Papers

Harnessed nonclassical resources to enhance the performance of quantum batteries is an important goal of quantum technology. In this work, we investigate multi-emitter batteries coupled to a one-dimensional waveguide driven by a broadband squeezed-vacuum reservoir, and determine how the waveguide geometry controls the battery performance and and their thermodynamic features. We show that for a single emitter, the squeezed reservoir deposits finite energy while the state remains passive, yielding zero ergotropy. For two emitters, however, phase-sensitive reservoir correlations generate coherence and can drive the steady state into a fully nonpassive regime. For three emitters, collective thermal dynamics already supports finite ergotropy, while squeezing further increases the extractable component of the stored energy. Crucially, because the collective and phase-sensitive couplings depend on the emitter positions, geometry provides direct control over the nonclassical correlations and, consequently, over the nonpassivity of the steady state. The ergotropy can therefore be strongly modulated while the stored energy changes only weakly, and in the two-emitter configuration geometry alone can switch the battery between a passive steady state and one in which all stored energy is unitarily extractable.

Differentiable programming connects scientific computation with gradient-based inference, learning and design. Extending these capabilities across a heterogeneous software ecosystem requires specialized effort to implement derivatives, integrate interfaces and evaluate quality. AI coding agents can accelerate this transformation, but translating their capabilities into useful scientific software requires identifying research needs and evaluating how well implementations meet them. We present an environment for agent-driven evolution of differentiable scientific software that connects demand identification, development and quality evaluation. A unified differentiation interface exposes reusable derivative rules alongside existing numerical routines, allowing research tasks to share these capabilities. Research requirements guide development, with implementations assessed through independent derivative checks, workflow tests and performance evaluation. Validated software, research programs and tests become shared resources for subsequent studies. We construct and validate automatic differentiation extensions across 20 packages spanning physical, chemical and biological modeling, with research workflows demonstrating reuse across tasks. Benchmarks demonstrate computational savings over finite differences in gradient evaluation and complete parameter estimation. Research-driven revisions make previously unsupported workflows differentiable, correct derivatives of scientific observables and eliminate redundant computation. Quantum-control and thermal-design studies revise objectives in response to physical evaluation, improving designs while reusing existing derivatives. This work provides a practical approach to expanding differentiable programming across established scientific software and organizing AI agents around the recursive improvement of a shared computational ecosystem.

We study the quantum query complexity of maximizing a non-negative submodular function, considering both the unconstrained setting and, for monotone functions, a cardinality constraint $k$ on an $n$-element ground set. In the exact reversible digital value-oracle model, our unconstrained algorithm achieves an expected $(1/2-\varepsilon)$-approximation using only $O_\varepsilon(\log n)$ queries. In contrast, any classical randomized algorithm that attains a fixed expected ratio above $1/4$ requires $\Omega(n/\log n)$ queries (Li, Feldman, Kazemi, and Karbasi, 2022), establishing an exponential separation in query complexity. For cardinality-constrained maximization, we give a bounded-error quantum algorithm that achieves a $(1-1/e-\varepsilon)$-approximation using $\widetilde O_\varepsilon(\min\{\sqrt n,n/k\})$ queries. When $k=o(n)$, our algorithm achieves at least a quadratic speedup up to logarithmic factors over classical randomized algorithms (Mirzasoleiman, Badanidiyuru, Karbasi, Vondrák, and Krause, 2015; Peng and Rubinstein, 2025). Moreover, when $k=cn$ for any fixed rational $c<1-1/e-\varepsilon$, the query complexity reduces to $O_{\varepsilon,c}(\log n)$, yielding an exponential separation from the classical $\Omega(n/\log n)$ lower bound (Li, Feldman, Kazemi, and Karbasi, 2022). We further prove quantum lower bounds of $\exp(\Omega(\varepsilon^2n))$ queries for achieving a ratio beyond $1/2+\varepsilon$ without constraints, and $\exp(\Omega(\varepsilon^2k))$ queries for exceeding $1-1/e+\varepsilon$ when $k/n\le\varepsilon$. These barriers demonstrate that quantum computation offers no exponential speedup at these approximation thresholds.

