Papers

We consider the nuclear recoil spectrum following allowed $\beta$ decay as a laboratory for Beyond Standard Model searches, and perform an exhaustive treatment of the Standard Model prediction. We consider final state interactions, nuclear structure corrections, kinematic corrections and radiative corrections, derive new results and show that the nuclear recoil spectrum is theoretically exceptionally clean. We construct a clean statistical framework and analyze the Fisher information for extracting exotic current constraints and testing Cabibbo-Kobayashi-Maskawa top-row unitarity, and consider a number of sterile neutrino scenarios. In addition, we find that for select isotopes separate measurement of the $\beta$-asymmetry and recoil spectrum can achieve an increase in the statistical power of up to a factor 40.

Experimental demonstrations of the Mpemba effect in a colloidal-particle system have imposed an instantaneous temperature quench via an initial condition where individual particle trajectories are drawn from a high-temperature Boltzmann distribution and then evolve in a bath at lower temperature. The potential used for the high-temperature distribution has had two walls that impose a finite range of initial positions, even at effectively infinite temperatures. The potential for evolution in the bath had no walls and matched that used for the initial condition over its support. For low bath temperatures, the difference between the dynamics with and without walls is negligible. Nonetheless, it has been speculated that the walls are perhaps more important than they seem and might even be required for the Mpemba effect to occur. Here, we introduce a new potential that lacks walls and use it for both the initial high temperature state and for subsequent evolution. This new potential then allows us to investigate by simulation Mpemba effects at finite-quench rates. Our results help clarify intuitions concerning the existence of a Mpemba effect and show that the Mpemba effect appears only for bath-temperature quenches faster than a critical quench rate.

We prove that 3d Lovelock gravity, the Horndeski theory obtained from the regularized Lovelock invariants in three dimensions, admits a holographic c-theorem at all orders and for arbitrary values of the couplings. In the minisuperspace of domain wall solutions, the equation of the Horndeski scalar is a total derivative at every order, which locks the derivative of the scalar to that of the warp factor along the flows we consider and allows the null energy condition to be integrated into a monotonic c-function. The linear scalar profile of the resulting vacuum breaks the special conformal transformations, so the dual theory is scale-invariant but not conformal, and the central charge is defined as the coefficient of the logarithmic divergence of the on-shell action on the sphere. We compute it exactly for the Gauss-Bonnet case and asymptotically for the full tower, and find that it is linear in the couplings and matches the UV value of the c-function. Since all results depend on the couplings only through two generating functions, we give the resummed Lagrangians, c-functions and central charges in closed form for the choices of couplings that lead to regular black holes, and classify the resummed theories by the positivity of the effective Newton constant on the vacuum and the uniqueness of the vacuum with a non-trivial scalar.

Starting from the constant-roll condition, which involves the constant-roll parameter $\beta$, which is a fundamental constant in the constant-roll inflationary models, we derive the scalar power spectrum and obtain an analytic expression for the scalar spectral index $n_s$ in terms of $\beta$ and the number of remaining e-folds $\tilde N$. The resulting relation is non-monotonic in $\beta$, allowing two distinct constant-roll branches, one with $\beta<0$ and one with $\beta>0$, to reproduce nearly the same observed scalar tilt. We constrain $\beta$ using Planck 2018 CMB data, and further using the combined Planck 2018 + ACT DR6 data. For Planck 2018, the posterior distribution of $\beta$ exhibits a bimodal structure associated with the two analytical branches, while the combined Planck+ACT analysis tightens the allowed range of $\beta$ and shows continued consistency with the $\beta=0$ slow-roll-like spectral point. The data constrain $\beta$ to be small, but do not require it to vanish exactly. We also estimate the inflationary mass scale $M$ by using the observed scalar-amplitude normalization at the pivot scale. Both the negative and positive $\beta$ branches give a high-scale inflationary normalization of order $M\sim10^{-5}M_{\rm Pl}$. We show that the $\beta \to 0$ limit is only spectrally slow-roll like, but does not reproduce standard slow-roll dynamics. Our results show that constant-roll inflation is observationally competitive with the usual slow-roll inflationary paradigm. The constant roll inflation model is supported by the latest CMB observations equally well or marginally better when compared with the slow roll inflation model.

Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate alone, and DNS relabeling is performed offline once per selected state. Experiments on $128^3$ turbulence show that OAS increases the median time to failure from 21 to 721 steps. The compared baselines achieve medians of at most 110 steps, and the advantage holds across training seeds. OAS also achieves the lowest pointwise error at step 15 and the best long-horizon statistics among the compared methods. OAS integrates physical models into neural simulation by extending supervision from fixed reference trajectories to states where the surrogate is likely to fail. This principle can guide the development of more reliable scientific surrogates when deployment takes models beyond the coverage of their training data.

We present a graph neural network-based learning framework trained to jointly predict electron densities and molecular energies. The model is trained to predict electron densities calculated with a Generalized Gradient Approximation (GGA) functional while simultaneously learning to predict molecular energies obtained with hybrid functional calculations at the B3LYP level of theory. Our results indicate that the rich spatial information in electron density distribution can be used to improve and accelerate the learning of accurate energies. By sharing an equivariant molecular representation across density and energy prediction heads, the model learns complementary molecular quantities within a unified framework. This provides a new promising route for practical use cases of many recent charge density learning frameworks for atomic scale simulations.

The interpretation of polarized spectral lines requires models that combine statistical equilibrium with polarized radiative transfer accounting for atomic polarization, the Hanle effect, and Zeeman and Paschen-Back splitting. The aim is to provide an open-source Python implementation of the irreducible spherical tensor formalism of Landi Degl`Innocenti and Landolfi (2004), hereafter LL04, for forward synthesis of Stokes profiles with interchangeable atomic descriptions. SolRaT solves the statistical equilibrium and polarized transfer problem for interchangeable multi-term and multi-level atomic descriptions. The multi-term model retains coherences between fine-structure levels of the same term and treats the magnetic Hamiltonian by exact diagonalization, allowing the magnetic splitting to be followed from the linear Zeeman regime to the incomplete and complete Paschen-Back regimes. The widely used multi-level model in turn assumes only the linear Zeeman regime, resulting in a simpler and more developed formalism. The implementation is checked against analytic results from LL04, the Unno-Rachkovsky solution for local thermodynamic equilibrium (LTE) Zeeman transfer, the Hazel2 He I D3 synthesis, and published self-consistent non-LTE scattering benchmarks. The examples show how the intra-term magnetic mixing produces departures from a linear Zeeman multi-level description, and how a J-constrained multi-term approach can be used to isolate this effect on a chosen fine-structure component. Synthesizing the same spectral line with interchangeable multi-term and multi-level descriptions under identical conditions isolates the signatures of intra-term magnetic mixing and inter-J coherences from the linear Zeeman response. Such controlled comparisons are central to developing scattering polarization diagnostics applicable across multiple atomic descriptions.

We generalized the seminal work of Law & Eberly, and propose a protocol to generate arbitrary quantum states with a three-level atom as an ancilla in a more efficient manner. This protocol moves two excitations in parallel in each control step, thus reducing the number of evolution steps by half. Full analytical expressions for the control field strengths and timings are derived. The system dynamics is exposed to less chance of error accumulation in the timing and amplitudes of the control fields, and quantitative study in the context of the quantum speed limit is also considered.

This work presents a fabrication process to realize sub-10 nm-thick, high-aspect-ratio Si fins using high-resistivity float-zone single-crystal Si wafers. Following anisotropic wet etching, a digital etching process based on repeated rapid thermal annealing (RTA) oxidation and vapor-phase hydrofluoric acid (VHF) etching of the resulting oxide was developed, enabling thinning of Si fins into the sub-10 nm regime. Cross-sectional scanning transmission electron microscopy confirms fin thicknesses as thin as 6 nm, although with a tapered profile resulting from the initial anisotropic wet etch. Tapering of the fin was reduced by using an N{_2}/O{_2} (5:1) ambient together with a reduced ramp rate during the temperature ramping for the RTA oxidation process. A thickness variation of 3 nm along a 1.2 {\mu}m tall fin was achieved on a fin with 12 nm near the top and 15 nm near the base. The developed process provides a pathway for fabricating Josephson junctions, setting a foundation toward reproducible and scalable superconducting qubit fabrication with single-crystal Si dielectric barriers using readily available Si processing technology.

