We present a comprehensive chemical and age orbital cartography of the Galactic high-$α$ disc using subgiant stars with precise ages, element abundances, and full phase-space information from the \textsl{LAMOST--Gaia} data set. Specifically, we map how average [Fe/H], [$α$/Fe], and age vary across present-day kinematic and orbital coordinates. We analyse the data in full and across mono-abundance populations to measure element abundance-orbital and age-orbital gradients across orbital actions and angular-momenta. Our results show that the high-$α$ disc exhibits clear and coherent gradients in [Fe/H], [$α$/Fe], and age with orbits; these gradients are much stronger and sharper in orbital space than in present-day kinematics, showing that orbital diagnostics recover the intrinsic disc structure of old disc populations more effectively than instantaneous kinematic coordinates. We find that older high-$α$ populations display qualitatively similar element abundance--orbital and age--orbital trends to stars in the low-$α$ disc, although the high-$α$ gradients are generally shallower. The presence of these ordered correlations indicates that the old high-$α$ disc is structured, and preserved a strong fossil record of its early assembly despite the Milky Way's subsequent accretion history. This result implies that later mergers did not fully erase the chemical-orbital and age-orbital structure imprinted during the high-$α$ disc's earliest formation epoch. All together, these findings indicate that the Galactic high-$α$ disc formed mainly through inside-out and upside-down growth.

Whether the complex numbers of standard quantum theory are experimentally indispensable has remained open for decades. Real quantum theory (RQT), obtained by replacing complex amplitudes with real ones while retaining the usual Kronecker-product composition rule, reproduces all single-party and bipartite Bell correlations of quantum theory (QT), but its lack of local tomography suggested that the two theories might diverge in more general local experiments. This possibility appeared to be confirmed by Renou et al., who argued that a bilocal network experiment can falsify RQT without falsifying QT. Here we show that this conclusion relies on an experimentally untestable assumption. The key distinction is between product-state independence, which constrains the mathematical form of source states, and operational independence, which is defined entirely by the absence of observable cross-source correlations. We prove that, once source independence is imposed operationally, every finite network correlation achievable in QT is also achievable in RQT with the same locality structure of the measurements. We then extend this equivalence to arbitrary finite sequential multipartite protocols involving channels and measurements with prescribed locality structure. Thus, as long as no violation of QT is observed, RQT cannot be experimentally falsified. Our results restore the empirical indistinguishability of QT and RQT, while showing that they support markedly different pictures of the correlation structure underlying the same observed world.

Interfacial hydrodynamic instabilities in multicomponent superfluids provide a versatile platform to explore nonequilibrium quantum dynamics beyond classical fluid analogues. We study dynamical interfacial instabilities in a quasi-two-dimensional three-component Bose-Einstein condensate confined in a harmonic trap, where rotation is applied selectively to the intermediate component to generate controlled relative motion at two interfaces. This selective rotation protocol enables the independent tuning of shear and counterflow across the inner and outer boundaries, allowing direct control over the nature and strength of the resulting instability mechanisms. Three regimes are examined: Kelvin-Helmholtz instability in the strongly immiscible limit, counter-superflow instability in the partially miscible regime, and a parameter window where both unstable mechanisms are present. The onset condition for the Kelvin-Helmholtz instability is derived using a hydrodynamic pressure-balance approach, and the subsequent nonlinear evolution is obtained from time-dependent Gross-Pitaevskii simulations. A Bogoliubov-de Gennes analysis is performed to identify the dominant unstable modes excited during the dynamical evolution of the system. The conniving features of the collective excitations and their spatial structures have been consistent with the density modulations observed during the dynamics. The results demonstrate that the presence of two interfaces and tunable intercomponent interactions in a three-component condensate modifies the instability mechanisms relative to binary mixtures and provides a controlled parameter regime to study multicomponent quantum hydrodynamics.