We present ClimateBench v2, a standardized protocol for evaluating climate models on diagnostics expected to be informative for their skill in projecting mid-century regional temperature and precipitation changes. The protocol is designed to evaluate any physics-based, data-driven, or hybrid climate model on equal footing using a common set of observational and out-of-distribution tests. We define three tiers of evaluation. Tier I establishes physical credibility through entry-ticket tests of energy conservation, coupled (co-)variability, and basic forced responses. Tier II scores models against post-2015 observations of surface temperature, precipitation, radiative fluxes, sea ice, and key modes of variability using fair CRPS as the primary probabilistic score, complemented by distributional and ensemble-consistency diagnostics. Tier III tests out-of-distribution generalization through paleoclimate simulations spanning the Last Interglacial, Last Glacial Maximum, and Mid-Holocene, and through perfect-model experiments in which data-driven models must predict the future climate of existing Earth system models from historical data alone. We reserve all observational data after 2015 for testing, and submissions must include multiple ensemble members to enable probabilistic evaluation. This reservation exploits a new opportunity provided by the decade of observations accumulated since the end of the CMIP6 historical experiment, which constitutes an out-of-sample record of forced climate change (and internal variability) for the current generation of models, and we quantify, in an idealized setting, the information it carries about mid-century warming. We provide the evaluation code, observational reference datasets, and perfect-model training data as an open benchmark to drive measurable progress in climate projection across all modeling approaches.

In quantum mechanics the modulus square of the wave function is the probability of an event — positivity is self-evident. Quantum field theory corresponds to quantum mechanics one-to-one: the wave function corresponds to the matrix element, so the probability of a process should be the modulus square of the matrix element, positive by construction. In the founding era of perturbative quantum field theory, however, Feynman, Schwinger and Tomonaga treated inclusive processes in quantum electrodynamics, where the truncation of the squared amplitude was forced by infrared cancellations and rendered harmless by the small coupling $\alpha\simeq1/137$. Carried over to exclusive processes in quantum chromodynamics, where the coupling is large, this practice produced negative decay and production rates already at NLO, persisting at NNLO. We point out that for exclusive processes, whose initial and final states are colorless for QCD and electrically neutral for QED, the infrared divergences cancel amplitude by amplitude and the KLN constraint is absent, so the complete modulus square of the truncated amplitude is the proper, manifestly positive definition of the probability. We formulate amplitude-level NRQCD factorization as the systematic prescription that restores positivity, show that every amplitude-level truncated observable admits the effective representation $\Gamma^{\mathrm{amp}}=\Gamma_{\mathrm{LO}}\bigl|1+\frac{\alpha_s}{\pi}(c_1+ic_2)+\frac{\alpha_s^2}{\pi^2}(c_3+ic_4)\bigr|^2$, and demonstrate, with the complete NNLO QCD corrections to $J/\psi\to3\gamma$, $\Upsilon\to3\gamma$, $e^+e^-\to J/\psi+J/\psi$ and the eight exclusive charmonium production channels at $B$ factories, that the prescription yields positive and better-converging predictions.

We determine the time required for local weak measurements to collapse to one occupied site in an initial superposition of $N$ alternatives in the model of PRA 111, 032217 (2025). For equal initial occupation probabilities and a fixed confidence threshold $1-\delta$, we prove $T_N/\ln N\to1/2$ in $L^1$, with time measured in units of the characteristic measurement time $\tau_m$ of each detector. We also connect the asymptotic stabilization theorem of that work to a finite measurement: the first site to reach $1-\delta$ is the eventual outcome with conditional probability exactly $1-\delta$. The result corrects the previously proposed double-logarithmic asymptotic scaling. The finite-range numerical fit does not determine a constant asymptotic correction or a precise finite-$N$ law.

The long observational record of He I 10830 Å offers a means to investigate solar morphology before modern extreme-ultraviolet (EUV) imaging. We adapt the Surya solar foundation model to predict Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) 94, 193, and 304 Å images and a coronal hole (CH) probability map from full-disk helium observations. A convolutional input adapter, low-rank backbone updates, and dedicated output decoders learn from temporally paired, geometrically registered observations, with Spatial Possibilistic Clustering Algorithm (SPOCA) catalog polygons providing CH supervision. On observations held out from downstream fine-tuning, the selected dedicated models achieve disk-restricted correlation coefficients (CCs) of 0.8196, 0.8885, and 0.8398 for the three AIA channels, respectively; the CH model achieves an intersection over union (IoU) of 0.4360. The predictions recover broad solar structure, although local agreement varies substantially by channel. An optional residual refiner addresses spatial detail, and its application on pre-SDO dates improves the correlation of synthetic AIA 304 with Solar and Heliospheric Observatory/Extreme-ultraviolet Imaging Telescope (SOHO/EIT) 304 references from 0.6511 to 0.7085. Together, these results support the feasibility of helium-conditioned EUV morphological proxies and motivate their use in historical reconstruction, within the scope of the downstream test and cross-instrument evaluation.

