Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical perspective, viewing it as a quantitative enrichment of categories of stochastic matrices. We consider two natural monoidal structures on stochastic matrices, given by the Kronecker product and the direct sum. Our main results are complete axiomatisations of Kullback-Leibler divergence and, more generally, of Rényi divergences of arbitrary order, for each such structure. Our axiomatic theories are formulated within the framework of quantitative monoidal algebra, using a graphical language of string diagrams enriched with quantitative equations.

Combining tensor network techniques with quantum autoregressive moving average models, we quantify the effects of time-correlated noise on quantum algorithms and predict their performance at scale. As a paradigmatic test case, we examine the quantum Fourier transformation. Building on our first technical result, which shows how stochastic tensor network calculations capture frequency correlations, our second result is the revelation that infidelity exponents (scaling from diffuse, to superdiffuse) are determined by the spectral features of the noise. This numerical result rigorously quantifies the common belief that the temporal correlation scale is a key predictive feature of noise's deleterious impact on multi-qubit circuits. To highlight prospects for predicting algorithmic performance, our third result quantifies how infidelity scaling exponents -- which are fits determined by training data at moderate scales (40-80 qubits) -- can be used to predict more computationally expensive simulation at larger scales (100-128 qubits). Aside from highlighting the scalability of our methods, this workflow feeds into our last result, which is the proposal of predictive benchmarking protocols connecting simulations to experiments. Our work paves the way for large-scale algorithmic simulations and performance prediction under hardware-relevant noise conditions informed by realistic device characteristics.

The Orion Nebula is the closest high-mass star-forming region, making it an ideal laboratory to investigate physical processes in complex star-forming environments. At radio frequencies, the dominant emission mechanisms are thermal bremsstrahlung and non-thermal synchrotron. HII regions typically emit thermal radiation tracing the ionised gas; however, detecting and characterising non-thermal emission can provide insights into magnetic fields and the energy distribution of relativistic particles in star-forming regions. We have utilised the upgraded Giant Metrewave Radio Telescope (uGMRT) to study radio emission in the Extended Orion Nebula (EON) region. We present results from wide-band interferometric observations using uGMRT bands 3 and 4, probing a frequency range not covered by other sensitive radio interferometers. We produced deep continuum images with RMS noise levels of $\sim400\,μ$Jy~beam$^{-1}$ in band 3 and $\sim200\,μ$Jy~beam$^{-1}$ in band 4. We further generated in-band and broad-band spectral index maps using these images. To establish the robustness of the spectral index measurements, we conducted a detailed analysis using simulated uGMRT data. From the continuum spectral index analysis, we report the unambiguous presence of non-thermal radio emission in the EON region. To investigate its plausible origin, we correlated our results with multiwavelength observations, identifying a strong association between non-thermal emission and outflows from young stellar objects, while also exploring alternative explanations. In future, reliable broad-band radio spectral index measurements, together with dedicated multiwavelength observations, will be invaluable for resolving the origin of non-thermal emission in the Orion Nebula and other star-forming regions.

This paper introduces a canonical Polish groupoid associated to any separable unital C*-algebra, termed the unitary conjugation groupoid. It is defined as the semidirect product of the algebra's dual space by its unitary group, acting by conjugation. Classical groupoid models for C*-algebras typically require additional structure such as a Cartan subalgebra and rely on the locally compact Hausdorff framework. In contrast, our construction is entirely canonical but forces a paradigm shift: the natural topologies on the dual space and the unitary group are not locally compact. To address this, we equip the dual space with a Polish topology derived from the weak-star topology on pure states and the unitary group with the strong operator topology. This yields a Polish groupoid admitting a continuous Haar system. We prove that the associated reduced groupoid C*-algebra is Morita equivalent to the original algebra tensored with the compact operators, establishing that the groupoid encodes the K-theory of the algebra. A key feature is a canonical diagonal embedding of the original algebra into the groupoid C*-algebra, which is a unital injective star-homomorphism for separable Type I C*-algebras. We characterize commutativity via this embedding and establish functoriality of the construction under appropriate star-homomorphisms. The theory is illustrated with detailed computations for three fundamental classes: finite-dimensional matrix algebras, commutative algebras over compact metrizable spaces, and the unitized compact operators. These examples demonstrate that our general constructions reduce to familiar objects. We also discuss limitations by analyzing the irrational rotation algebra, a non-Type I algebra not covered by our construction, highlighting directions for future research.

