Approximating multivariate periodic functions in weighted Korobov spaces via rank-1 lattices is fundamentally limited by frequency aliasing. Existing optimal-rate methods rely on randomized constructions or large pre-computations. We propose a fully deterministic multiple-shift lattice algorithm without pre-computation. First, we develop a simplified multiple shift framework for aliased frequency fibers that reduces sampling costs. Second, leveraging the Chinese Remainder Theorem and the Weil bound, we introduce an adaptive hybrid construction that algebraically guarantees the full rank and bounded condition number of the reconstruction matrix. We rigorously prove that this deterministic method maintains the optimal convergence rate in the worst-case setting. Furthermore, we extend this framework to non-periodic, half-period cosine spaces via the tent transformation. By establishing a strict projection equivalence, we prove that the algorithm attains optimal $L_2$ and $L_\infty$ approximation orders in the half-period cosine space, successfully resolving an open theoretical problem posed by Suryanarayana et al. (2016). This mathematically also validates the proposed algorithm as a generic meshless spectral solver for high-dimensional boundary value problems, such as the Poisson equation with Neumann conditions. Numerical experiments corroborate the theoretical bounds, demonstrating an order-of-magnitude reduction in sampling complexity over probabilistic baselines while ensuring absolute deterministic stability.

The evolution of the superconducting transition temperature ($T_c$) in FeSe was investigated under in-plane, out-of-plane, and hydrostatic compression. For pressures up to 0.6 GPa, $T_c$ increases regardless of the compression mode, consistent with the suppression of nematic ordering. However, once nematicity is suppressed, $T_c$ exhibits a striking directional dependence: out-of-plane compression shows behavior similar to the hydrostatic case, with a sharp increase in $T_c$, whereas in-plane compression suppresses superconductivity. First-principles calculations suggest that in-plane compression shifts a hybridized band of Se $p_z$ and Fe $d_{x^2-y^2}$ character so that it crosses the Fermi level along the $Γ$-Z direction, leading to the emergence of an additional metallic band. This leads to an increased three-dimensionality of the electronic structure and may be interpreted as a possible Lifshitz-type change in the Fermi surface.

We set up a cochain complex $C^\bullet_{\mathrm{mix}}(\mathcal{M})$ whose cohomology controls deformations of the mixed associator of a module category $\mathcal{M}$ over a $\Bbbk$-linear monoidal category $\mathcal{C}$. We show that $C^\bullet_{\mathrm{mix}}(\mathcal{M})$ is isomorphic to the Davydov-Yetter (DY) complex of the representation functor $ρ: \mathcal{C} \to \mathrm{End}(\mathcal{M})$. Using our previous results on DY cohomology (arXiv:2411.19111), we prove that if $\mathcal{C}$ and $\mathcal{M}$ are finite then the cohomology $H^\bullet_{\mathrm{mix}}(\mathcal{M})$ is isomorphic to the relative Ext groups $\mathrm{Ext}^\bullet_{\mathcal{Z}(\mathcal{C}),\mathcal{C}}(\boldsymbol{1},\mathcal{A}_{\mathcal{M}})$ for the usual adjunction between the Drinfeld center $\mathcal{Z}(\mathcal{C})$ and $\mathcal{C}$, where $\mathcal{A}_{\mathcal{M}}$ is the so-called adjoint algebra of $\mathcal{M}$. This allows us to give a dimension formula for $H^n_{\mathrm{mix}}(\mathcal{M})$ in terms of certain Hom spaces in $\mathcal{Z}(\mathcal{C})$, and also to prove that $H^{>0}_{\mathrm{mix}}(\mathcal{C}) = 0$. We also show that the algebra $\mathcal{A}_{\mathcal{M}}$ is the ``full center'' of an algebra in $\mathcal{C}$ realizing $\mathcal{M}$. We furthermore establish a generalized version of Ocneanu rigidity for monoidal functors with coefficients, and provide its application to general (non-exact and non-finite) $\mathcal{C}$-module categories over a fusion category $\mathcal{C}$ such that $\dim(\mathcal{C}) \neq 0$. We spell out these results for module categories defined by finite-dimensional comodule algebras over finite-dimensional Hopf algebras. Examples based on comodule algebras over Sweedler's Hopf algebra are worked out in detail and yield new continuous families of inequivalent non-exact module categories.