Cavity Quantum Electrodynamics (Cavity-QED) offers a powerful framework for controlling light-matter interactions, yet first-principles approaches commonly assume ideal, lossless cavity fields. Here, we introduce a minimal extension to the Pauli-Fierz Hamiltonian that accounts for cavity dissipation through the experimentally accessible cavity quality factor Q. The electromagnetic field is described as a damped harmonic oscillator within the very weak damping approximation. In this framework, cavity losses only enter the light-matter interaction and dipole self-energy terms, without introducing additional photonic degrees of freedom. A time-dependent unitary transformation yields a real-valued Hermitian Hamiltonian that can be incorporated into existing ab-initio QED methods without additional computational cost or changes in scaling. We combined the approach to the QED-CCSD method and investigated the effects of cavity dissipation on the optical spectrum of a p-nitroaniline molecule under strong light-matter coupling. We found that, for realistic quality factors, cavity dissipation can reduce the Rabi splitting by more than 20% compared to the ideal-cavity limit, even though the system remains in the strong-coupling regime. Convergence towards the ideal-cavity limit then requires substantially higher quality factors than those needed to establish strong coupling. These results demonstrate that cavity dissipation can significantly affect polaritonic energetics and highlight the importance of incorporating experimentally realistic cavity losses into quantitative ab-initio Cavity-QED simulations to accurately guide experimental protocols.

We describe the implementation and on-sky commissioning of a two-input spectrometer/correlator built on a Xilinx ZCU208 Radio Frequency System-on-Chip (RFSoC) and deployed on the Baryon Mapping eXperiment (BMX) interferometric array at Brookhaven National Laboratory. The system combines direct RF sampling, FPGA-based correlation, and 100 Gigabit Ethernet (GbE) visibility transport. Two inputs are digitized directly at 1050 MHz without analog downconversion and channelized into 2048 frequency channels. The correlator forms two autocorrelations and the real and imaginary parts of the cross-correlation, accumulates them in on-chip memory, and transmits the spectra as UDP packets at a fixed firmware-controlled rate. Two independent campaigns using 500 ms and 100 ms accumulation times produced 958,918 consecutive accumulations with no lost, duplicated, or malformed packets. A Cauchy-Schwarz bound is satisfied across all 1.96e9 channel-samples, confirming correct field identification and scaling. On-sky validation includes compact-source transits in six GNSS bands with the expected fringes, coherent detection of the Cygnus A zenith transit at the predicted time, and a Galactic HI plane crossing detected independently in autocorrelation on both dishes. The correlator is parameterizable in input count, with arithmetic scaling quadratically. For extension to BMX's full eight-input dual-polarization system, an occupancy model validated against the deployed firmware indicates that visibility buffering fits when moved to UltraRAM, while multi-tile synchronization, logic utilization, and timing closure remain to be demonstrated in an eight-input implementation.

We propose a distribution-free metric to rate individual skill in “player-versus-environment” settings, where participants face heterogeneous tasks without direct opponents. Such settings are common in digital platforms, games, education, finance, and the benchmark evaluation of AI agents. They combine high randomness, tasks of widely varying difficulty, and unknown heterogeneity across individuals. Our metric maps each task outcome to a bounded performance score with zero population mean and variance bounded by $1/3$, regardless of the outcome distribution, so that scores are directly comparable across tasks. Aggregating these scores over tasks yields an interpretable skill score for each individual (the “Solo” rating), and a reshuffling null model tests whether that score exceeds what chance alone would produce. We validate the approach on the progression of $2\times10^5$ players in the mobile games Candy Crush Saga and Bubble Witch 3 Saga. The metric identifies high- and low-skill players with high statistical confidence, their classification persists over hundreds of subsequent levels, and a windowed version of the score tracks changes in performance along progression.

