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1. Einstein–Klein–Gordon system via Cauchy-characteristic evolution: computation of memory and ringdown tail

   https://doi.org/10.1088/1361-6382/adaf6f  

   Ma, Sizheng; Nelli, Kyle C; Moxon, Jordan; Scheel, Mark A; Deppe, Nils; Kidder, Lawrence E; Throwe, William; Vu, Nils L (February 2025, Classical and Quantum Gravity)

   Abstract Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price’s power-law tail ( $u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$tail at future timelike infinity. 

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2. Wave optics of imaging with contact ball lenses

   https://doi.org/10.1038/s41598-023-32826-8  

   Maslov, A V; Jin, B; Astratov, V N (December 2023, Scientific Reports)

   Abstract Recent progress in microspherical superlens nanoscopy raises a fundamental question about the transition from super-resolution properties of mesoscale microspheres, which can provide a subwavelength resolution$$\sim \lambda /7$$ $\sim \lambda /7$, to macroscale ball lenses, for which the imaging quality degrades because of aberrations. To address this question, this work develops a theory describing the imaging by contact ball lenses with diameters$$30 $30<D/\lambda <4000$covering this transition range and for a broad range of refractive indices$$1.3<2.1$$ $1.3<n<2.1$. Starting from geometrical optics we subsequently proceed to an exact numerical solution of the Maxwell equations explaining virtual and real image formation as well as magnificationMand resolution near the critical index$$n\approx 2$$ $n\approx 2$which is of interest for applications demanding the highestMsuch as cellphone microscopy. The wave effects manifest themselves in a strong dependence of the image plane position and magnification on$$D/\lambda $$ $D/\lambda$, for which a simple analytical formula is derived. It is demonstrated that a subwavelength resolution is achievable at$$D/\lambda \lesssim 1400$$ $D/\lambda \lesssim 1400$. The theory explains the results of experimental contact-ball imaging. The understanding of the physical mechanisms of image formation revealed in this study creates a basis for developing applications of contact ball lenses in cellphone-based microscopy. 

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3. Do black holes remember what they are made of?

   https://doi.org/10.1088/1361-6382/ad56ed  

   Bandyopadhyay, Harshraj; Radice, David; Prakash, Aviral; Dhani, Arnab; Logoteta, Domenico; Perego, Albino; Kashyap, Rahul (June 2024, Classical and Quantum Gravity)

   Abstract We study the ringdown signal of black holes formed in prompt-collapse binary neutron star mergers. We analyze data from 47 numerical relativity simulations. We show that the $(\ell =2,m=2)$and $(\ell =2,m=1)$multipoles of the gravitational wave signal are well fitted by decaying damped exponentials, as predicted by black-hole perturbation theory. We show that the ratio of the amplitude in the two modes depends on the progenitor binary mass ratioqand reduced tidal parameter $\tilde{\mathrm{\Lambda }}$. Unfortunately, the numerical uncertainty in our data is too large to fully quantify this dependency. If confirmed, these results will enable novel tests of general relativity in the presence of matter with next-generation gravitational-wave observatories. 

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4. Low rank representations for quantum simulation of electronic structure

   https://doi.org/10.1038/s41534-021-00416-z  

   Motta, Mario; Ye, Erika; McClean, Jarrod R.; Li, Zhendong; Minnich, Austin J.; Babbush, Ryan; Chan, Garnet Kin-Lic (May 2021, npj Quantum Information)

   Abstract The quantum simulation of quantum chemistry is a promising application of quantum computers. However, forNmolecular orbitals, the$${\mathcal{O}}({N}^{4})$$ $O\left(N^4\right)$gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with$${\mathcal{O}}({N}^{3})$$ $O\left(N^3\right)$gate complexity in small simulations, which reduces to$${\mathcal{O}}({N}^{2})$$ $O\left(N^2\right)$gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with$${\mathcal{O}}({N}^{3})$$ $O\left(N^3\right)$gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have$${\mathcal{O}}({N}^{2})$$ $O\left(N^2\right)$depth on a linearly connected array, an improvement over the$${\mathcal{O}}({N}^{3})$$ $O\left(N^3\right)$scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 10⁵non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes. 

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5. 3D Mirror Symmetry for Instanton Moduli Spaces

   https://doi.org/10.1007/s00220-023-04831-5  

   Koroteev, Peter; Zeitlin, Anton M. (September 2023, Communications in Mathematical Physics)

   Abstract We prove that the Hilbert scheme ofkpoints on$${\mathbb {C}}^2$$ $C^2$($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ ${\text{Hilb}}^k\left[C^2\right]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$${\mathbb {C}}^\times _\hbar $$ $C_{ħ}^{\times }$-action. First, we find a two-parameter family$$X_{k,l}$$ $X_{k,l}$of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ ${\text{Hilb}}^k\left[C^2\right]$is obtained via direct limit$$l\longrightarrow \infty $$ $l⟶\infty$and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$\hbar $$ $ħ$-opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-Nsheaves on$${\mathbb {P}}^2$$ $P^2$with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual. 

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