We introduce a measurement-induced quantum neural network (MINN), an adaptive monitored-circuit architecture in which mid-circuit measurement outcomes determine the entangling gates in subsequent layers. In contrast to standard monitored circuits where sites and gates are sampled randomly, the gates are parametrized and variational, producing correlated history-dependent dynamics and injecting nonlinearity through measurement back-action. A generic MINN is not expected to be efficiently classically simulable. To demonstrate feasibility, we study a matchgate MINN that admits exact fermionic simulation and can be trained with gradient estimators. We apply the architecture to continuous optimization, image classification, and ground-state search in the Sherrington-Kirkpatrick spin glass, finding effective training and performance over a broad range of monitoring rates.

Large Eddy Simulations with flamelet-based thermochemistry are used to investigate the behaviour of a premixed hydrogen-air flame stabilised by a bluff-body. Validation against experimental data is carried out first to demonstrate the model's ability to predict both velocity field and flame structure. The capability of the model in predicting differential diffusion effects is then assessed, in particular regarding the coupling between differential diffusion, tangential strain and curvature, and their effect on mixture fraction redistribution and reaction rate variation. Results indicate that unstretched flamelet thermochemistry is capable of capturing the increase in mixture fraction caused by positive resolved strain, as well as negative variations of mixture fraction due to negative curvature. Furthermore, the model is observed to mimic the effects of negative Markstein length to a certain extent, so that positive tangential strain causes reaction rate increase. The interplay between resolved stretch and preferential diffusion is also shown to lead to a shorter flame length which is in better agreement with experimental observations as compared to simulations under unity Lewis number assumption. These findings highlight that the macroscopic effects of differential diffusion and stretch on the premixed hydrogen flame, characterised by significant strain levels, can be predicted using a flamelet-based approach and without recurring to strained flamelets database, which implies important simplifications in the combustion modelling of turbulent hydrogen-premixed flames and offers valuable insights for the design of novel combustors.

The role of tetraquark operators in studying the isodoublet strange $κ$ and isovector nonstrange $a_0(980)$ scalar mesons in lattice QCD is examined using an ensemble with $m_π\approx230$ MeV and spatial extent $L$ such that $m_πL\approx4.4$. Hermitian correlation matrices using both single-meson, meson-meson, and tetraquark interpolating operators are used to extract the spectrum of finite-volume stationary states in the appropriate symmetry channels. Hundreds of local and extended tetraquark operators are explored. Determinations of the spectrum in each channel are found to be unreliable without the inclusion of at least one tetraquark operator. For example, the inclusion of tetraquark operators with isospin 1/2 and strangeness 1 quantum numbers reveals the existence of an additional energy level in the $Kη$ sub-system below the $Kη$ threshold. The implications of this on parametrizing the scattering $K$-matrix through a well-known quantization condition to extract properties of the $κ$ and $a_0(980)$ scalar meson resonances are discussed.

We numerically simulate the two-dimensional inertial flow with the van der Waals effect in a straight periodic channel around the Poiseuille and Couette stationary states. Even though the flow remains laminar macroscopically, we observe complex dynamics and power decay of the Fourier spectra of small fluctuations of the density, velocity divergence, vorticity and kinetic energy of the flow near their respective stationary background states. Remarkably, pinning the vorticity to its background state, and leaving only the density and velocity divergence as the variables, results in the dynamics and power decay of the Fourier spectra qualitatively similar to those of the full system. This strongly indicates that the underlying physics of the power spectra reside primarily in the density and velocity divergence variables, and are not directly related to the vorticity of the flow.

We investigate how the defining statistical features of three-dimensional turbulence respond to systematic reductions of the Fourier-space triadic interaction network. Using direct numerical simulations of both fractally and homogeneously decimated Navier-Stokes dynamics, we show that progressive thinning of the set of active modes leads to a systematic suppression of intermittency and, most strikingly, to the vanishing of the mean dissipation rate in the large-Reynolds-number limit. Structure-function exponents collapse onto their dimensional values, the multifractal singularity spectrum contracts, and the analyticity width extracted from the exponential spectral tail increases monotonically with decimation-each indicating a substantial regularization of the velocity field. Together, these results provide direct evidence that anomalous dissipation in incompressible turbulence is not a generic property of the Navier-Stokes equations, but instead requires the full combinatorial richness of their triadic nonlinear interactions.