Null homogeneous Petrov spaces $V^*_4(N)$ are considered. The geometry of $V^*_4(N)$ is determined by the geometry of the three-dimensional homogeneous Riemannian space $V_3(N)$, which is invariant under the action of the three-parameter motions group $G_3(N)$ ($N$ corresponds to the group number in the Bianchi classification). The canonical frame of the space $V_3(N)$ is used to construct the metric tensor of the space $V^*_4(N)$ and the components of the vector potential of the invariant electromagnetic field. Using this reper, we obtain Maxwell vacuum equations containing only the structure constants of the groups, the non-holonomic components of the contravariant metric tensor and vector potential, and their derivatives with respect to the wave variable. All non-equivalent exact solutions of Maxwell vacuum equations are found for the case of solvable motions groups $G_3(I)-G_3(VII)$. All solutions of Maxwell vacuum equations obtained in this article are written explicitly in terms of arbitrary independent functions of wave variable. Therefore, when integrating the Einstein-Maxwell equations, it has to consider only the remaining systems of Einstein equations which reduce to systems of ordinary differential equations that include only these independent functions.

We investigate the dynamics of charged test particles around a rotating black hole embedded in a King-type dark matter halo and subjected to a prescribed, asymptotically uniform magnetic field. We adopt an effective rotating geometry constructed from a static halo seed through a modified Newman–Janis prescription and a test electromagnetic field that generally requires supporting currents in the nonvacuum background. In the absence of magnetic coupling, the timelike Hamilton–Jacobi equation separates and admits a Carter-type constant, providing an integrable reference system. We characterize the orbital dynamics using Poincaré sections and tangent-vector growth diagnostics, including fast Lyapunov indicators and finite-time Lyapunov exponents, with mass-shell monitoring and numerical refinement checks. For the sampled initial conditions, increasing the magnetic coupling can produce a transition from regular motion to scattered Poincaré sections with sustained positive finite-time growth rates. At fixed magnetic coupling, the two higher-density halo cases yield larger finite-time exponents for a representative chaotic orbit family, whereas the weak-halo correction is not resolved consistently under numerical refinement. A different initial condition yields a closed Poincaré curve and a decreasing finite-time exponent over an extended integration, supporting regular motion despite the nonzero magnetic coupling. These results show that the King-type halo modulates magnetic-field-induced orbital instability in an initial-condition-dependent manner, while regular motion persists within the magnetized system.

We study the charge resolved structure of the pairwise mode entanglement produced by the Schwinger effect. Using the $U(1)$ electric charge of quantum electrodynamics, we decompose the entanglement of the reduced density matrices of momentum modes into individual charge sectors, applying the symmetry resolved entanglement entropy to the pure bipartition reductions and the charge imbalance resolved negativity to the mixed particle-antiparticle pair. For a constant electric field we obtain closed form results for every mode pairing, with all field dependence controlled by the single pair production probability $|\beta|^2=e^{-\pi\mu}$. For the particle, particle and antiparticle antiparticle pairs the entanglement entropy within each charge sector is field independent, so that the field acts only by redistributing statistical weight among the sectors; for the mixed particle antiparticle pair the populated sector additionally carries a field dependent entropy. The vacuum created pair is the richest case: its resolved negativity is distributed over three imbalance sectors and is transported from one sector to the next as the field increases, the sectors contributing equally only at the critical field. The entanglement across a fixed momentum bipartition, by contrast, is frozen at its initial value because pair creation conserves the sector charge. Symmetry resolution thus refines the total entanglement measures into a sector resolved picture, exposing where in charge space the entanglement of the Schwinger mechanism resides and how the electric field moves it, information beyond that contained in the total measures or in particle number distributions.

We report on the status and prospects of precision weak neutral current interaction measurements in fixed target scattering, atomic parity violation, as well as future collider measurements at momentum transfer $\sqrt{Q^2} \ll M_Z$, including the experiments in parity-violating electron scattering under construction at Jefferson Laboratory and at Mainz that are expected to commence data collection in the very near future.