This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach enables element-local refinement of the polynomial degree, concentrating computational effort specifically in regions with strong gradients. Thus, the method significantly reduces the global number of degrees of freedom compared to uniform high-order methods. The proposed method is implemented in the open-source framework PICLas and validated through a series of benchmark test cases, including a dielectric sphere and a one-dimensional plasma sheath. Finally, a two-dimensional axisymmetric simulation of an ion optic demonstrates the method's capability to efficiently model complex plasma phenomena but also highlights current limitations.

Ensuring that a PDE model is well-posed is a necessary precursor to any form of analysis, control, or numerical simulation. Although the Lumer-Phillips theorem provides necessary and sufficient conditions for well-posedness of dissipative PDEs, these conditions must hold only on the domain of the PDE -- a proper subspace of $L_{2}$ -- which can make them difficult to verify in practice. In this paper, we show how the Lumer-Phillips conditions for PDEs can be tested more conveniently using the equivalent Partial Integral Equation (PIE) representation. This representation introduces a fundamental state in the Hilbert space $L_{2}$ and provides a bijection between this state space and the PDE domain. Using this bijection, we reformulate the Lumer-Phillips conditions as operator inequalities on $L_{2}$. We show how these inequalities can be tested using convex optimization methods, establishing a least upper bound on the exponential growth rate of solutions. We demonstrate the effectiveness of the proposed approach by verifying well-posedness for several classical examples of parabolic and hyperbolic PDEs.

The orbital, spin and valley degrees of freedom in silicon quantum dots support many modes of spin qubit operation. However, it is generally challenging to obtain information about the energy level spectrum over large ranges of parameter space. We demonstrate a form of spectroscopy that is capable of mapping the energy level structure of a double quantum dot as a function of level detuning, interdot tunnel coupling, and magnetic field. In the one electron regime, we directly observe the transition from the atom like energy levels of isolated quantum dots to molecular like bonding and anti bonding states with increasing interdot tunnel coupling. We also resolve the Zeeman splitting of ground and excited valley states in a magnetic field. In the two electron regime, we gain access to the detuning dependent singlet triplet splitting. Our work may be extended to a broader class of systems, such as strong spin-orbit materials or proximitized quantum dots, allowing the direct extraction of various energy gaps.

Continuous variable (CV) quantum computation offers an alternative to qubit-based computing by exploiting the infinite-dimensional Hilbert space of bosonic modes. Despite recent progress, superconducting platforms have yet to demonstrate a scalable architecture capable of universal computation. Here, we design and numerically simulate a two-layer superconducting architecture that implements all five interactions of the universal CV gate set (rotation, displacement, squeezing, Kerr, and beam splitter) within experimentally accessible regimes. To this end, we employ a DC-SQUID as the bosonic mode, a fluxonium qubit to mediate nonlinear interactions, and two ancillary qubits that enable Gaussian and multi-mode operations. By tuning fluxes and frequencies, we achieve high fidelities ($\geq 98\%$) across all gates within state-of-the-art parameter ranges. The modular nature of the design allows straightforward scaling, establishing a feasible pathway toward high-fidelity, universal CV quantum computation based on superconducting circuits.

We present a lattice quantum chromodynamics calculation of the $x$-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}_2$ moment of the twist-3 PDF $g_T(x)$ for the first time in the $\overline{\rm MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing $a$ = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta $P_z=\{0, 0.25, 1.02, 1.53\}$ GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for $g_T(x)$, we obtain $\tilde{d}_2^{u-d}(2\ {\rm GeV})=0.0024(46)$ at next-to-leading order in $\overline{\rm MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the $x$-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{\rm MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region $x\in[0.25,0.75]$ with controlled systematic uncertainties. The end-point regions are then parameterized, combined with the LaMET prediction at moderate $x$, and fitted to the short-distance matrix elements in coordinate space.

With the increasing penetration of inverter-based resources (IBRs) in power grids, system-level coordinated optimization of IBR controllers has become increasingly important for maintaining overall system stability. Unlike most existing methods that rely on simplified or linearized dynamic models and focus on small-signal stability or isolated tuning of individual facilities, this paper proposes a novel simulation-based, model-free framework for the coordinated optimization of IBR control parameters to enhance grid transient dynamic performance. The framework uses a high-fidelity power system simulator to accurately evaluate grid transient dynamic responses, and a projected multi-point zeroth-order optimization algorithm with adaptive moment estimation, termed PMZO-Adam, is proposed to solve the problem in a model-free manner, thus eliminating the need for explicit mathematical models of complex nonlinear system dynamics. The proposed framework enables direct optimization of grid transient dynamic behavior and system-wide coordinated tuning of IBR controllers. Extensive simulations demonstrate the effectiveness of the proposed approach in optimizing IBR control parameters to improve grid transient frequency response under large disturbances.

