We identify, for a general physically realizable Mueller transformation, the only intrinsic geometricphase structure that can be assigned to it in an invariant manner: the retarding part of the characteristic pure component selected by the characteristic decomposition, which defines a canonical holonomic content. A Mueller matrix does not, in general, determine a unique observed interferometric (Pancharatnam) geometric phase, since the latter depends on the specific physical realization of the transformation and on the interferometric readout. The remaining characteristic layers may modify the measured complex visibility, and even its observed argument through convex averaging, but they do not define a unique geometric holonomy of their own. We further establish the quantum analogue for open two-level dynamics within the Choi representation.

Collective decision-making requires aggregating multiple noisy information channels about an unknown state of the world. Classical epistemic justifications of majority rule rely on homogeneity assumptions often violated when individual competences are heterogeneous. This paper studies endogenous epistemic weighting in binary collective decisions. It introduces the Epistemic Shared-Choice Mechanism (ESCM), a lightweight and auditable procedure that generates bounded, issue-specific voting weights from short informational assessments. Unlike likelihood-optimal rules, ESCM does not require ex ante knowledge of individual competences, but infers them endogenously while bounding individual influence. Using a central limit approximation under general regularity conditions, the paper establishes analytically that bounded competence-sensitive monotone weighting strictly increases the mean quality of the aggregate signal whenever competence is heterogeneous. Numerical comparisons under Beta-distributed and segmented mixture competence environments show that these mean gains are associated with higher signal-to-noise ratios and large-sample accuracy relative to unweighted majority rule.

GitHub and GitLab are widely used collaborative platforms whose issue-tracking systems contain large volumes of unstructured text, including logs, code snippets, and configuration examples. This creates a significant risk of accidental secret exposure, such as API keys and credentials, yet these platforms provide no mechanism to warn users before submission. We present \textsc{IssueGuard}, a tool for real-time detection and prevention of secret leaks in issue reports. Implemented as a Chrome extension, \textsc{IssueGuard} analyzes text as users type and combines regex-based candidate extraction with a fine-tuned CodeBERT model for contextual classification. This approach effectively separates real secrets from false positives and achieves an F1-score of 92.70\% on a benchmark dataset, outperforming traditional regex-based scanners. \textsc{IssueGuard} integrates directly into the web interface and continuously analyzes the issue editor, presenting clear visual warnings to help users avoid submitting sensitive data. The source code is publicly available at \href{https://github.com/disa-lab/IssueGuard}{https://github.com/disa-lab/IssueGuard} , and a demonstration video is available at \href{https://youtu.be/kvbWA8rr9cU}{https://youtu.be/kvbWA8rr9cU} .

Collective excitations of Fractional Quantum Hall (FQH) liquids at long wavelengths are thought to be of a generally covariant geometric nature, governed by area-preserving diffeomorphisms ($\mathrm{SDiff}$). But current analyses rely solely on the corresponding perturbative $w_\infty$ Lie algebra. We argue this is insufficient: We identify a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory which carries unitary $\mathrm{SDiff}$ equivariance. But this turns out to be non-differentiable, suggesting underappreciated subtleties when the usual Hilbert space truncation is removed.

In the $Λ$CDM paradigm, stellar halos form through the accretion and disruption of satellite galaxies. We introduce new semi-analytic modeling within the SatGen framework to track the ex-situ stellar components of Milky Way--like galaxies across large ensembles of merger trees, enabling a statistical study of the stochastic nature of galaxy assembly. We find that accreted stellar halos are typically built by only a few progenitors and are highly sensitive to the fate of the most massive satellite, producing order-of-magnitude variations in accreted stellar halo mass even at fixed host halo mass. Different stellar components trace distinct phases of host halo growth: central and accreted stellar mass correlate most strongly with early assembly, while surviving satellites trace more recent accretion. Finally, using Random Forest Regression, we quantify how well observable galaxy properties can recover halo assembly histories, providing a framework for interpreting upcoming low-surface-brightness observations of stellar halos.