Following the work of Katzarkov--Kontsevich--Pantev--Yu concerning the irrationality of the very general complex cubic fourfold, we prove the following: for every rational smooth complex cubic fourfold, the primitive cohomology is isomorphic as a Hodge structure to the (twisted) middle cohomology of a projective K3 surface.

We investigate the thermodynamic properties of finite Su-Schrieffer-Heeger (SSH) chains in thermal equilibrium at fixed temperature and chemical potential. Using the canonical and grand canonical ensembles, we calculate the energy density, particle number density, entropy, and heat capacity as functions of temperature, chemical potential, and hopping asymmetry. Our analysis reveals the emergence of a metastable thermodynamic phase characterized by a local minimum in the heat capacity for non-dimerized configurations, signaling a second-order phase transition distinct from the topological phase transition. This metastable phase becomes more pronounced as the hopping asymmetry increases and the chain length grows. We demonstrate that while the topological properties are determined by boundary states, the bulk thermodynamic behavior exhibits rich phase structure that can be tuned through the hopping parameter ratio. These findings provide insights into the interplay between topology, finite-size effects, and thermal fluctuations in one-dimensional topological systems, with potential implications for experimental realizations in cold atoms, photonic systems, and topoelectrical circuits.

Supernovae provide among the most powerful probes of weakly-coupled new particles in the MeV mass range, where laboratory experiments lose sensitivity. In this work, we derive improved supernova constraints on CP-even scalars mixing with the Higgs boson, combining an updated production rate calculation, which improves the cooling bound by more than an order of magnitude, with new decay-based constraints from the galactic 511~keV positron flux and energy deposition in low-energy Type~II-P supernovae. Together, these constraints probe mixing angles as small as $\sinθ\sim 10^{-9}$, more than five orders of magnitude below existing collider bounds. We also extend our analysis to a hadrophilic scalar model, constraining Yukawa couplings down to $y_N \sim 10^{-10}$. Our results demonstrate that the combination of astrophysical and collider probes covers over nine orders of magnitude in coupling for these classes of models, probing a large region of parameter space motivated by dark matter considerations.

We present far-ultraviolet (FUV) images and catalogs from the Hubble Space Telescope (HST) Advanced Camera for Surveys/Solar Blind Channel (ACS/SBC) F150LP (about 1600 Angstrom) of three extragalactic fields: GOODS-S, GOODS-N, and COSMOS. The data comprise 365 orbits of high-resolution imaging of 151 pointings covering an area of 44.7 square arcmin to typical depths of FUV about 28.7 AB (3-sigma, 0.5 arcsec diameter aperture). We provide a new model of the spatially varying dark "glow" created from all 365 orbits of data, and scale and subtract it from all pointings. We provide drizzled image mosaics, weight maps, and exposure time maps matched in coordinates and pixel scale to the Hubble Legacy Fields (HLF) frame, and the original COSMOS tiles. Galaxy photometry is measured within isophotes defined with existing deep Hubble F606W or F814W optical filters. We detect 1068 galaxies and provide catalogs of all optical detections, including matched IDs to existing 3D-HST and CANDELS catalogs. The redshift distribution of FUV-detected galaxies peaks at z about 0.6 and declines to z = 1.2, where the Lyman limit shifts redward of any filter transmission. These data fill the redshift gap of high-resolution far-UV imaging between z about 0 and z > 1, enabling studies of star-forming regions, dust properties, the FUV extragalactic background, and Lyman continuum emission from galaxies at z > 1.2.