Exoplanetary astronomy has entered its Golden Age, with humanity having found over 6000 exoplanets to date. The majority of these discoveries have been achieved through transit-photometry and radial-velocity (RV) techniques. While transit surveys lead in discovery numbers, the RV method persists as a vital and indispensable technique in exoplanetary science, particularly in the most prevalent stellar population – M dwarfs. Their low masses make them the theoretical favourites for RV detections, since exoplanet signals are stronger over the same period, and are therefore easier to detect and measure accurately. Nevertheless, the stellar activity M dwarfs exhibit introduces significant challenges, particularly when seeking RV semi-amplitudes to the order of 1 m$\,$s$^{-1}$, or lower. Stellar activity is known to mimic or suppress planetary signals, and its effects manifest across all time scales: from short-lived signals due to convective motion (lasting minutes to days), through active regions on the stellar surface (days to months), to long-term magnetic cycles (years to decades). These issues highlight the urgent need for robust methodologies that are capable of reliably disentangling stellar variability from genuine planetary signals. This doctoral dissertation explores these challenges through the application of Gaussian-process (GP) modelling. I present three distinct but interconnected publications that integrate high-precision spectroscopy and photometry with a unified GP-based approach in two cases, and that enable robust disentanglement of planetary signals from stellar activity. Together, these three studies illustrate how observations of different origin can be combined with appropriate statistical machinery for the sake of detecting exoplanets, with the possibility of interpreting stellar activity.

Symmetry has long provided the organizing principle for understanding how materials respond to external perturbations. Here we show that what is permitted by symmetry need not be what actually emerges from the underlying system, and this distinction becomes particularly consequential for symmetry-related gapless Dirac fermions such as in altermagnets. A perturbation that shifts the Dirac points drives a Lifshitz reconstruction and generates an intrinsically nonanalytic effective potential, giving rise to undiscovered singular responses. In Dirac altermagnets, this nonanalyticity acquires a magnetic manifestation through $C$-paired spin-polarized Dirac cones: breaking the pairing symmetry $C$ lifts their degeneracy and converts the associated Lifshitz reconstruction into an itinerant magnetization. As a consequence, piezomagnetism, the induction of a net magnetization by a mechanical strain, becomes nonlinear and nonanalytic, with $M\propto\mathrm{sgn}(\varepsilon)\varepsilon^2$, whereas the linear response is absent despite being allowed by symmetry. Accordingly, the leading response cannot be inferred from the conventional symmetry-based paradigm of material response built upon the cornerstones of Neumann's principle and analytic Landau expansion. First-principles calculations identify the monolayer Fe$_2$S as a candidate material realization for such singular magnetic responses. These results suggest quantum singularities as a new degree of freedom for engineering material responses.

Harnessing integrability at arbitrary interaction strength, we build long-lived and spatially localized soliton-like excitations in the 1D Bose gas with contact repulsion (Lieb-Liniger model). We show how these density profiles, built from selective superpositions of multi-hole eigenstates, display long lifetimes tunable through parameters like dispersion width and number of holes. We further illustrate a scaling protocol that in principle enables unbounded increase in lifetimes in the thermodynamic limit. Our results showcase classical-like excitations originating from unitary quantum dynamics, away from the semi-classical regime, and in regions where interactions cannot be treated perturbatively.

The Zel'dovich-inspired (ZI) transform is a local nonlinear transform of the density field that can Gaussianize the late-time matter field and recover information from higher-order $N$-point correlation functions through its power spectrum, with the parameter $\eta$ controlling the weighting of higher-order information. Using Fisher-matrix analyses of halo catalogs from the Quijote and Quijote-PNG simulations, we study the redshift-space monopole power spectrum of the ZI-transformed halo density field. The joint statistic $P_{\rm ZI,0}$, constructed from three representative transforms with $\eta=1$, $10$, and $+\infty$, yields substantially tighter constraints than the conventional halo power spectrum $P_{\rm h,0}$ on standard cosmological parameters, the summed neutrino mass, and primordial non-Gaussianity amplitudes, while outperforming the marked power spectrum for many parameters. We further calibrate a scale-dependent noise correction for the ZI power spectrum, with an effective noise amplitude that depends on wavenumber, and find that the correction further tightens the constraints. In particular, the noise-corrected $P_{\rm ZI,0}$ improves the constraints on $f_{\rm NL}^{\rm equil}$, $f_{\rm NL}^{\rm ortho}$, $M_\nu$, and $n_{\rm s}$ by factors of $5.6$, $5.5$, $5.2$, and $5.8$, respectively, relative to $P_{\rm h,0}$. These results demonstrate the potential of ZI power spectra as a complement to standard two-point statistics for extracting nonlinear cosmological information. Our forecasts may be conservative because the halo catalogs have substantially lower number densities than those expected from forthcoming galaxy surveys.