We initiate the study of quantum state tomography—the experimental reconstruction of the complete spin density matrix—of massless and massive quark-antiquark pairs produced at the future Electron-Ion Collider (EIC). We show that all components of the spin density matrix can be accessed through azimuthal angular correlations between hadron and dihadron pairs generated by the Collins and dihadron fragmentation functions. This enables the experimental investigation of a variety of quantum information properties at the EIC, such as entanglement and Bell-nonlocality. We predict that the recently discovered maximal entanglement in the heavy-quark sector is signaled by a strong modification of the usual Collins angular dependence $\cos(\phi+\phi')$

Higher-order networks take group interactions as given. I ask what happens when a group interaction is made by pairwise dynamics on a graph, and follow it through the transition that decides whether it matters at large scale, Anderson localisation. An emergent hyperedge is a $k$-body bound state of a Hamiltonian whose terms live on the vertices and edges of the graph, Borromean when none of its $(k-1)$-body faces is bound, detected on a finite graph by a $k$-fold coincidence that survives the thermodynamic limit while the $(k-1)$-fold ones vanish. Sparse random graphs produce one from the simplest pairwise dynamics: three distinguishable particles with on-site attraction $U$ and hopping $t$ bind into a trimer before any pair binds. The thresholds are obtained on the Bethe lattice, in closed form for the pair, in both sectors that an expander graph has and a lattice lacks, the one a condensate sees and the one a Fermi liquid sees. On a disordered graph the emergent hyperedges nucleate on rare deep sites and localise before their parts: the compact trimer, with a narrow band and a threefold sensitivity to site energies, undergoes the Anderson transition at a disorder of $1.6t$, against $17t$ for a single particle and $4t$ for a pair, and the Fermi liquid of trimers is a glass above a line between $1.5t$ and $1.7t$, where a liquid of single particles at the same density needs $15t$ to $16t$. The transition is the single-particle cavity transition with the composite's hopping and effective disorder. A group interaction made by pairwise dynamics is an order of magnitude more fragile to heterogeneity than the network that makes it.

We report the epitaxial growth of high-quality water-soluble strontium aluminate films via sputtering deposition. We systematically investigate the dependence of the films structural quality on the growth conditions and we show that we can selectively grow, using the same target, both the cubic Sr3Al2O6 and the tetragonal Sr4Al2O7 phases by varying the atmosphere during growth. Using these water-soluble sacrificial layers we then synthesize ferromagnetic freestanding Sm2NiMnO6 membranes. By means of X-ray diffraction, synchrotron spectroscopic techniques and SQUID magnetometry, we demonstrate that our freestanding films exhibit properties comparable to epitaxial films.

The Euclid mission is delivering an unprecedented volume of high-resolution galaxy imaging, posing new challenges for standardized and reproducible reuse across morphological analyses. We present a scalable pipeline that converts released VIS cutouts into standardized $224\times224$ model inputs and uses a pretrained DINOv2 ViT-S/14 feature extractor to construct a 365,513-row, 384-dimensional cutout-and-embedding product from the Galaxy Zoo Euclid (Q1) catalogue. Initial production of the 365,513 released cutouts required approximately 48 hours, corresponding to an estimated end-to-end rate of $2.12$ cutouts s$^{-1}$. The service supports batch task management, while persistent reuse of generated products avoids repeating mosaic extraction for matching requests; together with released-scale production, these mechanisms define the operational scalability considered here. The representation is evaluated with held-out regression, few-label classification, anomaly-candidate prioritization, and similarity retrieval. Held-out ridge probes yield $R^2=0.377$–$0.596$ across four catalogue quantities. Under a one-percent total labelled budget that includes validation, frozen MLP macro-F1 is 0.802–0.861 for three tasks but 0.484 for the strongly imbalanced spiral task; limited final-block fine-tuning gives 0.810–0.850 for those three tasks and 0.520 for spiral. The historical anomaly workflow identifies 1,681 configuration-dependent candidates, and the displayed examples illustrate image-quality failures without estimating their prevalence. These results show that a standardized image interface and a reusable pretrained embedding can support several downstream analyses at the scale of the released Euclid Q1 sample, while the quantitative performance and interpretation remain task dependent under the declared input and evaluation contracts.