In a previous work, we studied the momentum fraction and hard--scale dependence of double parton scattering (DPS) in proton--proton collisions and the resulting dependence of the effective cross section on the final--state observables. In this paper, we extend those results to heavy--ion ($pA$ and $AA$) collisions, accounting for nuclear effects in the relevant kinematic region, namely shadowing and antishadowing. In addition to modifying the longitudinal parton distributions, these effects also alter the transverse parton distribution of the nucleus, for which we propose a simple model. We further hypothesize that partons inside a bound nucleon are more widely separated than in a free proton. We compute the effective cross section for the available $p$Pb data, obtaining reasonable agreement, and provide predictions for future measurements at the LHC. The observed dependence of our predictions on the final state indicates that DPS in heavy--ion collisions can be used to probe the transverse profile of the free proton and the bound nucleon, primarily in $pA$ collisions, as well as the transverse structure of the nucleus, mainly in $AA$ collisions.

Ultra-faint dwarf (UFD) galaxies are a promising probe for dark matter (DM) physics as they are the most DM-dominated systems known. The Milky Way (MW) hosts many UFDs for which the properties of their DM distribution have been inferred from measurements of their stellar kinematics. If DM has self-interactions beyond gravity, the UFD halos may undergo a gravothermal evolution, giving rise to a population of galaxies with more diverse DM density profiles. We investigate DM densities of MW UFDs in self-interacting dark matter (SIDM) models, with an aim of determining the stage of gravothermal evolution for their halos. Therefore, we employ idealised high-resolution SIDM N-body simulations targeted to a MW-like system and compare the properties of simulated satellites to those of the observed UFDs. We find that the gravothermal evolution of SIDM halos produces diverse DM distributions, aligning with observations of the MW UFDs. Most of the UFDs have high DM densities, indicating that their halos have passed the period of maximum core expansion and entered the collapse phase, i.e., their central density may increase with time. The depth to which they have evolved into the gravothermal collapse may vary strongly across the satellites. This allows SIDM to account for the diversity in their DM densities. Moreover, the acceleration of the gravothermal evolution by tidal stripping goes hand-in-hand with explaining the diversity of the UFDs, as the ones with smaller pericentre distances require having evolved further into the gravothermal catastrophe. Large SIDM cross-sections of $σ/ m_χ\approx$ 80 cm$^2$ g$^{-1}$ at a velocity of $v \approx$ 20 km s$^{-1}$ are plausible, as the halo densities of MW UFDs are consistent with the gravothermal evolution predicted in SIDM, with most of them being in the collapse phase.

We study the strong coupling expansion of large $N$ QCD in various dimensions, reformulating the Kogut-Susskind Hamiltonian on a square lattice in terms of (constrained) one dimensional spin chain models. We study the integrability properties of the spin chain obtained this way: there is large class of integrable subsectors, but we show that the full spin chain is not integrable, at least when viewed from a description based on Bethe ansatz. We demonstrate that the spin chains no longer possess integrability due to the constraints arising from the zigzag symmetry of the confining strings. The spin chain description properly estimates the roughening transition point by extrapolating the first-order analytical results based on integrability of some subsectors. The generalization to higher dimensions are also considered, where we also find the small subsectors without the zigzag constraints to be integrable.

Observations of the rest-frame far-infrared (far-IR) emission of galaxies suggest a mild increase of dust temperature $T_{\rm dust}$ with redshift, although constraining $T_{\rm dust}$ in high-redshift systems remains challenging due to limited sampling of the far-IR spectral energy distribution (SED). We present and discuss the redshift evolution of $T_{\rm dust}$ predicted by a cosmological galaxy evolution simulation with dust treatment, and interpret its dependence on other galaxy physical properties. We use a semi-analytic model of galaxy formation that includes an explicit treatment of dust, post-processed with radiative transfer. Dust temperatures are derived by applying modified blackbody SED fitting to the simulated galaxies, mirroring the methodology adopted in most observational studies. The dust temperature of simulated galaxies increases with redshift, in broad agreement with observational results. A feature-importance analysis reveals that the star formation rate surface density $Σ_{\rm SFR}$ and the dust-to-gas ratio (DTG) are the main drivers of dust temperature, tracing the intensity of the interstellar radiation field and the optical depth of warm molecular clouds, respectively. Galaxies with higher star formation rate surface density and lower DTGs $-$ common conditions at high$-z$ $-$ are associated with warmer dust. We provide a simple relation to estimate DTG from $Σ_{\rm SFR}$, $T_{\rm dust}$, and redshift. Variations in dust grain size and chemical composition have a negligible impact on $T_{\rm dust}$. Our results are particularly relevant to the study of dust properties with observations of high-z galaxies, where far-IR dust emission is not fully sampled.