The $μ$-$e$ conversion process is one of the most powerful ways to test lepton-flavor-violating (LFV) interactions involving charged leptons. The standard model with massive neutrinos predicts an extremely low rate for $μ$-$e$ conversion, making this process an excellent probe for testing LFV arising from new physics. Among many theoretical models that can induce LFV, the Supersymmetric model with R-parity violating interactions is one of the most studied for $μ$-$e$ conversion. In this work, we revisit trilinear R-parity violating interactions for $μ$-$e$ conversion, considering renormalization group (RG) running effects from high to low energy scales. The $μ$-$e$ conversion, $μ\to e γ$, and $μ\to eee$ experimental data are compared to give upper limits on the relevant 15 combinations of the trilinear $λ^{\prime}$ couplings and 6 combinations of the $λ$ couplings, certain of which are underexplored in previous studies. We find that RG running effects influence the limits by no more than 30\% in most cases, but can improve constraints by $\sim$80\% in certain combinations, which cannot be neglected. In the near future, COMET and Mu2e are expected to begin data-taking and aim to provide the most stringent constraints on $μ$-$e$ conversion. These next-generation $μ$-$e$ experiments have the ability to give much more comprehensive examinations on most trilinear coupling combinations than the $μ\to eγ$ and $μ\to 3e$ decay experiments. The $μ$-$e$ experiments will not only deepen our understanding of LFV but also provide a crucial way to examine the underlying new physics contributions.

We present a systematic study of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in MnBi$_2$Te$_4$ films under both dark and illuminated conditions. In the dark, the intrinsic magnetism of MnBi$_2$Te$_4$ is shown to yield a stronger anisotropic RKKY spin model compared to nonmagnetic topological insulators, providing a clear signature for differentiating these systems. Furthermore, key band properties -- such as energy gap, band degeneracy/splitting, and topological deformations of the Fermi surface -- imprint distinct signatures on the RKKY interaction, enabling clear discrimination between axion insulators (AI) and quantum anomalous Hall (QAH) insulators in even- and odd-septuple-layer (SL) films. This discrimination manifests in multiple ways: through the Fermi-energy dependence or spatial oscillations of the interaction for impurities on the same surface, or via the presence versus absence of spin-frustrated terms for those on different surfaces. Under off-resonant circularly polarized light, additional phase-transition-related fingerprints also emerge to distinguish these two phases, such as sign reversals of spin-frustrated terms in even-SL films versus chirality-selective double-dip structures of collinear RKKY components in odd-SL films. Overall, this work establishes RKKY interactions as a sensitive magnetic probe for distinguishing between AI phase (even-SL) and QAH phase (odd-SL), thereby complementing conventional electrical measurements while providing new insights into the influence of intrinsic magnetism on the surface-state band structure.

We prove that $\mathrm{deg}(f) \leq \widetilde{O}(\mathrm{rdeg}(f)^3)$ for every Boolean function $f$, where $\mathrm{deg}(f)$ is the degree of $f$ and $\mathrm{rdeg}(f)$ is the rational degree of $f$. This resolves the second of the three open problems stated by Nisan and Szegedy, and attributed to Fortnow, in 1994.

This work presents Bio-RV, a compact and resource-efficient RISC-V processor intended for biomedical control applications, such as accelerator-based biomedical SoCs and implantable pacemaker systems. The proposed Bio-RV is a multi-cycle RV32I core that provides explicit execution control and external instruction loading with capabilities that enable controlled firmware deployment, ASIC bring-up, and post-silicon testing. In addition to coordinating accelerator configuration and data transmission in heterogeneous systems, Bio-RV is designed to function as a lightweight host controller, handling interfaces with pacing, sensing, electrogram (EGM), telemetry, and battery management modules. With 708 LUTs and 235 flip-flops on FPGA prototypes, Bio-RV, implemented in a 180 nm CMOS technology, operate at 50 MHz and feature a compact hardware footprint. According to post-layout results, the proposed architectural decisions align with minimal energy use. Ultimately, Bio-RV prioritises deterministic execution, minimal hardware complexity, and integration flexibility over peak computing speed to meet the demands of ultra-low-power, safety-critical biomedical systems.