In this work, we investigate the structural, magnetic, and microwave magnetic dynamics of multilayered \([{\rm LSMO}/{\rm SRO}]_n\) heterostructures \((n = 1 \text{ and } 5)\) grown on SrTiO\(_3\) (001) substrates. X-ray diffraction confirms high crystallinity and atomically sharp interfaces. Magnetic measurements reveal strong interfacial magnetic coupling, with a distinct two-step magnetization switching observed in the \(n = 5\) heterostructure, while this feature is significantly suppressed in the \(n = 1\) structure. Ferromagnetic resonance (FMR) analysis shows a broad linewidth, pronounced positive magnetic anisotropy, and Gilbert damping on the order of \(10^{-2}\), with damping decreasing as the number of multilayer repetitions increases. These observations demonstrate that Ru--Mn exchange coupling at the interface critically governs the magnetic response and dynamic behavior of the system. The tunable switching and damping properties highlight such oxide heterointerfaces as promising platforms for exploring spin textures, magnetic domain behavior, and room-temperature spintronic applications.

We review recent progress in the understanding of the preheating stage of Higgs inflation formulated within the Einstein-Cartan framework of gravity. This setup smoothly interpolates between the metric and Palatini formulations of the theory, leading to a distinctive phenomenology in an intermediate regime. Following the end of inflation, the Higgs field undergoes a non-trivial out-of-equilibrium evolution driven by tachyonic instabilities and nonlinear self-interactions, which fragment the inflaton condensate and give rise to well-localized oscillon configurations. While early studies suggested the formation of long-lived oscillons and the possibility of an extended matter-dominated phase, more recent analyses show that self-interactions at small field values render these objects transient, eventually triggering their decay and the onset of radiation domination. We discuss the implications of this dynamics for the thermal history of the Universe, the inflationary observables, and the generation of stochastic gravitational waves.

The inclusion of a mass-like term for the gluon in Yang-Mills theories quantized in the Landau gauge has proven to be an effective way of reproducing lattice results for gauge-fixed correlation functions within perturbative computations. Since those quantities are gauge dependent, it is natural to question how general this prescription is for describing the infrared behavior of gluon and Faddeev-Popov ghost propagators in different gauges. In this work, we provide a systematic investigation of this issue in the maximal Abelian gauge, which cannot be deformed into the Landau gauge and has been investigated in gauge-fixed lattice simulations. We compute the one-loop non-Abelian and diagonal gluon propagators and perform fits to lattice data in the case of $SU(2)$. Our results show that the transverse component of the non-Abelian gluon propagator as well as the diagonal gluon propagator, are in good agreement with lattice data in the infrared.

We present a comprehensive global analysis of Energy-Energy Correlation (EEC) data in electron-positron annihilation into hadrons, spanning a wide range of center-of-mass energies ($7.7\,\,\text{GeV}\!\leq\!\sqrt{s}\!\leq\! 91.2\,\,\text{GeV})$. In the back-to-back (two-jet) region, we resum to all orders the logarithmically-enhanced contributions up to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. The resummed results are consistently matched to fixed-order calculations up to $\mathcal{O}(α_S^3)$. Our resummation formalism also incorporates dominant heavy-quark mass effects and models non-perturbative power corrections by means of an analytic dispersive approach. A simultaneous fit yields an excellent description of experimental data across all energies, enabling a precise determination of the strong coupling, $α_S(m_Z^2) = 0.119 \pm 0.002$, as well as the non-perturbative parameters, including those characterizing the Collins--Soper evolution kernel. Our analysis includes, for the first time in a global fit, datasets from the ALEPH and AMY collaborations.