We consider the evolution of open quantum systems coupled to one or more Gaussian environments. We demonstrate that such systems can be described by a Markovian quantum master equation (MQME) up to a correction that decreases exponentially with the inverse system-bath coupling strength. We provide an explicit expression for this MQME, along with rigorous bounds on its residual correction, and numerically benchmark it for an exactly solvable model. The MQME is obtained via a generalized Born-Markov approximation that can be iterated to arbitrary orders in the system-bath coupling; our error bound converges asymptotically to zero with the iteration order. Our results thus demonstrate that the non-Markovian component in the evolution of an open quantum system, while possibly inevitable, can be exponentially suppressed at weak coupling.

Altermagnets are a newly identified class of magnets with nodal spin-split band structures, providing a fertile platform for studying unconventional superconductivity and intertwined orders. Here we investigate multicomponent superconductivity and fluctuation-induced intertwined orders in an interacting $d$-wave metallic altermagnet that is invariant under a combination of a fourfold rotation $C_4$ and time-reversal symmetry $T$. Within mean-field theory, the superconducting ground-state manifold is described in terms of two equal-spin two-component $p$-wave gap functions $(Δ_A^x,Δ_B^y)$ and $(Δ_A^y,Δ_B^x)$, where $A$ and $B$ refer to the two spin-polarized Fermi surfaces related by $C_4T$ symmetry. Because these two sets of gap functions condense at different temperatures, a rich phase diagram with multiple superconducting phase transitions emerges. Distinct fluctuations of sub-leading normal-state instabilities that compete with altermagnetism lift the degeneracy of the multicomponent pairing state in different ways. While nematic fluctuations enhance competition between distinct superconducting components and stabilize nematic superconducting phases, spin current-loop fluctuations promote coexistence and select a pair of chiral states. Our results uncover the pairing structure and elucidate how intertwined sub-leading fluctuations shape superconducting order in altermagnetic metals, suggesting a route toward realizing nematic and topological superconductivity.

Characterizing the ultimate rates of entanglement distribution is essential for both foundational research and the practical deployment of quantum technologies. To investigate these limits, we introduce an erasure-Pauli channel model describing the distribution of polarization entanglement in optical fiber. For this channel, we derive bounds on the rates of entanglement distribution and related quantum resources under optimal local operations and two-way classical communication (two-way assisted capacities). This framework allows us to determine the optimal repeaterless performance achievable over realistic optical fibers affected by polarization mode dispersion, thereby providing a rigorous benchmark for long-distance polarization-based quantum communication. Finally, we show that both our model and capacity bounds remain robust under the inclusion of detector dark counts.

Black holes and gravitational waves are consequences of the nonlinear character of the Einstein equations. Yet, the remarkable properties of General Relativity point to the existence of other effects. Here we uncover new nonlinear facets of gravity. We establish higher harmonic generation, spectral broadening and focusing in the Einstein Klein-Gordon system. In vacuum, we show that scattering of monochromatic waves at quadratic order is weakly sensitive to frequency, at large wavelengths. These aspects can both explain the seemingly smooth behavior of mergers, but also caution us against too simplistic an interpretation of waveforms.

Increasing demand for computational power has initiated the hunt for energy efficient and stable memory devices. This is the overarching motivation behind the recent rise of \textit{orbitronics}, which looks to harness the orbital angular momentum of charge carriers in computing devices. Orbitronic devices require materials with efficient generation of orbital angular momentum (OAM). In 2D materials, OAM can be electrically generated via the orbital magneto-electric effect (OME). In this paper we report the calculation of the OME in 2 dimensional hole gases (2DHGs). We show that the OME in Ge holes is very large, for an applied electric field of the order $10^4$ V$/$m the OAM density is of the order $10^{12}$ $\hbar/$cm$^{2}$. Furthermore, we find the OME to be an order of magnitude larger than the Rashba-Edelstein effect in 2DHGs. The OME we calculated in 2DHGs generates OAM aligned in the plane and arises due to transitions between heavy and light hole states, which is unique to this system. Our results put Ge, as well as other p-type semiconductors, forward as strong candidates for building future orbitronic devices.

