Nonequilibrium response theory is a fundamental framework for understanding how physical systems respond to perturbations. Recently, a mutual linearity has been discovered for Markov jump processes using linear algebra analysis. This mutual linearity states that two observables are linearly dependent on each other in the long-time limit when the transition rate of a single edge is altered. It has also been extended to non-stationary cases for current observables. In this work, we provide a trajectory-based derivation of mutual linearity utilizing the trajectory-level linear response theory. The trajectory approach allows us to generalize the mutual linearity to non-stationary relaxation dynamics for state observables and counting observables. Our results shed light on the fundamental response properties far from equilibrium and the trajectory-level origin of mutual linearity. Our trajectory-based approach makes it possible to generalize the mutual linearity to a broader class of systems, including diffusion processes and open quantum systems.

We study, to our knowledge, the first tractable multistage ex-ante distributionally robust regret optimization (DRRO) formulation for stochastic control. We consider finite-horizon LQR under common stage-law ambiguity: disturbances are independent across time but share an unknown stage law whose mean and covariance lie in a Gelbrich ball around nominal parameters. Unlike the single-stage quadratic case, the nominal certainty-equivalent (CE) controller is generally not regret-optimal, because reuse of the stage law makes past disturbances informative for future decisions. Despite the general NP-hardness of DRRO, we show that over linear disturbance-feedback policies the resulting multistage DRRO-LQR problem admits an exact semidefinite programming reformulation. The optimal controller is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction. We also characterize worst-case distributions and show that those for the DRRO-optimal policy are nonunique. Numerical results show that, relative to the corresponding DRO controller under the same ambiguity set, DRRO is often substantially less conservative while preserving the intended regret guarantee, and that its correction coefficients empirically approach the certainty-equivalent feedforward coefficient.

Motivated by the continued interest in Fermi-surface reconstruction without symmetry breaking, we present an analytically tractable microscopic model of a fractionalized Fermi liquid (FL$^*$) on a square lattice and discuss its potential relevance to the cuprates. As in ancilla-qubit constructions, the model is related to Kondo lattice systems, but in this case, the conduction electrons interact with a $\mathbb{Z}_2$ spin liquid of the Yao--Lee type, with a Majorana Fermi surface. The associated $\mathbb Z_2$ gauge theory is static so that the model can be analytically solved to leading-logarithic accuracy. There are two phases: one in which the fractionalized fermions of the spin liquid hybridize with conduction electrons to form a common Fermi surface violating the naive Luttinger count, and one in which they remain decoupled. We discuss the salient features of the small Fermi-surface phase, including analytically derived momentum dependent coherence factors responsible for the appearance of Fermi arcs à la Yang-Rice-Zhang. We further discuss the impact of quantum and thermal fluctuations, including a strong diamagnetic response and a logarithmically divergent Sommerfeld coefficient at the onset of the pseudogap.

The Peierls-Boltzmann transport equation (PBE), which governs non-equilibrium phonon transport, suffers from the curse of dimensionality due to its high-dimensional phase space including both real and modal spaces. We explore the use of matrix product states (MPS) for numerical simulation of the PBE. We show that an MPS configuration based on scattering events combined with a dimensionless form of the solution can drastically increase the locality of correlations between tensors in the MPS representation, enhancing its effectiveness in dimension reduction. We further examine the effects of index ordering in an MPS and find that the highest locality is achieved when tensor chains associated with both real and modal spaces are connected from the coarsest grid to each other in the center of the MPS. Using this optimal configuration and a solver inspired by the density matrix renormalization group, we solve the PBE discretized by a finite volume method (FVM). The solution is obtained for crystalline silicon across ballistic, quasi-ballistic, and diffusive transport regimes. An MPS truncated to the compression ratio of $10^{-3}$ suffices to reproduce reference solutions with high fidelity. The computational cost scales sublinearly with the number of grid points in both real and modal spaces, achieving roughly an order of magnitude reduction in computational time compared to the FVM with sparse matrix operation.

Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise. In this work, we ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics (QED), building on and extending earlier works that established a bridge between gauge systems, stabilizer codes, and quantum reference frames (QRFs). For Abelian gauge groups, we show that explicit recovery operations can be constructed using group-theoretical methods for error sets determined by both ideal and non-ideal QRFs. Applied to lattice QED, this yields two QECC structures: one in the pure-gauge sector and one including fermions. We construct a gauge-field QRF based on spanning trees of the lattice and a fermionic field QRF from the matter field, thereby making explicit how physical information is encoded. While the syndromes of gauge-violating errors associated with constraint measurements are generically degenerate, QRFs resolve this degeneracy and single out families of correctable errors. This establishes lattice QED as a QECC beyond the stabilizer setting and shows concretely how gauge symmetry provides an encoding structure that supports error correction.