We propose a non-perturbative description of the moduli spaces encoding p-form generalized Maxwell theories in any dimension, using derived differential geometry. Our approach synthesizes the Batalin--Vilkovisky formalism with differential cohomology. Within this framework we formulate Dirac charge quantization and show how such charge-quantized moduli spaces exhibit abelian duality between generalized Maxwell theories of different types. We also describe the compactification of generalized Maxwell theories along closed Riemannian manifolds by computing the pushforward of the underlying sheaves of cochain complexes that model differential cohomology.

Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the Euclidean correlator to the spectral function via an inhomogeneous Fredholm equation of the first kind. Several different methods are on the market to resolve this issue, each taking different approaches and assumptions. In this proceedings we focus on implementing and testing a machine learning framework for spectral reconstruction, as well as implementing a novel method of estimating the behavior of the spectral function in the vicinity of vanishing frequency, which we denote as multipoint method, and compare these methods to well established spectral reconstruction techniques from the literature using mock data. As a physics application, we apply the reconstruction techniques to quenched lattice data for the correlation function in the vector channel at non-zero external magnetic field to extract the spectral function and the electric conductivity through its behaviour at vanishing frequency via a Kubo formula.

Dynamic metasurface antennas (DMAs) are an emerging hybrid-MIMO technology distinguished by an ultrathin form factor, low cost, and low power consumption. In real-world DMA prototypes, mutual coupling (MC) between meta-elements is generally non-negligible; some architectures even deliberately exploit strong MC to enhance wave-domain flexibility. In this paper, we address channel estimation (CE) for DMAs with known MC by formulating it as a tensor-decomposition problem. We develop a generalized block Tucker alternating least squares (BTALS) algorithm, together with specialized variants for cases with known direct and/or feed channel. We also develop a reciprocity-aware bilinear factorization method for the case with known direct channel. We experimentally validate our algorithms using an 18 GHz DMA prototype whose 7 feeds and 96 meta-elements are strongly coupled via a chaotic cavity. Our general BTALS algorithm reaches an accuracy of 43.1 dB, only 0.3 dB below the upper bound imposed by experimental noise. All proposed algorithms generally outperform the prior-art reference scheme thanks to the superior noise rejection enabled by the tensor-based framework. We further study the minimum number of required measurements as a function of the number of feeds and demonstrate the importance of MC awareness by comparison with an MC-unaware benchmark. Finally, we apply BTALS to a second setup enabling the prediction of the DMA's full dual-polarization 3D radiation diagram. We also measure the latter for DMA configurations optimized for channel-gain enhancement based on the estimated channels. Altogether, our work establishes the practical relevance of MC-aware tensor methods; beyond DMAs, it applies to all wireless systems with wave-domain programmability enabled by tunable lumped elements.

We assess the impact of non-ideal, continuously rotating half-wave plates (HWPs) on cosmic microwave background (CMB) polarization measurements targeting large angular scale signal. Such hardware solutions are used in or planned for multiple modern CMB efforts, both ground-based, for instance, small aperture telescopes of Simons Observatory or satellite borne, such as LiteBIRD. Using a frequency-dependent parametric model based on the Mueller matrix formalism, we characterize the induced mixing of Stokes parameters. Through end-to-end simulations, we propagate these effects from time-ordered data to cosmology via map-making and component-separation stages, quantifying their impact on the $B$-modes power spectrum and the tensor-to-scalar ratio, $r$. Our analysis shows that neglecting the frequency dependence of a three-layer HWP gives rise to significant polarization leakage, biases foreground spectral parameters, and leads to residual contamination in the recovered CMB maps. To mitigate these effects, we investigate multiple analysis strategies progressively incorporating a more complete description of the instrumental response. At the map-making level, this requires generalizing the standard pointing matrix to account for the full time- and frequency-dependent instrumental response. We find that standard HWP models, reduce the biases only down to $r \sim 10^{-2}$, while a more advanced approach based on a generalization of both map-making and component separation, implemented using JAX, can suppress it down to $r \sim 7 \times 10^{-4}$. Finally, we extend this approach to a time-domain component-separation, enabling a statistically consistent treatment of instrumental response in the presence of time-domain features. We demonstrate its feasibility and validate it by performing a full end-to-end analysis, recovering results in good agreement with the map-based ones.