The preparation and certification of quantum states is a fundamental challenge across quantum information technology. We introduce a tomography-free state certification method that lower-bounds the fidelity by estimating expectation values of engineered parent-Hamiltonian terms from local measurement data. We apply this framework to construct a parent Hamiltonian that enables certification and variational optimization across the Dicke-state family, which includes the single-excitation $W_n$ state. We experimentally validate the framework on IBM quantum hardware, certifying genuine multipartite entanglement for $W_n$ states up to six qubits and establishing positive lower bounds on the state fidelity up to thirteen qubits. For Dicke states with two- and three-excitations, we certify genuine multipartite entanglement up to seven qubits. Within this stringent certification framework, these results constitute among the largest witness-certified demonstrations of such states on a programmable quantum processor.

We propose a concrete realization of a triangular ladder for ultracold atoms, which simultaneously hosts geometric frustration and unusual two-body interactions, and in particular controllable pair hopping and density-induced tunneling. This is done by means of a spin-dependent Kronig-Penney lattice created using a spatially-dependent tripod-type atom-light coupling. We apply density matrix renormalization group (DMRG) calculations to derive the quantum phase diagram. We find that pair tunneling stabilizes a robust pair superfluid, characterized by power-law decay of pair correlations. Additionally, a chiral superfluid arises from frustration induced by competing nearest neighbor (NN) and next-nearest neighbor (NNN) tunnelings. Finally, in the high barrier regime, we map our system onto the XXZ spin model and find the exact phase transition points.

We investigate gravitational reheating in the Starobinsky model in the Jordan frame, where inflation is driven by an $R^2$ modification of gravity with no explicit inflaton field. In this description, reheating proceeds exclusively through gravitational particle production triggered by the oscillations of the Ricci scalar after the end of inflation. We analyze the post-inflationary background evolution and show that an effective fluid emerging from the modified gravitational dynamics behaves as pressureless matter during the oscillatory phase. Including the backreaction of the produced particles, we demonstrate that the Ricci scalar oscillations acquire an exponential damping, consistently terminating particle production. Solving the coupled background and Boltzmann equations, we obtain a reheating temperature $T_{\mathrm{reh}} \sim 2 \times 10^{9}$ GeV. We finally compare the Jordan and Einstein frame descriptions and argue that, although classically equivalent, they can lead to distinct microphysical interpretations and quantitative predictions for reheating once quantum effects are taken into account.

We consider the degenerate minima arising from scalar potentials invariant under $Σ(36\times 3)$, or under its subgroups $Δ(54)$ and $Δ(27)$ (with or without imposed CP symmetries), for a triplet of those symmetries. In this framework, we classify the distinct Domain Walls between the degenerate minima and calculate the respective tensions.

We analyze how the geodesic motion in the 3- and 4-vortex sectors of the Abelian-Higgs model at critical coupling is deformed by the excitation of a massive bound mode. We find that the geodesics corresponding to BPS solutions with enhanced symmetry remain unchanged, although the direction of the actual motion depends on the mode-generated force, i.e., a force arising from the change of the mode frequency along the geodesic. In a generic case, for example in head-on collisions between the axially symmetric 1- and 2-vortex or between two 2-vortices, the vortex trajectories can differ strongly from the BPS geodesic. This enhances the chaotic behavior in the formation of the final state.

Within the known landscape of quantum gravity, most theories satisfy the Lattice Weak Gravity Conjecture (LWGC), which requires a superextremal particle at every site in the electric charge lattice $Γ$. However, counterexamples to the LWGC exist, and it was recently hypothesized that such counterexamples necessarily feature fractionally charged confined monopoles. In this work, we verify this hypothesis in toroidal orbifold compactifications of the heterotic string, which notably feature LWGC violation in both the abelian and nonabelian gauge sectors. In all the cases we consider, there exists a discrete subgroup of the center of the gauge group $K \subseteq Z(G)$ such that superextremal particles exist at every site in the charge lattice of the quotient group $G/K$, while (confined) monopoles exist at all sites in the magnetic charge lattice of $G/K$. This suggests that LWGC violation cannot occur for gauge groups with trivial centers, and more generally the degree of LWGC violation in a nonabelian gauge theory is bounded in terms of the maximal order of the center.