Low-frequency Drude response does not by itself determine which nearly conserved sector carries an electric current. We classify the leading cubic retarded response of an isolated, inversion-symmetric slow vector by its pole topology. Constitutive nonlinearity produces only incoming-frequency poles, whereas nonlinear relaxation adds a propagator at the emitted frequency; coupling to a second scalar slow mode generates pair-frequency poles. We then compute the full complex third-harmonic response of finite-density Dirac–Born–Infeld probe branes in Lifshitz black-brane backgrounds. In the marginal $z=2$ theory, the dense infrared response approaches the relaxation topology, with a signed infrared weight $p_{\rm IR}=0.994\pm0.002$ and a normalization-independent zero at $\omega_\times/\Gamma_J=0.2918$. Nonmarginal $z=1$ and $z=3/2$ backgrounds instead realize mixed constitutive–relaxation weights, demonstrating that the topology is selected dynamically rather than imposed by the DBI square root. The exact nonlinear dc solution further yields a parameter-free dense-limit scaling function and a crossover field $E_{\rm nl}\propto T^{3/2}$ at $z=2$. These results connect emergent higher-form slow currents, nonlinear response theory, and holographic transport, while the two-mode extension identifies the additional pole structures expected when energy or deformation modes remain slow.

Accreting X-ray pulsars (XRPs) are strongly magnetized neutron stars (NSs) distinguished by a periodic variability pattern related to the rotation of their magnetospheres (pulsations). Many of these objects show complex asymmetric pulse profiles that are difficult to explain in the framework of existing models. We calculate the pulsations of X-ray radiation from a magnetized NS in the regime of supercritical accretion, when the radiation shock wave is high above the NS surface, and the observed radiation comes from two optically thick accretion columns located downstream of the shocks. We show that the accretion column beam pattern calculated from the first principles has a potential of reproducing the variety of XRP pulse shapes. The surfaces of the columns are assumed to radiate locally as blackbodies with the temperature distribution following the solution of Basko and Sunyaev (1976). The adopted geometry of the field is an inclined dipole. It is taken into account that the two accretion flows above the shocks attenuate and scatter the radiation of the accretion columns. Using the ray-tracing technique, we obtain a vast variety of pulse shapes controlled by the mass accretion rate, magnetic angle, the direction towards the observer, and the parameters that determine the particular set of magnetic field lines being loaded with accreting matter. We propose a universal dimensionless parameter describing the asymmetry of a pulse quantitatively. The model naturally produces asymmetric pulse profiles observed in many XRPs. Its applicability, however, is limited to the brightest objects like pulsating ultraluminous Xray sources and strong flares of Galactic XRPs.

Comets are thought to have largely preserved the primordial material from which they formed. Therefore, cometary studies provide important clues about the processes involved in the formation of the Solar System. During the last weeks of ESA's Rosetta mission, the COSIMA (COmetary Secondary Ion Mass Analyser) instrument performed a series of measurements, which involved long-term sputtering of dust particles captured from comet 67P/Churyumov-Gerasimenko. These post-sputtering analyses revealed the subsurface composition of 8 particles, which we compare here with surfaces composition measured on 59 un-sputtered particle fragments for 9 elements. We found that the analysed surfaces are strongly depleted in metals, such as Mg and Fe, compared to solar abundances, while the subsurface material is consistent with solar values. Because the dust captured by COSIMA fragmented upon impact with the collection targets, this metal depletion cannot reside exclusively on the outer surface of the bulk particles. Instead, these depletion layers must coat the surface of smaller, unfragmented mineral subunits. Such depletion layers, which are often called 'rims', are common at the surface of small regolith dust particles found on airless bodies in our solar system and are attributed to space weathering. We suggest that these mineral cometary subunits experienced pre-accretional solar wind irradiation in the inner regions of the solar nebula during the early stages of Solar System formation. The small irradiated dust constituents must then have been transported to the outer regions of the solar nebula, where they mixed with ices to form the nucleus of the comet.

The structure of the neutron-rich nucleus $^{21}$B is investigated within a three-body model consisting of a $^{19}$B core and two neutrons. The three-body wave functions are computed using the hyperspherical adiabatic expansion method combined with the complex-scaling technique. Four potential parametrizations compatible with the available experimental information on $^{20}$B are considered. The calculations predict a low-lying $\frac{3}{2}^-$ state below the experimentally observed resonance at 2.47~MeV. An analysis of the dependence on the three-body interaction shows that this state cannot be shifted to the experimental resonance energy; instead, it remains either bound or becomes a near-threshold resonance with a rapidly increasing width. These results indicate that the observed resonance is more naturally interpreted as the second $\frac{3}{2}^-$ state, whereas a lower-lying $\frac{3}{2}^-$ state, dominated by an $s_{1/2}$ configuration, has so far eluded experimental observation. Momentum correlations are obtained for the experimentally observed resonance. In addition, the existence of other resonances is investigated.