This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.

We provide a new proof of a result of Bessenrodt on the relation among the generating series of reversed plane partitions and skew plane partitions, motivated by the geometric DT/PT wallcrossing formula for local curves recently proved by the third author. This also recovers a result of Sagan. We moreover establish various new closed formulas for the weighted enumeration of reversed and skew plane partitions, proving a result dual to a theorem by Gansner, we find a new identity on the generating series counting internal and external hooks of a given Young diagram, and we combine the latter with Bessenrodt's theorem. Finally, we interpret our results as identities in the Fock space via the bosonic/fermionic formalism.

Considering a general framework of bootstrap with exchangeable weights, we show some concentration inequalities for the supremum of the bootstrap empirical process. On the one hand, we discuss the concentration of the bootstrap empirical process around its conditional expectation with respect to the original data, and on the other hand, the concentration of the latter quantity around its mean. For the concentration conditional on data, we build on Chatterjee's exchangeable pairs approach to concentration. To attain optimal concentration rates, we develop some refined arguments for the convergence of transposition walks on the symmetric group. The conditional expectation of the bootstrap empirical process is proved to be self-bounding, thus extending a well-known property for conditional Rademacher averages. To illustrate the interest of these concentration inequalities, we provide some new results pertaining to confidence regions for the estimation of a mean vector, as well as non-asymptotic bounds for the two-sample permutation test.

First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial selloff. While typical formulations involve diffusive motion, many stochastic processes are better described as velocity jump processes, characterized by persistent motion interrupted by stochastic velocity changes. Despite their ubiquity, first-passage properties of velocity jump processes remain underdeveloped in higher dimensions, especially under directional bias. We present a general framework to estimate the mean first passage time (MFPT) and higher moments of the survival probability for fixed-speed velocity jump processes where possible reorientations range from strong alignment to full angular anisotropy. For low Knudsen numbers, when the mean free path is small compared to the distance to the target, we derive a universal form for the MFPT in which two bias functions encode broad classes of angular distributions, including von Mises-Fisher, wrapped Cauchy, and elliptical families. In the narrow capture limit of a vanishingly small target, directional persistence induces anomalous scaling, including regimes where the MFPT remains finite whereas standard diffusion would predict divergence. Finally, we obtain a Langevin representation that accurately reproduces first-passage statistics. Analytical predictions are confirmed by numerical simulations.

While battery aging is commonly studied at the cell-level, evaluating aging and performance within battery modules remains a critical challenge. Testing cells within fully assembled modules requires hardware solutions to access cell-level information without compromising module integrity. In this paper, we design and develop a hardware testing platform to monitor and control the internal cells of battery modules contained in the Audi e-tron battery pack. The testing is performed across all 36 modules of the pack. The platform integrates voltage sensors, balancing circuitry, and a micro-controller to enable safe, simultaneous cell screening without disassembling the modules. Using the proposed testing platform, cell voltage imbalances within each module are constrained to a defined reference value, and cell signals can be safely accessed, enabling accurate and non-invasive cell-level state-of-health assessments. On a broader scale, our solution allows for the quantification of internal heterogeneity within modules, providing valuable insights for both first- and second-life applications and supporting efficient battery pack maintenance and repurposing.

Nanoscale thermal transport is governed by the phonon Boltzmann transport equation (BTE). However, simulating the sub-continuum dynamics remains computationally prohibitive due to the high dimensionality of the phase space and the intrinsic nonlinearity of the scattering collision operator. Traditional numerical solvers and standard physics-informed neural networks (PINNs) inherently struggle with these integro-differential equations due to deterministic quadrature limitations, artificial thermalization introduced by the relaxation time approximation (RTA), and multiscale spectral bias. This work introduces a multiscale auxiliary physics-informed neural network (MTNet) to solve the generalized equation of phonon radiative transfer (GEPRT). By leveraging an auxiliary formulation, this mesh-free framework recasts the GEPRT into a fully differential system, enabling the analytical evaluation of scattering operators via automatic differentiation and facilitating scalable multi-GPU parallelization. To circumvent optimization stiffness, the architecture employs a decoupled, shallow neural network explicitly constrained by radiative equilibrium. MTNet is validated by simulating steady-state cross-plane transport in a silicon thin film, successfully capturing ballistic-diffusive regimes and characteristic boundary slips across extreme temperature gradients ($ΔT = 100$ K) beyond the standard linearization approach. Furthermore, we show that our framework successfully solves a geometric inverse problem in a slab geometry, retrieving the unknown slab thickness based only on interface temperature constraints in the mesoscopic regime. Ultimately, MTNet establishes a robust, fully differentiable foundation for predicting high-fidelity kinetic transport and extracting material properties in next-generation nanostructures.