The realization of unconventional quantum phases in frustrated and spin-orbit coupled materials remains at the forefront of quantum materials research. Here we report the synthesis and discovery of NiIrO3, the first honeycomb iridate with coupled 3d-5d magnetic sublattices, through a soft topotactic reaction. Structural analysis reveals an ilmenite-type stacking of edge-sharing NiO6 and IrO6 octahedral honeycomb sublattices in a Kitaev geometry. Comprehensive magnetic and electrical transport measurements unveil its long-range ferrimagnetic order below 213 K, which is in sharp contrast to the predominantly antiferromagnetic order in the known honeycomb iridates. Notably, the titled compound displays an exceptionally large magnetocrystalline anisotropy energy of 32.2 meV/f.u. and a giant coercivity with coercive field exceeding 17.3 T below 4.2 K, both ranking among the highest observed in iridates to date. Combined experimental and theoretical investigations indicate that the exceptional anisotropy and coercivity originate from the synergistic effect between strong lattice frustration in the coupled 3d-5d honeycomb lattice network and the robust spin-orbit coupling of the Ir4+ (Jeff = 1/2) state. This work positions NiIrO3 as a promising platform to investigate low-dimensional and frustrated quantum spin systems, and highlights its potential for spintronic applications through the targeted engineering of 3d-5d interactions.

In the context of increasing appreciation for the coupling between the Galactic bar and the halo, we introduce a new framework using stars trapped in resonance with the bar to probe the Galactic dark matter subhalo population. Since resonant stars occupy a finite width in action space, perturbations from subhaloes can shift a star's actions beyond this width, causing them to circulate out of resonance. Physically, the dark substructure in the Milky Way may dissolve, puff-up, or re-order the resonance features in the stellar halo. To explore the utility of this framework, we treat individual encounters in the impulse approximation and model their cumulative effect as diffusion in the relevant action. The resulting diffusion coefficient allows us to link the survival of resonant populations to the subhalo mass function, whose properties depend on the particle nature of dark matter. Test particle integration validates the impulse treatment for low-mass subhaloes and quantifies its regime of applicability. For a Milky Way-like bar, we find individual subhaloes with $M<10^7$ M$_{\odot}$ have negligible impact on stars in co-rotation resonance, where as the full cold dark matter (CDM) population could erase the resonance over the bar's lifetime. The persistence of resonances therefore implies a suppression of the local subhalo density to less than 1/3 of CDM expectations, consistent with tidal disruptions and previous literature. The narrow widths of higher-order resonances will increase the constraining power of this framework, and therefore motivates searches for bar-resonant halo features in observational data.

Pandora is a SmallSat mission dedicated to understanding exoplanets and their host stars by disentangling the impact of stellar heterogeneity on exoplanet transmission spectra. Selected as a NASA Astrophysics Pioneers mission in 2021, Pandora will provide simultaneous long-term visible photometric monitoring (0.4--0.7 $μ$m) and low-resolution near-infrared (NIR) spectroscopy (0.9--1.6 $μ$m) of transiting systems for the purposes of monitoring host star variability and characterizing exoplanetary atmospheres. Pandora's year-long prime mission from 2026 to 2027 coincides with the middle of a decade defined by targeted efforts for atmospheric characterization of exoplanets, offering a key opportunity to leverage this new resource to maximize science with JWST and other observatories. Here we investigate Pandora's anticipated performance for the general exoplanet population accessible to transit spectroscopy, from hot Jupiters to temperate sub-Neptunes. By modeling the atmospheres of five test cases broadly consistent with the bulk properties of HD~209458~b, HD~189733~b, WASP-80~b, HAT-P-18~b, and K2-18~b, we find that Pandora may provide abundance constraints as precise as $\sim$1.0\,dex for main atmospheric absorbers such as H$_2$O and CH$_4$. Then, we explore the synergies between Pandora and JWST. Our results suggest that targets with JWST data in the near-infrared can benefit from the addition of Pandora observations and result in more reliable abundance estimates than with JWST data alone. Moreover, Pandora can serve the community by providing precursory observations of targets of interest for JWST atmospheric characterization. We conclude by outlining strategies for the use of Pandora as a standalone observatory and in synergy with JWST.