We identify the limit free energy of all mean-field multi-species spin glasses defined on products of spheres. In particular, we do not make any convexity assumption on the covariance function of the Hamiltonian, and we allow for the presence of external fields. We also obtain a one-species reduction of the formula in the special case of balanced models.

We study two bilinearly coupled harmonic oscillators driven by a common time-dependent spring. A fixed normal-mode transformation reduces the pair to two parametric oscillators, each solved exactly by its Lewis-Riesenfeld invariant and Ermakov-Pinney amplitude, including the ladder-operator construction and the Lewis-Riesenfeld phase. For invariant-vacuum inputs the physical two-mode covariance matrix is obtained in closed form, and the logarithmic negativity collapses to $E_{N}=\frac{1}{2} \operatorname{arcosh}(X/2)$, where a single dimensionless invariant $X \geq 2$ measures the relative phase-space deformation of the two normal modes. We give a normalization-explicit account of the Duan–Simon comparison: after local symplectic optimization the Duan test and the positive partial transpose share the entanglement threshold for this pure exchange-symmetric Gaussian family, but the optimized Duan quantity is a witness, not an independent measure, with $D_{\rm opt}/D_{\rm sep}=e^{-E_N}$. We carefully separate a genuinely separable product preparation from the already-entangled ground state of the coupled Hamiltonian, and use only the former for claims of entanglement generation. Under sinusoidal stiffness modulation a separable input shows bounded correlations away from resonance and sustained growth near parametric resonance, and we demonstrate numerically that the initial width and chirp act as two independent, experimentally accessible controls of the entanglement at a chosen target time. An $SU(1,1)$ formulation identifies $2 E_{N}$ with the hyperbolic separation of the two normal-mode squeezing trajectories on the $SU(1,1)/U(1)$ disk and shows that entanglement is governed by both the relative squeezing magnitude and the relative squeezing angle; ; we exhibit regimes in which nearly equal magnitudes still produce strong entanglement through the angle alone.

In this work, we introduce a precursor-level strategy by substitutionally doping the Ti3AlC2 MAX precursor with a small amount of Yttrium during top-down MAX preparation. This allows permanent structural changes that are retained in the resulting Ti3C2Tx MXene. Density functional theory (DFT) calculations identify the outer Ti(4f) site, facing the Al layer, as the preferred incorporation site for Y under the Al-excess synthesis conditions used here, rather than the inner Ti(2a) or Al(2b) sites. This site-specific substitution is consistent with the experimentally observed lattice expansion and carbide-like Y bonding and provides a microscopic basis for the structural changes retained in the resulting Ti3C2Tx MXene. Y incorporation expands the MXene interlayer spacing due to an increase in the amount of hydroxyl surface terminations, creating more favorable pathways for lithium-ion transport. Comprehensive structural characterization (including XRD, XPS and TEM) confirms these modifications. As a result, the Y-doped Ti3C2Tx cathode shows diffusion-controlled charge storage with a Li diffusion coefficient of 10-9-10-11 cm2/s. It delivers a reversible capacity of about 130 mAh/g at 0.2 C and retains 74 mAh/g after 1000 cycles at 2 C with nearly 100% Coulombic efficiency. The electrode also achieves a high power density of up to 3970 W/kg, outperforming the undoped MXene and previously reported multilayered MXene cathodes. These results show that substitutional doping of the MAX precursor is a promising strategy for controlling the interlayer structure of MXenes and improving ion transport, providing a new route for the development of high-power energy-storage electrodes.