Gamma-ray bursts (GRBs), the most energetic transients in the Universe, are traditionally classified into long-duration ($T_{90}>2$ s) and short-duration ($T_{90}<2$ s) events, associated with the core collapse of massive stars (Type II) and the merger of compact binary systems (Type I), respectively. The two classes exhibit distinct observational properties that serve as key diagnostic criteria for classification. Here we report GRB 160425A, a peculiar event comprising two sub-bursts separated by four minutes: a short-duration burst ($G_1$) and a long-duration burst ($G_2$). Nearly all standard prompt-emission diagnostics, including pulse morphology, duration, hardness ratio, minimum variability timescale, spectral properties, and established empirical correlations, consistently categorize $G_1$ as a short-like (Type I, merger-origin) and $G_2$ as a long-like (Type II, collapsar-origin) GRB. The coexistence of merger and collapsar signatures in a single event challenges existing progenitor frameworks and calls for a re-evaluation of GRB classification schemes and progenitor scenarios.

We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis system describing the interaction between healthy tissue, damaged fibers, immune cells and inflammatory signals. We establish the global well-posedness of the system and investigate the early-stage dynamics through linearization around the healthy equilibrium. Our analysis shows that diffusion does not induce Turing instabilities, so that spatial heterogeneity cannot arise from diffusion-driven mechanisms. Instead, disease progression occurs through invasion processes. We derive explicit conditions for the onset of invasion, interpreted as an effective damage reproduction threshold and characterize the minimal propagation speed of pathological fronts, showing that the dynamics is governed by a pulled-front mechanism. Numerical simulations support the analytical results and confirm the transition between decay and invasion. These results provide a mathematical framework for early-stage disease progression and indicate that spatial spreading arise from the expansion of localized damage rather than from intrinsic pattern-forming mechanisms.

The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings composed with the scaled softmax function. The authors of the aforementioned work provide proofs for the existence and approximate position of such attractive fixed points. For the softmax function alone, the fixed point structure has been fully characterized in earlier work by P. Tiňo, from which it turns out that for sufficiently large scaling factors there are exponentially more unstable fixed points than attractive ones. In this work, we complement the findings of Ramsauer et al. by showing that, under natural geometric conditions on the vectors defining the continuous Hopfield network, unstable fixed points must occur, analogous to the findings of Tiňo. Our results show that, under these geometric conditions, continuous Hopfield networks necessarily admit additional unstable fixed points associated with higher-dimensional faces of the pattern polytope.

Large language models (LLMs) are increasingly used in software development, generating code that ranges from short snippets to substantial project components. As AI-generated code becomes more common in real-world repositories, it is important to understand how it differs from human-written code and how AI assistance may influence development practices. However, existing studies have largely relied on small-scale or controlled settings, leaving a limited understanding of AI-generated code in the wild. In this work, we present a large-scale empirical study of AI-generated code collected from real-world repositories. We examine both code-level properties, including complexity, structural characteristics, and defect-related indicators, and commit-level characteristics, such as commit size, activity patterns, and post-commit evolution. To support this study, we develop a detection pipeline that combines heuristic filtering with LLM-based classification to identify AI-generated code and construct a large-scale dataset for analysis. Our study provides a comprehensive view of the characteristics of AI-generated code in practice and highlights how AI-assisted development differs from conventional human-driven development. These findings contribute to a better understanding of the real-world impact of AI-assisted programming and offer an empirical basis for future research on AI-generated software.