The NANOGrav 15-year stochastic gravitational wave background (SGWB) amplitude $A_{\rm yr} \approx 2.4 \times 10^{-15}$ lies at the upper edge of population synthesis predictions for supermassive black hole binaries (SMBHBs), motivating exploration of additional cosmological sources. We present a phenomenological framework based on an $\text{SU}(3)_D$ gauge theory that can simultaneously accommodate the gravitational wave signal and resolve small-scale structure anomalies via Self-Interacting Dark Matter (SIDM). The dark matter candidate is a heavy dark baryon $χ= QQQ$ with mass $m_χ\approx 40$~GeV, which self-interacts through a light pseudo-dilaton $d$ $m_d \approx 20$--$50$~MeV as a pseudo-Goldstone boson of approximate scale invariance arising in near-conformal gauge theories with $N_f \sim 6$--$8$ light flavors. A first-order phase transition at the MeV scale, enabled by walking dynamics near the conformal window, produces gravitational waves in the PTA band. For representative parameters $T_n \approx 5$--$6$~MeV, $α\sim 500$--$1000$, $β/H_* \sim 30$--$50$, the model provides a fit to NANOGrav data comparable to SMBHB while naturally connecting the gravitational wave amplitude to the dark matter relic density through entropy dilution $D \approx α^{3/4}$. We present explicit calculations of the bounce action, bubble wall velocity, and $ΔN_{\rm eff}$, demonstrating that the benchmark parameters are theoretically consistent and cosmologically safe ($ΔN_{\rm eff} \lesssim 0.1$ for $m_π> 2m_d$). The distinctive spectral shape ($f^3 \to f^{-4}$) provides a robust prediction testable with future PTAs.

Security operation centers (SOCs) often produce analysis reports on security incidents, and large language models (LLMs) will likely be used for this task in the near future. We postulate that a better understanding of how veteran analysts evaluate reports, including their feedback, can help produce analysis reports in SOCs. In this paper, we aim to leverage LLMs for analysis reports. To this end, we first construct a Analyst-wise checklist to reflect SOC practitioners' opinions for analysis report evaluation through literature review and user study with SOC practitioners. Next, we design a novel LLM-based conceptual framework, named MESSALA, by further introducing two new techniques, granularization guideline and multi-perspective evaluation. MESSALA can maximize report evaluation and provide feedback on veteran SOC practitioners' perceptions. When we conduct extensive experiments with MESSALA, the evaluation results by MESSALA are the closest to those of veteran SOC practitioners compared with the existing LLM-based methods. We then show two key insights. We also conduct qualitative analysis with MESSALA, and then identify that MESSALA can provide actionable items that are necessary for improving analysis reports.

For any fixed irrational frequency and trigonometric-polynomial potential, we show that every type I energy with positive Lyapunov exponent that satisfies the gap-labelling condition is a boundary of an open spectral gap. As a corollary, for the almost-Mathieu operator in the supercritical regime the "all spectral gaps are open" property is robust under a small trigonometric-polynomial perturbation at any irrational frequency. The proof introduces a geometric, all-frequency approach built from three ingredients: (i) the projective action on the Lagrangian Grassmannian and an associated fibred rotation number, (ii) monotonicity of one-parameter families of (Hermitian) symplectic cocycles, and (iii) a partially hyperbolic splitting with a two-dimensional center together with a global symplectification (holonomy-driven parallel transport). This provides a partial resolution to the stability of the Dry Ten Martini Problem in the supercritical regime, and answers a question by M. Shamis regarding the survival of periodic gaps.