We study the inflationary bispectrum generated by the tree-level exchange of a massive hidden-sector scalar during inflation. When the interaction between the inflaton and the hidden sector arises only from the leading boost-breaking operator of the Effective Field Theory (EFT) of inflation, the equilateral bispectrum for principal-series scalar exchange is known to be universally negative, independent of the sign of the coupling. We revisit this result within the full EFT operator basis. Using bootstrap methods, we construct the de Sitter-invariant seed four-point function and obtain the inflationary bispectrum via weight-shifting operators and a soft-limit procedure. While the equilateral bispectrum remains strictly negative when only the leading interaction is present, additional operators generate independent cubic structures whose contributions compete in the equilateral configuration. As a result, the sign of the bispectrum is no longer universal. We derive a critical ratio of interaction coefficients that separates regions of positive and negative equilateral bispectrum. We further study the effects of reduced sound speed $c_s<1$ and the exchange of multiple particles. In both cases, the critical ratio is modified, and for multi-particle exchange a positive equilateral bispectrum can arise even when the higher-order operator is subdominant. Our results show that the negativity of the equilateral bispectrum from massive exchange is not generic, but reflects a restricted operator structure in the EFT of inflation.

We describe a class of sharply o-minimal structures, called analytically generated structures, whose definable sets and their complexity filtration are determined by the collection of definable complex cells. We prove a polynomially effective parameterization theorem using real complex cells for real sets definable in such structures. Following Binyamini--Novikov, this allows us to establish a polynomially effective version of the Yomdin--Gromov lemma on C^r-smooth parameterizations of definable sets, which implies Wilkie's conjecture on polylogarithmic bounds for the amount of algebraic points of bounded height and degree in the transcendental part of a definable set. In addition, we obtain a polynomially effective preparation theorem for definable functions, similar to the subanalytic preparation theorems of Parusinski and of Lion--Rolin.

Deep spectroscopic samples can be used to improve photometric redshift (photo-$z$) estimates and reduce uncertainties on redshift distributions. Such improvements can increase the cosmological constraining power of large imaging-based experiments such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and mitigate what may be a limiting systematic effect. We present results from the ``DESI-Deep pilot'' program, which was designed to assess the capability of the Dark Energy Spectroscopic Instrument (DESI) on the 4m Mayall telescope to measure redshifts of galaxies as faint as expected lensing samples for early LSST data ($m_i \leq 24.5$). We find that DESI is remarkably efficient at this task, with redshift success rates comparable to the results of observations from 10m-class telescopes with only $\sim2\times$ longer integration time (rather than $\sim 8\times$ longer as would be expected from aperture-area scaling), while simultaneously achieving $\sim30$ times larger multiplexing. We also find that the signal-to-noise ratio of the spectra scales as expected for background-limited observations even for the longest exposure times ($\sim 7$ hours) and faintest targets in the program. These results demonstrate that DESI could provide the definitive redshift sample for the early years of LSST with a modest investment of observing time. Based upon the results of this program, we provide updated predictions for the time required to collect benchmark samples for photo-$z$ training and calibration using a variety of spectroscopic facilities. Finally, we describe a potential "DESI-Deep" survey designed to train and calibrate photo-$z$'s for imaging experiments, and provide forecasts of its impact on cosmological inference.

In an optical cavity, strong light--matter coupling between excitons and photons has been widely reported as a way to enhance energy delocalization through spatially extended polaritonic states. In contrast, leveraging cavity-mediated light--matter effects to promote the reciprocal phenomenon, namely \textit{energy localization}, remains largely underexplored. In the present work, we address this question by focusing on a special form of energy localization arising from nonlinear matter interactions: \textit{Quantum Self-Trapping} (QST). We employ a generalized Tavis--Cummings model to investigate the transport of vibrational excitons -- \textit{i.e., vibrons} -- between two anharmonic vibrational modes and examine their interplay with cavity photons. In the absence of a cavity, the arising of true and complete QST -- \textit{i.e.}, an infinite-lifetime localization -- is not possible due to the symmetry of the system. The energy transfer between the two modes still occurs, slowed down by the many-body interactions. Coupling the system to a single-mode cavity strongly alters this behavior, with two emerging regimes. First, at weak light--matter coupling, destructive interference between newly opened transition pathways suppresses energy exchange, leading to cavity-enhanced self-trapping. As the coupling strength increases, these interference effects evolve leading to cavity-assisted energy transfer, where we observe an acceleration of the vibrational energy flow. Most notably, we identify critical coupling strengths that separate both regimes in which the dynamics almost totally freeze, suggesting the arising of a ``stabilized'' light-induced~QST of many-vibron bound states. These results suggest that optical cavities can not only enhance transport but could also stabilize energy localization phenomena, providing a new route to control energy flow in quantum systems.