Per- and polyfluoroalkyl substances are a class of synthetic chemical compounds widely used as coatings to lower surface energies. Yet the microscopic mechanisms of their weak interaction with water and organic compounds remain poorly understood. Here, we perform large-scale density-functional-theory molecular dynamics simulations to investigate water at self-assembled monolayers (SAMs) of fluorinated and non-fluorinated hydrocarbons. We analyze the interfacial water structure and compare it to the prototypical hydrophobic air-water interface. The interfacial water structure at both SAMs closely resembles that at the air-water interface, featuring a distinct depletion layer and a two-dimensional hydrogen-bond network parallel to the surface. Computed anisotropic infrared spectra reproduce key experimental signatures observed in surface-enhanced infrared absorption spectroscopy (SEIRAS), including the presence of free OH vibrations directly probing the local surface-water interactions. Notably, while the free OH stretch at the hydrocarbon SAM-water interface exhibits a red shift relative to the air-water interface, indicative of weak binding, the fluorinated SAM-water interface displays a weakly blue-shifted free OH mode, in agreement with experiment. This frequency behavior defies common interpretations based on the vibrational Stark effect. Further, we show that the reorientation dynamics of water molecules are significantly slower near the fluorinated surface, which we correlate with spectral line shapes, an effect rather expected at hydrophilic surfaces. This indicates that fluorinated SAMs, despite being macroscopically more hydrophobic than their unfluorinated counterparts, exhibit spectroscopic characteristics that neither qualify it as hydrophobic nor hydrophilic.

Data donation, an emerging user-centric data collection method for public sector research, faces a gap between participant willingness and actual donation. This suggests a design absence in practice: while promoted as "donor-centered" with technical and regulational advances, a design perspective on how data choices are presented and intervene on individual behaviors remain underexplored. In this paper, we focus on pre-donation data exploration, a key stage for adequately and meaningful informed participation. Through a real-world data donation study (N=24), we evaluated three data exploration interventions (self-focused, social comparison, collective-only). Findings show choice framing impacts donation participation. The "social comparison" design (87.5%) outperformed the "self-focused view" (62.5%) while a "collective-only" frame (37.5%) backfired, causing "perspective confusion" and privacy concerns. This study demonstrates how strategic data framing addresses data donation as a behavioral challenge, revealing design's critical yet underexplored role in data donation for participatory public sector innovation.

While large language models (LLMs) have accelerated 2D software development through intent-driven "vibe coding", prototyping intelligent Extended Reality (XR) experiences remains a major challenge. The fundamental barrier is not just the steep learning curve for human creators, but that low-level sensor APIs and complex game engine hierarchies are ill-suited for LLM reasoning, routinely exceeding context windows and inducing syntax hallucinations. To bridge this gap, we contribute XR Blocks, an open-source, LLM-native WebXR framework. Unlike traditional engines, XR Blocks introduces a semantic "Reality Model" that aligns spatial computing primitives (users, physical environments, and agents) with natural language, providing a robust, concise vocabulary optimized for generative AI. Building upon this foundation, we present Vibe Coding XR, an end-to-end prototyping workflow that leverages LLMs to translate high-level prompts (e.g., "create a dandelion that reacts to my hand") directly into functional, physics-aware mixed-reality applications. To minimize the friction of on-device testing, the workflow introduces a seamless desktop "simulated reality" to headset deployment loop. Finally, we introduce VCXR60, a pilot dataset of 60 XR prompts paired with an automated evaluation pipeline. Our technical evaluation demonstrates high one-shot execution success, enabling practitioners to bypass lowlevel hurdles and rapidly move from "idea to reality". Code and live demos are available at https://github.com/google/xrblocks and http://xrblocks.github.io/gem.

The weak binding and spatially extended neutron densities characteristic of drip-line nuclei give rise to a distinctive low-energy dipole response. The drip-line nucleus $^8$He is the most neutron-rich bound nucleus with a mass-to-charge ratio of $A/Z=4$. We measure the dipole response of $^8$He, including for the first time the four-neutron decay channel. A total dipole strength of $\sum B(E1)(E^*<15$~MeV$)=0.95(16)~e^2$fm$^2$ and a dipole polarizability of $α_D = 0.61(1)$~fm$^3$ are extracted from the differential Coulomb-excitation cross section and compared to state-of-the-art theoretical calculations employing coupled cluster and three-body approaches. We find that the dipole continuum is dominated, even at high excitation energies well above the $4n$ decay threshold, by two-neutron emission, pointing to a $^6$He$+2n$ structure of the excited dipole mode. No indication was found for a $4n$ final-state correlation, while pronounced $nn$ and $^6$He-$n$ final-state correlations are apparent.

Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in missing low-angle scattering data, which limits accurate real-space reconstruction. We develop an iterative algorithm to recover the missing low-angle signal in two-dimensional diffraction patterns. The method transforms between momentum-transfer and real-space domains using coupled Fourier and Abel transforms, while enforcing real-space support constraints to suppress reconstruction artifacts. Importantly, the algorithm requires only minimal a priori knowledge of the molecular structure, namely the approximate shortest and longest internuclear distances. We demonstrate accurate reconstruction of the missing signal using both simulated data and experimental diffraction patterns from laser-aligned trifluoroiodomethane (CF3I) molecules, enabling improved real-space structural retrieval from incomplete diffraction data. Our results remove a fundamental experimental limitation in ultrafast diffraction and establish a general route toward complete structural retrieval from incomplete scattering data.

We show that Grothendieck's real constant $K_{G}$ satisfies $K_G\geq c+10^{-26}$, improving on the lower bound of $c=1.676956674215576\ldots$ of Davie and Reeds from 1984 and 1991, respectively.

We study magnetic materials whose low energy physics can be effectively described by a Dicke model, which we term Dicke materials. We show how a Dicke model emerges in such materials due to a coexistence of fast-dispersing and slow-dispersing spins, which are strongly coupled. Analogous to the paradigmatic Dicke model describing light-matter interactions, these materials also exhibit signatures of a superradiant phase transition. The ground state near the superradiant phase transition is expected to be squeezed, making Dicke materials a resource for quantum metrology and witnessing entanglement in solid-state systems. However, as an entanglement measure, squeezing can be sensitive to perturbations that are otherwise irrelevant for usual correlation functions and order parameters. Motivated by the prospect of observing squeezing in such Dicke materials, we study the robustness of ground state squeezing under ubiquitous imperfections such as finite temperature, disorder, and local interactions. Using analytical and numerical techniques, we show that the squeezing obtained is perturbatively stable against these imperfections and quantitatively evaluate regimes promising for experimental observation.

We classify all maximal symmetry models of CR dimension 1, depending on their Bloom-Graham and Tanaka types, give coordinate realization to some of those models and prove a general extension principle.

We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians. As an application of this notion, for many prescribed sub-exponential growth rates $f(t)$, either monotone or oscillatory, we explicitly construct time-decaying perturbations of the one-dimensional quantum harmonic oscillator such that the Sobolev norms of solutions grow at the rate $f(t)$.

We present the first semi-empirical strong-line calibrations to determine metallicity in Active Galactic Nuclei (AGNs) that use the directly observable X-ray luminosity (Lx) instead of the dimensionless ionization parameter ($U$). The calibrations are derived from an extensive grid of photoionization models computed with the {\sc Cloudy} code, which are compared with observational data of Seyfert nuclei from the Burst Alert Telescope (BAT) AGN Spectroscopic Survey (BASS). In this first paper, we develop new calibrations for two key optical metallicity diagnostics based on the $N2$ and $O3N2$ indices, which are valid in a metallicity range of $8.0 \lesssim 12 + \log({\rm O/H}) \lesssim 9.1\, {\rm or}\, 0.2 \lesssim (Z/Z_{\odot}) \lesssim 2.6$, with precision of $1σ\approx 0.22$ dex ($N2$) and $\approx 0.20$ dex ($O3N2$). We systematically investigate the influence of the AGN spectral index $(α_{ox})$, narrow-line region (NLR) gas density $(N_{\rm e})$, the characteristic peak temperature of the Big Blue Bump $(T_{\rm BB})$, and Lx. We find a strong, opposing secondary dependence on Lx for both indices. We demonstrate that neglecting this parameter overlooks systematic offsets intrinsic to the diagnostics, leading to metallicity errors of up to $\sim 1.0$ dex, particularly for the least and most luminous sources. This framework offers a more precise characterization of chemical enrichment in the NLRs of AGNs by leveraging their intrinsic X-ray emission to mitigate these systematic biases.

We demonstrate that linear and nonlinear Thouless pumping can be realized in two-component elongated Bose-Einstein condensates using helicoidal spin-orbit coupling that slides with respect to a static optical lattice, identical for both spinor components. Stable quantized transport is found for solitons in semi-infinite and finite gaps, within certain intervals of chemical potentials and numbers of atoms. In the semi-infinite gap, the transport is arrested for solitons with sufficiently large number of atoms. We elucidate the important role of Zeeman splitting in the control of quantized transport, which disappears when the longitudinal component of the Zeeman field is removed.