We systematically investigate the electromagnetic properties of exotic states whose internal structures remain uncertain and for which different models have been proposed. In this work, we focus on the magnetic dipole moments of hidden-charm pentaquark states using QCD light-cone sum rules with four distinct interpolating currents. The analysis accounts for contributions from both light and charm quark sectors, as well as higher-dimensional operators, ensuring convergence of the operator product expansion and dominance of the ground-state pole. Our results demonstrate a strong dependence of the magnetic moments on the internal quark configurations and spin alignments, revealing substantial variations among the different currents despite identical quark content and quantum numbers. Comparisons with existing studies indicate that while molecular-type predictions show general agreement, compact configurations yield markedly different values, including significant differences in sign and magnitude. These findings therefore underscore the sensitivity of electromagnetic observables to the internal structure of exotic hadrons and highlight their potential as probes to discriminate between competing structural models for spin-parity assignments and underlying quark dynamics.

Understanding how optical excitation couples with polarization and interfacial electrostatics in van der Waals (vdW) ferroelectrics (FEs) is essential for the development of light-programmable nanoelectronic and optoelectronic devices. Here, we present direct nanoscale evidence of photoferroionic coupling in the vdW FE semiconductor CuInP2S6 (CIPS), where optical excitation jointly modulates electronic band bending, FE switching, and Cu+ ionic relaxation. The use of correlated Kelvin probe force microscopy, piezoresponse force microscopy, and conductive atomic force microscopy under above-bandgap illumination reveals illumination-induced enhancement of surface work function, persistent surface photovoltage, reduced coercive field, and positive imprint shifts. These effects arise from synergistic photocarrier redistribution and slow Cu+ migration that reshape interfacial depletion widths and internal electric fields. Illumination-assisted barrier lowering further enhances carrier injection and produces sweep-rate-dependent ferroionic transport hysteresis. Our results establish photoferroionic coupling as the governing mechanism for light-controlled band modulation and polarization stability in CIPS, providing a nanoscale framework for designing light-addressable FE memories, optoelectronic switches, and neuromorphic devices based on layered ferroionic materials.

We investigate the phenomenon of black hole superradiance in the presence of torsion within the framework of Poincaré gauge theory. In particular, in contrast to the classical approach of General Relativity, we show that the inclusion of torsion in the space-time geometry enables the energy extraction from rotating black holes by Dirac fermions via chiral asymmetry, while preserving the Pauli exclusion principle.

This paper presents a Hamiltonian reduction procedure for field theories over affine principal bundles introducing a canonical identification to describe the reduced multisymplectic space without the introduction of a connection. The main goal is to provide a Hamiltonian analogue of the Lagrangian reduction theory developed in M. Castrillón López, P. M. Chacón, and P. L. García. J. Geom. Mech., 5(4):399-414, 2013. The core of this work lies in the derivation of this canonical identification, the reduced Hamilton-Cartan equations, and a reduced covariant bracket that describes the dynamics. Finally, this theoretical framework is illustrated with a fundamental example: molecular strands.

Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE has mostly focused on sparse matrices; less effort has been devoted to data-sparse (e.g., rank-structured) matrices. In this work we examine a particular case of rank structure, namely, one-pair semiseparable matrices. We present a new block encoding approach that relies on a suitable factorization of the given matrix as the product of triangular and diagonal factors. To encode the matrix, the algorithm needs $2\log(N)+7$ ancillary qubits. This process takes polylogarithmic time and has an error of $\mathcal{O}(N^2)$, where $N$ is the matrix size.