We prove that every complete finite index immersed CMC hypersurface is either minimal or compact, provided that the ambient six-dimensional manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. This answers affirmatively a question posed by do Carmo, for this class of ambient spaces, and extends known lower dimensional results. As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in the space forms of positive curvature in dimension six. More generally, we study the class of Riemannian manifolds with bounded curvature and obtain several partial results. In particular, we show that a complete, finite index CMC hypersurface immersed in the hyperbolic six-space with mean curvature vector of length greater than seven is necessarily compact.

This paper presents a theoretical convergence analysis for an opinion-action coevolution model that integrates the opinion updating rule of the Hegselmann-Krause model with a utility-based decision-making mechanism. The model is reformulated into an augmented state-space representation, where the state matrix induces a time-varying social interaction digraph. The convergence analysis is grounded on two existing theoretical findings that establish convergence for the Hegselmann-Krause type of models and containment control systems with multiple stationary leaders, respectively. Results indicate that, if the structure of the interaction digraph stabilizes within finite time, the model either converges to consensus, where all agents' opinions and actions reach an identical state, or exhibits clustering, where some opinion nodes act as stationary leaders while the remaining nodes approach the convex hull formed by the leaders. Numerical simulations are then provided to validate the theoretical results.

Two-neutron halo nuclei offer a fascinating probe into the behaviour of quantum few-body systems at the limits of binding. Although few nuclei have already been clearly identified, many of their properties remain poorly constrained. $^{22}$C, one of the heaviest, still lacks a precise identification of its static and dynamic properties, such as its mass and dipole strength in the continuum. One main difficulty is that properties of two-neutron halo nuclei are inferred from experimental data using a theoretical model. Therefore, accurately determining the characteristics of two-neutron halo nuclei requires an accurate theoretical model and careful quantification of the uncertainties. In this work, we examine $^{22}$C with a three-body model, seeing $^{22}$C as a $^{20}$C core and two halo neutrons, and quantify for the first time the uncertainties associated with the $^{20}$C-$n$ interaction using a Bayesian approach. We propagate these uncertainties to properties of bound and scattering states of $^{22}$C, as well as its dipole strength. The comparison of our prediction for the matter radius to experimentally-derived values suggests that $^{22}$C is bound by less than 0.35~MeV and is dominated by a $(s_{1/2})^2$ configuration. Our analysis of the dipole strength shows that final-state interaction needs to be included for an accurate description, the uncertainties on the strength function are about 50\% and are mostly influenced by uncertainties on the ground-state properties, and partial-wave occupation of $^{22}$C depends on the scattering length and the $d_{3/2}$ resonance energy of the $^{20}$C-$n$ unbound system. Such sensitivity of the dipole strength to the properties of both $^{21}$C and $^{22}$C properties motivates a precise measurement of the $^{22}$C dipole strength function, that will allow to precisely and accurately resolve the spectroscopy of these nuclei.

In this work, we investigate the effects of Lorentz symmetry violation on the absorption cross section and quasinormal modes of a rotating acoustic black hole in (2+1) dimensions. The absorption cross section was analyzed analytically, using the low and high frequency regimes, and numerically, through integration of the radial equation. The results showed that Lorentz violation increases the absorption cross section at all energy scales, with a contribution from the rotation parameter $B$ appearing even in the low frequency regime. For the quasinormal modes, we observed that symmetry breaking decreases the real part of the frequencies and increases the magnitude of the corresponding imaginary part, indicating a faster damping of the oscillations.