We propose a covariant orbital-spin ($LS$) decomposed amplitude for the partial wave analysis using the massive spinor-helicity formalism. First we review the traditional-$LS$ method in the little group space and the Zemach tensor method in the double cover of the $\mathrm{SO}(3)$ space. To recover the $\mathrm{SO}(3,1)$ Lorentz covariance, several Lorentz covariant $LS$ tensors have been constructed in several different methods: covariant tensor, covariant projection tensor in pure-spin and general-spin schemes, but performing a intrinsic separation between $LS$ coupling while maintaining covariance is not obvious. We utilize the massive canonical-spinor variables to determine general three-point amplitudes, in which the spin-orbital decomposition is realized in single little group space by projecting little group indices of each particles into one, while the Lorentz covariance is ensured by the spinor form naturally. This covariant spinor method allows direct evaluation in any frame and a streamlined treatment of cascade decays within a single frame without additional alignment rotations in non-covariant treatment. As a benchmark, we implement the method in TF-PWA and analyze $Λ_c^+\toΛπ^+π^0$, finding consistent fit results across the helicity, traditional-$LS$, and canonical-spinor amplitudes. This validates the canonical-spinor amplitude as a practical tool for modern partial wave analyses of complex decay chains.

Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of existing metrics. In particular, we show how ergodicity and chaos improve the robustness of Hamiltonian learning to small errors and furthermore demonstrate that this robustness can be used as a metric for such phenomena. We analytically and numerically show that our metrics not only distinguish between integrable and ergodic regimes in various spin chains but also quantify chaos and ergodicity, allowing us to locate regions of parameter space displaying maximal ergodicity and maximal sensitivity to local perturbations. Our approach not only provides conceptual ways to study quantum chaos and ergodicity but also presents viable experimental methods for quantum simulators.

We employ multiparticle factorization to constrain deformations of tree-level open string amplitudes. Assuming minimal degeneracy among intermediate states of the same spin up through the second excited level, we find that the Regge intercept among all amplitudes of the Koba-Nielsen type can be uniquely fixed using seven-point factorization, precisely matching the bosonic string. Moreover, we produce novel constraints on deformations of the worldsheet integrand. We then turn to deformations of superstrings, with massless external states and arbitrary spectral degeneracy, using soft kinematics. Accounting for the infinite tower of higher-spin resonances, we obtain novel multipositivity bounds to leading and subleading order in the large-level limit. We apply these bounds to the simplest factorizable satellite deformation in the family of amplitudes found by Gross, showing that any deformation of four-point string amplitudes of this type is forbidden by unitarity. Our results reinforce the folklore that the higher-spin tower of string excitations is dramatically more rigid than any finite number of species.

Efficient code retrieval is critical for developer productivity, yet existing benchmarks largely focus on Python and rarely stress-test robustness beyond superficial lexical cues. To address the gap, we introduce an automated pipeline for code search datasets and present CLARC, a C/C++ benchmark built from real-world GitHub repositories. CLARC contains 1,245 query-code pairs for evaluation and 5,472 pairs for training. The benchmark incorporates LLM-generated natural language queries validated through rigorous human scoring and hypothesis testing. To analyze contextual requirements effectively, our pipeline starts by ensuring code compilability. It then categorizes code snippets by dependency complexity, distinguishing whether the code relies on custom-defined types or helper functions. The pipeline also enables CLARC to stress-test retrieval robustness by introducing challenging settings, including identifier anonymization and compilation to low-level languages like Assembly and WebAssembly. Under these conditions, our evaluation of six state-of-the-art models reveals sharp drops in retrieval effectiveness. The experimental results highlight the models' persistent reliance on lexical features rather than code semantic understanding. Our dataset is publicly available at https://huggingface.co/datasets/ClarcTeam/CLARC.