In this article, we generalize the following problem, which is called the rational angle bisection problem, to the $n$-dimensional space $k^n$ over a subfield $k$ of $\mathbb R$: in the coordinate plane, for which rational numbers $a$ and $b$ are the slopes of the angle bisectors between the two lines with slopes $a$ and $b$ rational? First, we provide several characterizations of when the angle bisectors between two lines with direction vectors in $k^n$ have direction vectors in $k^n.$ To find solutions to the problem in the case when $k = \mathbb Q,$ we derive a formula for the integral solutions of $x_1{}^2+\dots +x_n{}^2 = dx_{n+1}{}^2,$ which is a generalization of negative Pell's equation $x^2-dy^2 = -1,$ where $d$ is a square-free positive integer. Second, by applying the above characterizations, we establish a necessary and sufficient condition for the incenter of a given $n$-simplex with $k$-rational vertices to be $k$-rational. In the coordinate plane, we prove that every triangle with $k$-rational vertices and incenter can be obtained by scaling a triangle with $k$-rational side lengths and area, which is a generalization of a Heronian triangle. We also discuss certain fundamental properties of a few centers of a given triangle with $k$-rational vertices.

Valleytronics is a rapidly advancing field that explores the use of the valley degree of freedom in electronic systems to encode and process information. It relies on electronic states with spin valley locking, first predicted and observed in monolayer transition metal dichalcogenides such as MoS2. However, very few bulk materials have been reported to host spin valley locked electronic states. In this work, we present experimental evidence for a predicted, unique spin valley locked electronic state generated by Bi zigzag chains in the layered compound BaMnBi2. We observe remarkable quantum transport properties in this material, including a stacked quantum Hall effect (QHE) and a nonlinear Hall effect (NLHE). From the analysis of the QHE, we identify a spin valley degeneracy of four, while the NLHE provides supporting evidence for the anticipated valley contrasted Berry curvature, a typical signature of a spin valley locked state. This spin valley locked state contrasts with that observed in the sister compound BaMnSb2, where the degeneracy is two. This difference arises from significant variations in their orthorhombic crystal structures and spin orbit coupling. These findings establish a new platform for exploring coupled spin valley physics in bulk materials and highlight its potential for valleytronic device applications.

Optical skyrmions are topological structures of light whose defining property, the skyrmion number, is robust against perturbations. This makes them attractive for applications in quantum information storage, where resilience to decoherence is paramount. However, their preservation during coherent storage remains unexplored. We report the first experimental demonstration of storing and retrieving optical skyrmions in a cold $^{87}$Rb vapor using a dual-path electromagnetically induced transparency memory. Crucially, we show that the skyrmion number remains invariant for storage times up to several microseconds, even when subjected to imbalanced loss between the two paths and substantial perturbations in control beam power. Our work demonstrates the survival of a non-trivial topological invariant in a quantum memory, marking a significant step towards topologically protected photonic technologies.

This paper is the second in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belonging to an arbitrary ground field which is large enough. In this part we solve the linear preserver problem for the Cullis' determinant defined on the spaces of matrices of size $n\times k$ with $k \ge 4,\; n \ge k + 2$ and $n + k$ is odd. In comparison with the case when $n + k$ is even, in this case linear maps preserving the Cullis' determinant could be singular and are represented as a sum of two linear maps: first is two-sided matrix multiplication and second is any linear map whose image consists of matrices, all rows of which are equal.

In trapped Bose-Einstein condensates, interaction quenches which are abrupt changes of the interaction strength typically implemented via Feshbach tuning, are a practical and widely used protocol to address far-from-equilibrium collective modes. Using both numerical Gross Pitaevskii and analytical schemes we study these interaction-quench-induced collective modes in a harmonically trapped two-dimensional Bose--Einstein condensate contrasting the behavior found at low and high energies. In the low-lying regime, we characterize realistic circumstances in which there is a breakdown of the expected scale invariance so that the collective excitations follow hydrodynamic theory instead of the predictions given by SO(2,1) conformal symmetry. In the high energy regime, we focus on important trap effects associated with acoustic oscillations which have been of interest experimentally. This comprehensive analysis of the collective excitations in trapped two-dimensional Bose-Einstein condensates is experimentally accessible. Through their frequencies and damping, this reflects an important built-in spectroscopy of such many-body states.