Suppose that a function $F$ is meromorphic in the domain $\mathbb H(-m) = \{ z : \mathrm{Im}\, z > -m(\mathrm{Re}\, z) \}$, where $m$ is an even, positive, and continuous function that does not increase on $\mathbb R_{\ge 0}$, and suppose that $F$ omits there three distinct values. Then $F$ is of bounded type in the upper half-plane (i.e., is represented there as a quotient of two bounded analytic functions), provided that the logarithmic integral of the function $m$ is convergent. On the other hand, if the logarithmic integral of $m$ diverges, there exists a function $F$ meromorphic in $\mathbb H(-m)$, that omits there three distinct values, and which is of unbounded type in the upper half-plane. This result is motivated by a century old question originating with Rolf Nevanlinna, which remains unsettled.

Modern task-oriented chatbots present GUI elements alongside natural-language dialogue, yet the agent's role has largely been limited to interpreting natural-language input as GUI actions and following a linear workflow. In preference-driven, multi-step tasks such as booking a flight or reserving a restaurant, earlier choices constrain later options and may force users to restart from scratch. User preferences serve as the key criteria for these decisions, yet existing agents do not systematically leverage them. We present MAESTRO, which extends the agent's role from execution to decision support. MAESTRO maintains a shared preference memory that extracts preferences from natural-language utterances with their strength, and provides two mechanisms. Preference-Grounded GUI Adaptation applies in-place operators (augment, sort, filter, and highlight) to the existing GUI according to preference strength, supporting within-stage comparison. Preference-Guided Workflow Navigation detects conflicts between preferences and available options, proposes backtracking, and records failed paths to avoid revisiting dead ends. We evaluated MAESTRO in a movie-booking Conversational Agent with GUI (CAG) through a within-subjects study with two conditions (Baseline vs. MAESTRO) and two modes (Text vs. Voice), with N = 33 participants.

AI-generated non-consensual intimate imagery (AIG-NCII) is an emerging social problem due to the advancement of AI tools. While recent incidents in middle and high schools have highlighted the urgency of this issue, there is limited understanding of what concrete supports schools need to effectively address AIG-NCII. To fill this gap, we conducted an interview study with 20 educators in the U.S. and investigated their attitudes, experiences, and practices related to AIG-NCII. Educators expressed concerns about both students' and their own vulnerability, as AIG-NCII may cause moral decline among students, while educators themselves could become victims. Nevertheless, existing practices in schools are limited, and they lack both training and systematic policies. Challenges such as a lack of resources, unclear legal boundaries, and limited knowledge of AI make implementation difficult. The findings of this paper contribute to interactive educational tool design, curriculum design, and policy-making, especially regarding the need for multi-stakeholder strategies to address issues surrounding AIG-NCII.

The computational cost of concurrent multiscale finite element methods is dominated by the repeated solution of microscopic representative volume element (RVE) problems at macroscopic quadrature points. In this work, we introduce a quantum-classical framework for multiscale finite element analysis (QAFE$^2$) that leverages quantum parallelism to fundamentally alter the scaling of RVE-based homogenisation. At the single-RVE level, the proposed quantum solver attains polylogarithmic complexity with respect to the microscopic discretisation size, yielding an exponential asymptotic speedup over the best available classical solvers. More importantly, QAFE$^2$ exploits quantum superposition and entanglement to evaluate, in a single quantum execution, the entire ensemble of RVE problems associated with all macroscopic quadrature points. This capability is a form of intrinsic quantum concurrency with no classical analogue. Numerical experiments on one- and two-dimensional model problems with known analytical solutions confirm the accuracy of the proposed formulation and verify the theoretical computational scaling and parallel performance.

Astrophysical black holes appear well-represented by the Kerr metric, but this metric has the philosophical problem of a ring-like curvature singularity. We show that a phenomenological correction to the Kerr metric known as the Kerr-Hayward metric can eliminate the curvature singularity while preserving in detail many features of polarized black hole images now testable by the Event Horizon Telescope (EHT). To establish this, we produce new general relativistic magnetohydrodynamics (GRMHD) simulations of a magnetized plasma in a Kerr-Hayward spacetime, then we extend the EHT analysis framework to perform polarized radiative transfer in this spacetime. We detail our methodology for implementing this modified spacetime into an open-source pipeline. From fluid quantities such as the magnetic flux parameter and jet efficiency, to image quantities such as the polarization pattern and the photon ring structure, our results for the Kerr-Hayward metric appear functionally indistinguishable from the Kerr metric. Our study finds that under certain conditions, the singularity-free correction to the Kerr metric can yield observables that are effectively indistinguishable in EHT measurements.