Spin-orbit obliquity measurements of hot-Jupiter systems constrain giant planet migration and tidal evolution. In binary systems, combining stellar obliquities with the orbit-orbit angle ($γ$) between the planetary and stellar companion orbits provides further insight into the dynamical influence of stellar companions. Here we aim to determine the projected obliquity ($λ$) of the hot Jupiter TOI-1333Ab ($P\approx4.72$ d, $M_{\rm p}\approx2.4$ M$_{\rm J}$) and place the system in the context of hot-Jupiter migration and tidal realignment in binary systems. We analysed spectroscopic observations obtained during planetary transit to model the Rossiter-McLaughlin effect and derive the projected obliquity. We combined this measurement with published system parameters and constraints on the wide stellar companion orbit to assess plausible migration scenarios. We measure a projected obliquity of $λ=-5 \pm 10^\circ$, showing that TOI-1333Ab is well aligned with the stellar spin axis of its F-type host star. The low obliquity and its modest eccentricity ($e=0.073^{+0.092}_{-0.052}$) are consistent with either disc-driven migration or high-eccentricity migration followed by efficient tidal circularisation and realignment. With an effective temperature of $6274\pm94$ K, the host star lies above the canonical Kraft break where the systems are frequently misaligned. Despite this, we find the system to be well aligned. In comparison with other planetary systems in binaries, TOI-1333 occupies a relatively isolated region in projected obliquity-orbit-orbit angle ($γ=81.5\pm1.1^\circ$) space, making it a valuable system for studying the interplay between migration, tides, and stellar companions.

Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite dimensional spectral triple. Motivated by the fundamental question of the dependence of the spectra of Dirac operators under change of metrics, we prove the continuity of the spectra of Dirac operators for almost commutative models as functions of the underlying Riemannian metric. We allow both the Riemannian metric (in the $C^1$ topology) and the Dirac operator of the finite-dimensional factor to vary simultaneously. Since the physics of the system is fundamentally encoded in this spectrum, this result is a form of stability result regarding the geometry, or physical, content of these models. This result is based upon a novel approach to prove continuity of spectra of Dirac operators using the spectral propinquity. Notably, this method provides a new, different proof of the classical results as well. To illustrate the versatility of our new method, we also apply our results to completely non-commutative family of examples, including quantum tori and quantum solenoids.

We describe an empirical approach to identify low-weight combinations of columns of the decoding matrices of a quantum circuit-level noise model, for which belief-propagation (BP) algorithms converge possibly very slowly. Focusing on the logical-idle syndrome cycle of the low-density parity check gross code, we identify criteria providing a characterization of the Tanner subgraph of such low-weight error syndromes. We analyze the dynamics of iterations when BP is used to decode weight-four and weight-five errors, finding statistics akin to exponential activation in the presence of noise or escape from chaotic phase-space domains. We study how BP convergence improves when adding to the decoding matrix relevant combinations of fault columns, and show that the suggested decoder amendment can result in the reduction of both logical errors and decoding time.

This work develops a spherical-multipole expansion of Goldstein's acoustic analogy, for the prediction of tonal noise from rotating propellers. The acoustic field is expressed through spherical multipoles, which separate source integrals from the observer dependence. This decoupling leads to computational efficiency: once the multipole coefficients are computed from blade geometry and aerodynamics, the sound field at any observer location is obtained by a simple evaluation of spherical harmonics and radial propagation factors, avoiding repeated integrations for each observer point. Moreover, this enables a straightforward radiated power calculation, without resorting to far-field pressure integrals. For hovering subsonic propellers, the results show a rapid convergence of the expansion. For each harmonic, the dominant radiation is accurately captured by the first two non-zero multipoles, corresponding to the leading symmetric and antisymmetric contributions with respect to the plane of rotation. To interpret the physical content of these leading terms, two simplified descriptions of the source integral are developed. The first is a lifting-surface formulation, suited to blades at small incidence, in which the thin-airfoil approximation allows to separate lift-like loading, drag-like loading, and thickness contributions. The second is a lifting-line formulation, suited to high-aspect-ratio blades, in which the surface integral is reduced to spanwise integrals of compact sectional moments. The validity of the two formulations is assessed through comparisons of directivity, power distribution over harmonics and time-domain waveforms. The results show good accuracy in their respective regimes of validity, together with substantial computational savings.