Neuromorphic engineering makes use of mixed-signal analog and digital circuits to directly emulate the computational principles of biological brains. Such electronic systems offer a high degree of adaptability, robustness, and energy efficiency across a wide range of tasks, from edge computing to robotics. Within this context, we investigate a key feature of biological neurons: their ability to carry out robust and reliable computation by adapting their input responses and spiking patterns to context through neuromodulation. Achieving analogous levels of robustness and adaptation in neuromorphic circuits through modulatory mechanisms is a largely unexplored path. We present a novel current-mode neuron design that supports robust neuromodulation with minimal model complexity, compatible with standard CMOS technologies. We first introduce a mathematical model of the circuit and provide tools to analyze and tune the neuron behavior; we then demonstrate both theoretically and experimentally the biologically plausible neuromodulation adaptation capabilities of the circuit over a wide range of parameters. All theoretical predictions were verified in experiments on a low-power 180 nm CMOS implementation of the proposed neuron circuit. Due to the analog underlying feedback structure, the proposed adaptive neuromodulable neuron exhibits a high degree of robustness, flexibility, and scalability across operating ranges of currents and temperatures, making it a perfect candidate for real-world neuromorphic applications.

In this paper, we consider the exponential Diophantine equation \( (2^k-1)(b^k-1)=y^q \) with $k\ge 2$, odd integer $b$ and an odd prime exponent $q$ and obtain effective upper bounds for $q$ in terms of $b$. In particular, we show that $q\le \log_2(b+1)$ holds apart from a finite, explicitly determined set of exceptional pairs $(b,q)$ when $3\le b<10^6$. As an application, we prove that the related equation \( (2^k-1)(b^k-1)=x^n, \) has no positive integer solution $(k,x,n)$ for several specific odd values of $b$, including $b\in\{5,7,11,13,21,23,27,29\}$.

We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers of the different ways of producing extended formulations that replace a bounded general integer variable by a linear combination of a set of auxiliary binary variables linked by additional linear constraints. We show that MILP solvers perform very differently depending on which extended formulations is used and we interpret that different performance through the lens of cutting planes generation. Finally, we discuss a simple family of mixed-integer rounding inequalities that especially benefit from the reformulation, and we show its benefit within different MIP solvers. This provides methodological and practical guidelines for the use of those extended formulations in MIP and, to the best of our knowledge, this is the first extensive computational analysis of the topic. All our data and tables are publicly available at https://github.com/anton-derkach1/binarizations.

Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding the controlled time evolution operator of translationally invariant, local Hamiltonians into a quantum circuit. It achieves a near-optimal in time $t$ scaling for circuit depth $\mathcal{O}(t \text{ polylog}(t N/ε))$, while reducing the control overhead from a multiplicative to an additive factor. We report that this compression protocol enables the implementation of Iterative Quantum Phase Estimation with as few as 414 CNOT gates for a frustrated quantum spin system on a 6$\times$6 triangular lattice and delivers ground state energy errors below 1% (with $\pm$ 1.5% variation, calculated with a hardware noise aware pipeline) on a 4$\times$4 triangular lattice using the noisy emulator of the Quantinuum H2 trapped ion device.

The first four-dimensional amplitude analysis of the $B^{+} \to ψ(2S) K_{\text{S}}^{0} π^{+}$ decay is performed with proton-proton collision data collected by the LHCb experiment at $\sqrt{s} = 13~\rm{TeV}$, corresponding to an integrated luminosity of $5.4~\rm{fb^{-1}}$. The data cannot be fully explained by $B^{+} \to ψ(2S) K^{*+}$ contributions alone. A significantly better description of the data is obtained by adding a $T_{c\bar{c}}^{+}$ contribution decaying to $ψ(2S)π^{+}$. The properties of the $T_{c\bar{c}}^{+}$ structure are consistent with the exotic state $T_{c\bar{c}1}(4430)^{+}$ reported in the isospin-related $\bar{B}^{0} \to ψ(2S) K^{-} π^{+}$ decay. Effects of a possible $T_{c\bar{c}1}(4430)^{+} \to \bar{D}_{1}^{*}(2600)^{0} D^{+}$ decay mode on the $T_{c\bar{c}1}(4430)^{+} \to ψ(2S)π^{+}$ mass distribution are investigated through a Flatté parametrization, providing constraints on the relative decay strength. A description of the $T_{c\bar{c}1}(4430)^{+}$ structure using the triangle singularity mechanism is studied and also found to be consistent with the data.