We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the true energy in one-electron reduced density matrix functional theory, regardless of the strength of the interparticle repulsion. Conversely, any functional violating these conditions will necessarily underestimate the true energy for certain systems. These exact constraints impose a stringent restriction on density matrix functional approximations, as many existing functionals-including the Hartree-Fock functional-appear to violate them. This mathematical formalism, therefore, can guide the development of new approximate functionals and numerical algorithms.

This work introduces coset Bombe codes, a novel class of multilevel coset codes that generalize polar codes to dense lattice structures. By leveraging multilevel coding with non-binary codes designed for the lattice modulations and making use of Voronoi shaping, Bombe codes integrate the geometric strengths of dense lattices such as $D_4$ with the capacity-approaching properties of polar codes. Experimental results in additive white Gaussian noise (AWGN) channels demonstrate that coset Bombe codes significantly outperform both BICM and MLC state-of-the-art schemes on 16-QAM. The proposed scheme simulated on AWGN achieves up to 0.8 dB of gain and reduces block size latency by half while maintaining superior bit and block error rate (BER/BLER) performance on codewords of 256 and 1024 bits.

We consider a sequence of random Hamiltonians $H_n(h,σ)=\sum^n_{i=1}h_i(σ_i-m)$, and study the asymptotic ($n\to \infty$) distribution of the energy levels $(H_n(h,σ))_{σ\in \{-1,1\}^n}$, where $h_1,h_2,\cdots$ are i.i.d. random variables. We show that, when $e^{O(n)}$ configurations are sampled at random, the corresponding collection of energy levels converges in distribution to a Poisson point process with exponential intensity measure. This establishes the Random Energy Model (REM) universality for the present model. Our results strengthen earlier works on local REM universality by characterizing the distribution of $O(1)-$order fluctuations of $H_n$. In addition, we improve upon the REM universality by dilution studied by Ben Arous, Gayrard, Kuptsov by allowing an exponentially large number $e^{O(n)}$ of sampled configurations, instead of $e^{o(\sqrt{n})}$. Finally, we derive the asymptotic distribution of the Gibbs weight.

The interaction between cavitation bubbles and surrounding droplets plays a central role in applications such as surface cleaning, ultrasonic emulsification, and therapeutic delivery. These processes depend on bubble-driven microjets that drive the deformation and breakup of the droplets, which are significantly influenced by geometric confinements. Here, we investigate the hydrodynamic interaction between cavitation bubbles and oil droplets within a thin water layer considering the coupling confinements of a free surface and a rigid wall. We reveal two distinct regimes of droplet response to cavitation bubble collapse: the rupture regime, where oil droplets fragment into smaller droplets, and the no-rupture regime, where the droplet remains intact. By deriving a non-dimensional Kelvin impulse to represent the momentum of the bubble-induced jet, we establish a scaling law that correlates the criterion for droplet rupture to a characteristic Weber number and the bubble-to-droplet size ratio for the first time. This framework delineates the rupture boundary and even extends to predict the rupture of particle-laden droplets driven by cavitation bubbles. Our findings reveal the hydrodynamic principles underlying the cavitation bubble-driven droplet rupture and provide predictive criteria for controlling performance in engineering and biomedical systems involving cavitation bubble dynamics.

We revisit conformal time $η$ in a spatially flat Friedmann--Robertson--Walker universe and use a $1+1$-dimensional setting as a technically transparent pedagogical arena. Our purpose is to clarify the relation among cosmic time $t$, conformal time $η$, and the scale factor $a(t)$, and then to follow how this relation governs the geodesics of freely moving particles and the curvature of the corresponding manifold. The radiation-dominated, matter-dominated, and exact vacuum-only de Sitter cases are treated separately, because each of them produces a distinct conformal-time dependence and therefore a distinct geodesic structure. We then write the affine-parameter formalism in a form that is genuinely general for any spatially flat conformal metric, and we record the straightforward extension to the spatially flat $3+1$ case. The presentation remains elementary in spirit, but the notation, the curvature formulas, and the de Sitter interpretation are kept explicit.

We prove a Kaufman-type exceptional set estimate for sets in $\mathbb{R}^n$ that have optimal oracles, a class of sets that strictly contains the analytic sets and sets with equal Hausdorff and packing dimension. As a consequence, we generalize the conditions under which Marstrand's projection theorem for $k$-planes is known to hold. Our proofs use effective methods, especially Kolmogorov complexity, and along the way, we introduce several new tools for studying the information content of elements of the Grassmannian.