In this paper we use the topological vertex formalism to derive a structural formula for the leading terms of the generating series of Gromov–Witten invariants of local $\mathbb P^2$. Then we give two applications of this formula. First we use this result to derive an explicit formula for the leading terms of the transformed Gopakumar–Vafa invariants of local $\mathbb P^2$. This is an extension of a formula of Guo–Zhou \cite{gz} from degree $2d-5$ to $3d-1$, and shares some similar features with the famous Göttsche–Yau–Zaslow formula. And as the second application, we prove Guo–Wu–Moreira's Conjecture \cite{gw} about the leading Betti numbers of the moduli space of one-dimensional Gieseker semistable sheaves on $\mathbb P^2$.

Pulsar glitches are thought to involve sudden unpinning and fast transport of large numbers of pinned vortices, possibly triggered by breaking of the neutron star crust solid. Such a vortex avalanche can take place on a fast timescale only if there are pathways for fast vortex motion. Formation of local vortex “traps” (regions containing larger than average density of pinned vortices) will provide vortex-free regions surrounding the traps, which can connect to form pathways for fast vortex motion. We propose a simple two-dimensional model for the neutron star crust superfluid, with the vortex pinning landscape tiled into traps and surrounding vortex-free regions which can connect to azimuthal pathways for fast vortex motion. The trap and tile sizes are estimated from the physics of the crust solid and vortex pinning, namely the critical strain angle of the crust solid and the critical velocity for vortex unpinning. Unpinned vortices move with the superfluid flow in the azimuthal direction while also scattering radially outward, by a small angle, due to mutual friction. The model qualitatively explains the glitch parameters and their evolution in young pulsars and provides an explanation for the bi-modality in the distribution of glitch magnitudes. Laboratory experiments and simulations on vortex systems with spatially inhomogeneous vortex pinning landscapes are likely to be more realistic models for pulsar glitches. Breaking the spatial scale-invariance and monitoring the results may also lead to better understanding of collective behaviour in pinned vortex systems in general.

The Wen-Zee term is a mixed gauge-curvature coupling in the topological Chern-Simons description of a quantum Hall fluid, encoding the electric charge bound to spatial curvature. We investigate a Lorentz-covariant generalisation of this coupling, expanding its scope to black-hole spacetimes and determine its contribution to horizon entropy. Such a coupling arises naturally in three-dimensional Chern-Simons gravity based on the Maxwell algebra. We show that its Wald entropy contribution is a horizon boost charge, given by a loop integral of the additional gauge field projected along the tangent to the bifurcation circle. This contribution can be nonzero even when the mixed term vanishes on shell. We show that the integral admits an Abelian holonomy interpretation when the projection direction is covariantly constant. We evaluate the charge on a flat cosmological solution and, using smooth horizon fields and a specified thermal ensemble, on an AdS-Lorentz black hole. These results connect the geometric response familiar from quantum Hall physics to gravitational horizon thermodynamics.

The quest for a quantum theory of gravity remains a central challenge in modern physics, driven by the goal of unifying general relativity and quantum mechanics. Direct experimental access to quantum gravitational effects is notoriously difficult due to the inaccessibility of the Planck scale. Recent proposals, however, suggest that gravitationally induced quantum entanglement between two massive particles, realized through advanced quantum interferometric techniques, could provide empirical evidence for the quantum nature of gravity. We demonstrate that the geometrical configuration of an interferometer plays a decisive role in entanglement generation. Our analysis reveals that geometric optimization can substantially enhance the gravitationally induced phase shift, thereby improving the prospects for experimental detection of gravity-mediated entanglement. Moreover, we show that standard approximations employed in prior proposals may severely limit predictive accuracy and compromise experimental feasibility.

