime point the geometry, leading to both a spacetime-dependent source of dark energy and gravitational coupling, described by combinations of scalars built from spacetime curvature, torsion and the matter content of the theory. The action becomes asymptotically topological when the gauge action contribution to dark energy vanishes.
Abstract Phonons in a class of viscoelastic fluids have been shown to obey modified dispersion relations analogous to those arising in doubly special relativity (DSR). Here, we extend this analogy by demonstrating that these systems admit a deformed Lorentz symmetry, whose generators, together with translations (and rotations in higher dimensions), define a polynomial deformation of the Poincar\'e algebra. A time-dependent unitary transformation maps the phonon dynamics to an auxiliary field of Bogoliubov quasiparticles, in which the boost generator and the associated finite transformation can be constructed exactly by integrating the corresponding flow equations. Mapping the symmetry back to the original phonon variables, the corresponding infinitesimal boost generator remains a finite-order local differential operator. While the analogy does not straightforwardly extend to multiparticle sectors it nevertheless provides a concrete physical setting for exploring aspects of DSR phenomenology, such as the inequivalence of kinematical and spectral gamma factors.
Abstract Matched filtering provides the foundation for gravitational-wave detection, with waveform similarity traditionally described through the local geometry of the template-space metric. We investigate whether the exact pairwise matched-filter mismatch (PMM) over a finite waveform bank can instead be used to learn a global coordinate system for gravitational-wave templates. As a controlled proof of concept, we consider finite banks of nonspinning \texttt{IMRPhenomD} binary-black-hole waveforms over a fixed component-mass range. We formulate this as a supervised representation-learning problem in which physically computed PMM provides the supervision signal, and train a neural network so that Euclidean distances between latent coordinates approximate the mismatch between waveform pairs. Across waveform banks containing up to 8192 templates, the learned representation preserves both global pairwise mismatch relationships and local matched-filter neighborhoods while consistently outperforming Euclidean retrieval in the physical coordinate systems considered. Comparison with Classical Multidimensional Scaling shows that the learned encoder provides a competitive low-dimensional approximation of the finite-bank mismatch geometry while simultaneously learning an explicit mapping applicable to previously unseen waveforms. For previously unseen query waveforms drawn from the same waveform family and parameter distribution, the learned representation recovers the exhaustive best-matching template for 99.02% of queries using only 10 candidate templates from an 8192-template bank and for all queries using 20 candidates, reducing the number of exact matched-filter evaluations by factors of 819.2 and 409.6, respectively. Within this controlled setting, these results demonstrate that pairwise matched-filter mismatch provides an effective supervision signal for learning global geometric representations of waveform similarity and establish a proof of concept for mismatch-supervised organization and candidate retrieval in finite waveform banks.
Abstract We isolate a measure-theoretic point in one-dimensional reformulations of the optical Gauss--Bonnet curvature integral for black-hole lensing. For a static, spherically symmetric optical metric $\dd\sigma^2=E(r)\dd r^2+G(r)\dd\phi^2$, a constant-$r$ level set intersects the lifted lensing domain in an intrinsic arc of length $2\sqrt{G(r)}\,\psi(r;b)$, where $2\psi$ is the multiplicity-weighted angular separation of the two ray branches. The co-area Jacobian then gives the radial curvature contribution $2\Kopt\sqrt{EG}\,\psi\,\dd r$. After conversion to positive optical arclength on the two monotone branches, the corresponding line kernel is $W_{\psi}=\sqrt{G-b^2}\,\psi$. These three objects are distinct from the Euclidean chord joining the shell-intersection points. One-dimensional Gauss--Bonnet reductions and their equivalence with geodesic bending are already established in the literature. The contribution here is the literal level-set/co-area identification, its treatment of winding multiplicity on the universal cover, and consequences of replacing the arc by a bare chord. Under explicit regularity and asymptotic-decay assumptions, an integration by parts recovers the standard null-geodesic quadrature exactly for every noncritical scattering ray in the stated class. Known Schwarzschild and Reissner--Nordstr"om elliptic, weak-deflection, and strong-deflection results are used as analytic checks. The strong-deflection logarithm is carried by the unwrapped angular width while the optical Gaussian curvature remains finite at the photon sphere, whereas the bare-chord expression remains finite. For equatorial Kerr lensing, the Gaussian-curvature domain term and the Randers boundary term are kept distinct and reproduce the known $-6\pi-4\pi=-10\pi$ linear-spin split at order $aM^2/b^3$. Independent numerical implementations, supplied in a reproducibility package, verify the stated identities.