In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM). We then examine the problem classes where quantum technologies currently show evidence of quantum advantage, drawing on established benchmarking initiatives such as QOBLIB, QUARK, QASMBench, and QED-C. These problem classes are subsequently mapped to representative industrial domains, including logistics, finance, and telecommunications. Our analysis indicates that quantum annealing currently exhibits the highest level of operational maturity, while QAOA shows promising potential on NISQ-era hardware. In contrast, QRL and QGM emerge as longer-term research directions with significant potential for future industrial impact.

The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local computation, and then use these scattering matrices to form a global linear system. The resulting coefficient matrix is relatively well-conditioned, even for problems involving a very large number of scatterers. The linear system is amenable to iterative solvers, and can readily be accelerated via fast algorithms for the matrix-vector multiplication such as the fast multipole method. The key point of the work is that the local scattering matrices can be constructed using potentially ill-conditioned techniques such as the method of fundamental solutions (MFS), while still maintaining scalability and numerical stability of the global solver. The resulting algorithm is simple, as the MFS is far simpler to implement than alternative techniques based on discretizing boundary integral equations using Nyström or Galerkin.

We derive analytical expressions for chemical potentials within the random phase approximation (RPA), equivalently the $GW$ energy functional evaluated using non interacting Green's functions ($G_s$). The chemical potential is obtained using two formally equivalent approaches: a direct derivative of the total energy with respect to particle number, and a functional derivative via the chain rule through $G_s$, both validated with finite difference benchmarks. We show that the functional derivative of the $GW$ correlation energy$\unicode{x2013}$i.e., the $GW$ correlation self energy$\unicode{x2013}$exhibits a discontinuity at integer particle numbers with finite jumps. This resolves the apparent inconsistency between accurate $GW$ quasiparticle energies and the large delocalization errors observed in RPA total energies, as standard $GW$ self energies neglect this nonanalytic behavior. Our results suggest that derivative discontinuities are a fundamental feature of correlation energy functionals, analogous to the known discontinuity in the exact exchange correlation energy.

Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions that make a convincing case for quantum hardness. In this work, we argue that decoding random quantum stabilizer codes -- a quantum analog of the well-studied LPN problem -- is an excellent candidate. This task occupies a unique middle ground: it is inherently native to quantum computation, yet admits an equivalent formulation with purely classical input and output, as recently shown by Khesin et al. (STOC '26). We prove that the average-case hardness of quantum stabilizer decoding implies the core primitives of classical Cryptomania, including public-key encryption (PKE) and oblivious transfer (OT), as well as one-way functions. Our constructions are moreover practical: our PKE scheme achieves essentially the same efficiency as state-of-the-art LPN-based PKE, and our OT is round-optimal. We also provide substantial evidence that stabilizer decoding does not reduce to LPN, suggesting that the former problem constitutes a genuinely new post-quantum assumption. Our primary technical contributions are twofold. First, we give a reduction from random quantum stabilizer decoding to an average-case problem closely resembling LPN, but which is equipped with additional symplectic algebraic structure. While this structure is essential to the quantum nature of the problem, it raises significant barriers to cryptographic security reductions. Second, we develop a new suit of scrambling techniques for such structured linear spaces, and use them to produce rigorous security proofs for all of our constructions.

We perform a search for an X-ray monochromatic line arising from dark matter (DM) decay in the halo of the Large Magellanic Cloud. An emission line can be expected from two well-motivated DM candidates: sterile neturinos and axion-like particles (ALPs). We analyze the eROSITA-DE DR1 datasets in the energy range between 1 and 9 keV. No evidence for a DM line is found, and we set lower limits on the DM lifetime. We then recast these bounds into upper limits on the active-sterile neutrino mixing angle $\sin^2(2θ)$ and on the ALP to photon coupling $g_{aγ}$, for DM masses between 2 and 18 keV. These results set new strong constraints for masses below 5 keV.