Vickers hardness characterizes resistance to indentation but does not distinguish the magnitude of local densification from the volume of glass affected. Here, low-coherence holotomography reconstructs three-dimensional refractive-index (RI) images of Vickers-indented fused silica, borosilicate, and soda-lime glass across applied loads and nominal dwell times. Analysis of RI changes using the Lorentz-Lorenz relation quantifies densification, while segmentation measures the spatial extent of the densified region. Cracks are observed within the same reconstructed RI images. Densified volume increased with load even when peak densification plateaued, and glasses with similar hardness showed different densification responses. Longer nominal dwell times were associated with larger volumes above fixed RI thresholds and comparatively small changes in peak densification. Joint analysis of densification and crack morphology thus characterizes subsurface indentation damage beyond hardness alone. Densification is quantified as an optical estimate under the Lorentz-Lorenz assumptions; residual stress, polarizability, and reconstruction can also affect RI.

A weakly nonlinear stability analysis is performed to investigate the influence of thermal buoyancy on phototactic bioconvection in a suspension of swimming microorganisms confined between horizontal boundaries and subjected to bottom heating or cooling. The objective is to examine how thermal forcing modifies the post-critical evolution of bioconvective instability through its influence on bifurcation behaviour and finite-amplitude convection. Linear stability theory is first employed to determine the critical conditions for the onset of convection. The corresponding direct and adjoint eigenvalue problems, together with the second-order resolvent system, are then solved numerically to derive the Stuart-Landau amplitude equation governing the nonlinear evolution of disturbances. A systematic analysis is carried out for varying thermal Rayleigh numbers. The results show that, as the thermal Rayleigh number approaches the classical Rayleigh-Benard critical value, the critical bioconvection Rayleigh number decreases to zero, indicating a gradual transition from phototaxis-dominated to thermally driven convection. The computed positive Landau coefficient predicts supercritical pitchfork and Hopf bifurcations for stationary and oscillatory instabilities, respectively. In parameter regimes with oscillatory onset, increasing the thermal Rayleigh number drives a transition from a supercritical Hopf bifurcation to a supercritical pitchfork bifurcation. The nonlinear dynamics are further characterized through amplitude evolution, phase portraits, potential functions, and finite-amplitude flow structures.

The stochastic gravitational-wave background is targeted by the millihertz observatories LISA, Taiji and TianQin, and its forecast precision rests on a Whittle approximation to the periodogram likelihood. The quoted scale is that of a joint fit a two-step forecast need not reach. We show that the residual risk of a two-step forecast lies in the estimator route rather than in the likelihood. At the exact Whittle form we separate the forecast error into a deterministic bias $\mathbf{b}$ and an efficiency gap $\mathbf{C}_b$, both in closed form. We find that this gap is governed by the span of the first-step nuisance fit. It decreases substantially as the span increases and vanishes when the first-step fit spans the entire band or when the response exhibits no within-bin structure. The gap does not arise as a cost of the prior. Across the LISA band the gap spans more than an order of magnitude, the amplitude and tilt inflation falling from about thirty and twenty to unity at a band-wide first step. A foreground from the released LDC2a population moves the mid-band gap by an order of magnitude. A two-step forecast should therefore report the span of its first-step fit with its intervals, since that span decides whether they sit at the Fisher scale or an order of magnitude above it.

In physics instruction, equations are often treated primarily as tools for obtaining numerical results. Yet physicists also use them to describe dependencies, explain why those dependencies hold, predict what happens in new situations, test expressions against physical knowledge, and explore consequences that are not immediately apparent. Although such uses appear throughout the physics education literature, they have not been brought together in a systematic account, and the terminology used to describe them remains inconsistent. Drawing on research in mathematics education on symbol sense and the function concept, we distinguish six epistemic functions of physics equations: calculating, describing, explaining, predicting, evaluating, and exploring. We then characterize six strategies through which these functions can be realized: dimensional analysis, order of magnitude analysis, covariational analysis, special case analysis, limiting case analysis, and formal analogies, illustrating each with examples from introductory physics. To examine how these strategies are viewed within the discipline, we surveyed 31 physicists at one university faculty about five of the strategies. Respondents regarded the strategies as indispensable to physics, judged limiting case analysis to be more difficult for students than dimensional analysis, and reported that their own courses could devote more time to them. By distinguishing what physicists use equations for from the strategies by which they do so, the paper provides a vocabulary for sensemaking of physics equations and specifies what explicit instruction in these strategies involves.