We provide an elementary pedagogical introduction to some basic concepts and techniques of soft (or Sudakov) resummation, specifically in QCD, paying particular attention to simple but useful tricks of the trade. We briefly review collinear (Altarelli-Parisi) and infrared (eikonal)factorization, cancellation of infrared singularities and factorization of mass singularities. We recall basic concepts on renormalization group invariance and the solution of renormalization group equations. We then show how threshold resummation can be derived from a renormalization group argument following from the cancellation of infrared singularities. We discuss various equivalent forms of the resummed result, and we briefly present transverse momentum resummation.

The functional renormalization group (fRG) is acknowledged as a powerful tool in quantum many-body physics and beyond. On the technical side, conventional implementations of the fRG rely on regulators for bare propagators only. Starting from Schwinger--Dyson and Bethe--Salpeter equations, we develop here an fRG formulation where both bare propagators and bare interactions can be dressed with regulators. The approach thus obtained is an extension of the multiloop fRG recently introduced for many-fermion systems. Using the single-boson exchange decomposition, we show that the underlying flow equations are simply interpreted as adding a regulator to the bosonic propagator and that such an extension scarcely changes the original structure of the flow equations. Overall, we provide a framework for implementing approaches that cannot be realized with conventional fRG methods, such as temperature flows for models with retarded interactions. For concrete applications, we analyze the loop convergence of our scheme against conventional cutoff schemes for the Anderson impurity model. Finally, we devise a new temperature-flow scheme that implements a cutoff in both the propagator and the bare interaction, and demonstrate its validity on a model of an Anderson impurity coupled to a phonon.

We study a two-player dynamic Stackelberg game where the follower's intention is unknown to the leader. Classical formulations of the Stackelberg equilibrium (SE) assume that the follower's best response (BR) function is known to the leader. However, this is not always true in practice. We study a setting in which the leader receives updated beliefs about the follower BR before the end of the game, such that the update prompts the leader and subsequently the follower to re-optimize their strategies. We characterize the optimality guarantees of the SE solutions under this belief update for both open loop and feedback information structures. Interestingly, we prove that in general, assuming an incorrect follower's BR may lead to a lower leader cost over the entire game than knowing the true follower's BR. We support these results with numerical examples in a linear quadratic (LQ) Stackelberg game, and use Monte Carlo simulations to show that the instances of incorrect BR achieving lower leader costs are non-trivial in collision avoidance LQ Stackelberg games.

We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed method from the observation that FOMs applied to QPs typically consist of piecewise-affine operators. We describe our Krylov subspace acceleration scheme, contrasting it with existing Anderson acceleration schemes and showing that it largely avoids the latter's well-known ill-conditioning issues in regions of slow convergence. We demonstrate the performance of our scheme relative to Anderson acceleration using standard collections of problems from model predictive control and statistical learning applications. We show that our method is faster than Anderson acceleration across the board in terms of iteration count, and in many cases in computation time, particularly for optimal control and for problems solved to high accuracy.

We establish that the dioperad $Y^{(n)}$, encoding bialgebras with a product of degree zero, a coproduct of degree $(1-n)$ and a rank three cyclic tensor, which satisfy a deformed version of the balanced infinitesimal bialgebra condition, is Koszul. This result is established by studying specific subcomplexes of the assocoipahedra of Poirier and Tradler. These subcomplexes are related to a certain type of meromorphic quadratic differential on $\mathbb{CP}^1$, which we call cloven Strebel differentials. Using that geometric interpretation, we can control the topology of the relevant subcomplexes and deduce the vanishing of higher cohomology of the corresponding dioperadic bar complexes.