We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature fluctuations in a single-plaquette model of quantum gravity, derivation of the Kaluza-Klein ansatz as a consequence of quantum spacetime, exactly conserved Noether charges from variational calculus on a lattice, and a new theory of classical and quantum geodesics. The latter leads to a theory of generally covariant quantum mechanics applicable in General Relativity with intriguing first results for the case of a black-hole. We discuss several open problems past and present, and how they might be addressed going forward. New results include a phase transition for Euclidean quantum gravity on a 4-pointed star.

In this paper, we study four-strategy conservative replicator dynamics induced by constant payoff matrices. We establish necessary and sufficient conditions for permanence to occur by associating the payoff matrix with its digraph, revealing exactly five distinct digraph classes governing the global behavior. We further show that, whenever the dynamics is permanent, every non-equilibrium trajectory in the relative interior of the simplex is a Lyapunov-stable periodic orbit. Together with the classification of the boundary phase portraits, these results provide a complete characterization of the global dynamics in the four-strategy case with permanence.

Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a sufficient basis for a conclusion. Across jurisdictions, current standards and practice manuals acknowledge such extensions, while the statistical design of sequential audit procedures has not been fully explored. This study formulates audit sampling with additional, sequentially collected items as a sequential testing problem for a finite population under sampling without replacement. We define null and alternative hypotheses in terms of a tolerable deviation rate, specify stopping and decision rules, and formulate exact sequential boundary conditions in terms of finite-population error probabilities. For practical implementation, we calibrate those boundaries by Monte Carlo simulation at least-favorable deviation rates. The exact design yields ex ante control of decision error probabilities, and the simulation-based implementation approximates that design while allowing the computation of expected stopping times. The framework is most naturally suited to attribute auditing and deviation-rate auditing, especially tests of controls, and it can be extended to one-sided, two-stage, and truncated designs.

We propose a neural-enhanced weak Galerkin (WG) finite element method for second-order elliptic problems with low-regularity solutions. The method augments the classical WG approximation space with neural network functions constructed via a residual-driven Galerkin enrichment procedure. This approach preserves the variational structure, symmetry, and stability of the WG formulation while enhancing its ability to approximate non-smooth and singular solution components. We establish a quasi-optimal error estimate in a discrete WG energy norm, incorporating both projection and consistency errors. In particular, the method retains optimal convergence rates for smooth solutions. For problems admitting a regular--singular decomposition, we further show that the neural enrichment effectively captures the singular component, yielding improved accuracy over standard WG methods.

$β$-Fe$_2$PO$_5$ is an emerging room-temperature d-wave altermagnet featuring quasi-one-dimensional crystal and magnetic structures, orthogonal transport channels for opposite spins, and large band spin splitting, which is a promising material for next-generation spintronics and magnonics. However, its crystal and electronic structures remain inconclusive. Here, joint experimental and theoretical studies confirm and explain the appearance of its monoclinic structure and semiconducting band gap. We discover that an electronic instability appears in the tetragonal metallic state as the joint effect of density functional theory and Hubbard U correction (DFT+U) and results in a charge disproportionation, which in turn stabilizes the monoclinic distortion with narrow gap formation. The successful capture of this effect within DFT+U requires accounting for the relevant symmetry-breaking energy-lowering channels -- charge disproportionation and structural distortion; otherwise, tetragonal-symmetry-constrained calculations yield only a metallic state. Fe$_2$PO$_5$ is thus best described as a correlation- and hybridization-assisted, distortion-coupled, charge-disproportionated semiconductor. It represents a rare room-temperature semiconducting d-wave altermagnet. It also provides a rare platform for studying the coexistence of altermagnetism and charge density wave in quasi-one-dimensional systems.

Nonlinear Four-wave mixing processes are a powerful technique to unravel ultrafast dynamics in solid-state systems. Here, we employ attosecond four-wave mixing spectroscopy with one extreme ultraviolet (XUV) pump and two independently delayed, noncollinear near-infrared (NIR) probes to resolve the ultrafast decoherence of both dipole-allowed and dipole-forbidden core excitons at the Na+ L2,3 edge in sodium fluoride (NaF). The decoherence times of the core excitons are observed to be much faster than the 8 fs limit of the instrument response time, which is attributed to strong exciton-phonon coupling. Furthermore, polarization control of the NIR probes (Perpendicular and parallel polarizations) reveals that the bright core excitons exhibit s-like orbital angular momentum, while dark core excitons, reached by two-photon excitation, exhibit p-like angular momentum.