Optical manipulation enables the control of microscopic particles using light and has become an active area of research in recent years. One particularly interesting aspect is the possibility of generating optical pulling forces with hyperbolic metamaterials (HMMs), which leads to unusual light-matter interactions. In this work, the pulling response of plasmonic, chiral, and dielectric nanorods is studied on an HMM substrate. The system is illuminated by a time-harmonic, plane-polarized laser beam propagating along the +Z to -Z direction. The analysis is carried out under two different configurations. In the first case, plasmonic, chiral, and dielectric nanorods are arranged in a heterogeneous cluster over the HMMs and analyzed for the optical force response under three environmental conditions: fully immersed in water, partially immersed (half air-half water), and fully in air. Full-wave simulations reveal that in all three environments, all the objects (plasmonic, chiral, dielectric) nanorods consistently experience an optical pulling force at the 1E(-20)N scales for clustered configuration. In the second case, each nanorod type was independently placed on the same HMMs substrate within a full-air medium and investigated their force behaviors, while the plasmonic experience 100 times more than others for the single setup, which is 1E(-19)N ranges. Like the case of the cluster, three nanorods alone demonstrate a stable optical pulling force, also getting the pulling force with the variation of length, radius, and distance between them, which makes this optical setup more practical. Plasmonic behavior changes a lot with the arrangement of the nanostructures. On the other hand, dielectric nanorods are affected more by their length than their position. In our results, optical pulling appears for all the nanorods even with a simple HMM structure...

We study Gaussian fluctuations of differential observables of centered stationary random fields on the discrete $d$-dimensional torus of mesh $1/N$. Our main result is a Central Limit Theorem for the fields $f\mapsto N^{-d/2-m}\sum_x\phi_x^N(Pf)(x/N)$, where $P$ is a scalar homogeneous constant-coefficient differential operator of order $m\geq0$ with Fourier symbol $p$, e.g., $P=\Delta$ and $m=2$. Under suitable assumptions on the spectral scaling limit $\gamma$ of the covariance and the normalized cumulants of order $r\geq3$, we prove convergence in law in a negative Sobolev space to a centered Gaussian random distribution with covariance multiplier $|p(k)|^2\gamma(k)$. The two factors separate the effects of the operator and the field and, notably, differentiation can compensate a low-frequency spectral singularity. For the lattice Gaussian Free Field, this gives a projected white-noise limit for the gradient. The proofs use Fourier analysis and the method of moments and cumulants, together with a tightness argument. Finally, we give two sufficient criteria for the cumulant assumption, namely a tree–graph bound and the Dobrushin uniqueness condition for finite-range Gibbs fields, and recover the white-noise limits of the centered Ising magnetization and Potts colour fluctuation fields at high temperature.

Nonreciprocal interactions have emerged as a fundamental driver of collective behavior far from equilibrium. Here, we show that nonreciprocal couplings between spin systems whose isolated dynamics favors ordered states, beyond the previously identified oscillatory (swap) phase, give rise to a richer nonequilibrium phenomenology, including a multistable regime where ordered and disordered states coexist, a scenario strictly forbidden in equilibrium. Crucially, we show that this nonequilibrium phenomenology is inherited directly from the critical properties of the underlying isolated model. In particular, tricriticality in the isolated system gives rise to multistability, hysteresis, and hard excitations in the oscillatory dynamics, while non-normal interactions further enrich the phase diagram by generating multistability. Moving beyond mean-field theory, we derive a universal field equation governing the onset of these nonreciprocal oscillations in finite dimensions. Our results establish a unified theoretical framework connecting critical phenomena, dynamical systems, and non-reciprocal collective dynamics, with applications ranging from opinion dynamics to active matter

Breakthrough Listen, humanity's most ambitious search for technosignatures, or evidence of extraterrestrial technology, is carrying out surveys across the sky and across the electromagnetic spectrum, in images, spectra, time series, catalogs, and alerts. Classical techniques still play a major role in the search, but the recent rapid growth in the capabilities of artificial intelligence is enabling new and more powerful algorithms and approaches to be deployed across enormous datasets. Surveys designed to look for technosignatures are still a major focus for the Breakthrough Listen program, but excitingly, the new strategies also enable comprehensive mining of archives and of general-purpose real-time data streams. We outline how artificial intelligence and machine learning are being used to scale up the search, including with the newly-commissioned Vera C. Rubin Observatory, in addition to radio telescopes around the planet. The chances of a detection have never been better.