We present a single-photon transduction scheme using 4-wave-mixing and quantum scattering in planar, cooperative Rydberg arrays that is both efficient and highly directional and may allow for terahertz-to-optical transduction. In the 4-wave-mixing scheme, two lasers drive the system, coherently trapping the system in a dark ground-state and coupling a signal transition, that may be in the terahertz, to an idler transition that may be in the optical. The photon-mediated dipole-dipole interactions between emitters generate collective super-/subradiant dipolar modes, both on the signal and the idler transition. As the array is cooperative with respect to the signal transition, an incident signal photon can efficiently couple into the array and is admixed into dipolar idler modes by the drive. Under specific criticality conditions, this admixture is into a superradiant idler mode which primarily decays into a specific, highly directional optical photon that propagates within the array plane. Outside of the array, this photon may then be coupled into existing quantum devices for further processing. Using a scattering-operator formalism we derive resonance and criticality conditions that govern this two-step process and obtain analytic transduction efficiencies. For infinite lattices, we predict transduction efficiencies into specific spatial directions of up to 50%, while the overall, undirected transduction efficiency can be higher. An analysis for finite arrays of $N^2$ emitters, shows that the output is collimated into lobes that narrow as $1/\sqrt{N}$. Our scheme combines the broadband acceptance of free-space 4-wave mixing with the efficiency, directionality and tunability of cooperative metasurfaces, offering a route towards quantum-coherent THz detection and processing for astronomical spectroscopy, quantum-networked sparse-aperture imaging and other quantum-sensing applications.

Measurements of the spectral emission properties of an iron-doped a beta-Ga2O3(010) photocathode at 300 K reveal the presence of an ultracold contribution to the total electron beam emission with a 6 meV mean transverse energy (MTE) in the 3.5-4.4 eV photon energy range (282-354 nm). This extreme sub-thermal photoemission signal is consistent with direct emission of electrons photoexcited from the Fe dopant states into the low effective mass and positive electron affinity primary conduction band, and it is superimposed on a stronger signal with a larger MTE associated with an (optical)phonon-mediated momentum resonant Franck-Condon (FC) emission process from a thermally populated and negative electron affinity upper conduction band. For photon energies above 4.5 eV, a transition from a long to a short transport regime is forced by an absorption depth reduction to below 100 nm and both MTE signals exhibit spectral trends consistent with phonon-mediated FC emission if the polaron formation self-energy is included in the temperature of the initial thermalized photoexcited electron distribution.

X-ray and neutron diffraction are foundational tools for determining crystal structures, but their resolution limits can lead to misassignments, especially in materials with subtle distortions or competing phases. Here, we demonstrate the use of nonlinear transport as a complementary approach to uncover hidden crystal symmetries, using the strongly correlated Ca$_3$Ru$_2$O$_7$ as a case study. Below 48 K (T$_S$), where the magnetic moments of the antiferromagnetic phase reorient from the a- to the b-axis, leading to a pseudogap opening, our measurements, with support of DFT, reveal a previously overlooked lower-symmetry phase. This is manifested by the emergence of longitudinal nonlinear resistance (NLR) along the b-axis below T$_S$, providing direct evidence of combined translational and time-reversal symmetry breaking. This response also suggests a transformation from a conventional antiferromagnet into an altermagnet. The lower-symmetry phase arises from a subtle lattice distortion (~0.1 pm) associated with the magnetic transition at T$_S$, below the detection limit of conventional diffraction. Moreover, this NLR below T$_S$ is accompanied by a nonlinear Hall effect, both of which are enhanced by the large quantum metric associated with Weyl chains near the Fermi surface. Our findings demonstrate nonlinear transport as a sensitive probe of hidden symmetry breaking and altermagnetism, complementing and extending beyond the reach of traditional diffraction and spectroscopic techniques.