We investigate Hawking radiation of a quantum-corrected Schwarzschild black hole with vacuum polarization and conformal anomaly effects. The corrected geometry has two horizons, a non-monotonic Hawking temperature that vanishes at a critical mass, and a logarithmic entropy correction. We compute greybody factors, spectra, and emission rates for massless bosonic fields of various spins and angular momenta. Quantum corrections suppress low-energy greybody factors and enhance high-energy ones. During late evaporation, where quantum influences become significant, the decreasing temperature strongly suppresses emission. In this case, the higher-spin modes become negligible, and the scalar $s=l=0$ mode dominates. The black hole lifetime is greatly extended as it asymptotically approaches a stable extremal remnant.

Wavefront shaping enables control over optical fields for applications ranging from imaging to photonic information processing. While conventional wavefront shaping relies on free-space systems comprising bulk optical components, compact and fully integrated approaches are comparatively unexplored. Here, we introduce a concept based on a single multimode waveguide with distributed thermo-optic perturbations for controlling multimode propagation. We develop a differentiable physical model and numerically demonstrate shaping the outgoing wavefront and programmable linear optical transformations, using gradient-based optimization. We achieve diffraction-limited focusing with 20 spatial modes and show that the theoretical focusing limit can be retained while maintaining more than $99\%$ of the input optical power. We extend this approach to complete input–output transformations and implement Sylvester–Hadamard matrix operations with dimensions up to $32\times32$ with correlations exceeding $99\%$. Reducing the number of tunable elements requires stronger individual perturbations, resulting in stronger and broader mode coupling that extends beyond the target modes. To mitigate this effect, we consider ancillary modes and realize a $4\times4$ transformation that reaches $93.8\%\pm4.8\%$ correlation with only $5N^2$ tunable elements, where $N=4$ denotes the number of spatial modes. The best-performing realization reaches $98.3\%$ correlation with the target. Our results demonstrate that thermo-optic control of multimode waveguides offers an approach to fully-integrated wavefront shaping and programmable linear optical transformations, with potential applications in classical and quantum photonic processing

We consider a reversible diffusion with unknown drift, observed through trajectories, and construct samplers of its invariant law. The trajectories contain samples of this law, but a sampler built from them by density or score estimation inherits the errors of these estimates, in particular on the barriers between metastable states. The trajectories also contain the dynamics, and for a reversible diffusion the ratio between the law of the process and its invariant law solves the backward Kolmogorov equation, so that the eigenpairs of the generator propagate it in closed form. Backward Kolmogorov transport (BKT) evaluates this ratio with eigenpairs estimated from the trajectories and coefficients computed once from the initial particles, and moves the particles along the Wasserstein gradient flow of the Kullback-Leibler divergence. The particles do not interact, BKT defines a transport map, and no density, score or drift is estimated. With exact eigenpairs BKT transports the spectral projection of the initial law exactly when this projection is positive. For estimated eigenpairs we prove a transport identity in which truncation enters only through the initial law and estimation only through the residual of the eigenpairs, and a local stability bound in the 2-Wasserstein distance. With coefficients computed from the transported particles, the sampling error of the retained modes cancels, and a central limit theorem identifies the asymptotic variance. Experiments on Ornstein-Uhlenbeck processes, multi-well potentials, separable products and alanine dipeptide, including comparisons with particle methods based on density estimates, agree with these results, and with an accurate spectrum the errors of BKT reach or fall below those of independent samples.

The compact four-dimensional manifold $\mathbb{CP}_2\# 3\overline{\mathbb{CP}_2}$ is known to admit a toric Kähler-Einstein metric $g_{\text{KE}}$, but the metric is not known in closed form, which makes it difficult to draw conclusions about its geometry. In this article, we use a combination of analytic and computer-assisted techniques to produce an approximate Einstein metric $g$ described explicitly herein, and also prove that the true Einstein metric $g_{\text{KE}}$ is close to $g$, where both the closeness and the topology are described explicitly. As an application, we prove bounds on the first invariant eigenvalue of the Laplace-Beltrami operator, and prove that this Kähler-Einstein metric does not have positive holomorphic sectional curvature everywhere.

Disc-type phase-change memory is a promising device architecture for analog in-memory computing, enabled by the unique physical properties of ultra-thin phase-change materials and the device geometry. In this study, we develop a comparative analytical framework using compact electro-thermal models to examine the state dependent readout and programming behavior of these devices. The framework provides insight into the fundamental physical mechanisms responsible for their enhanced functionality and highlights promising directions for further device optimization and performance improvement.

The energy spectrum and mass composition of cosmic rays are measured by two complementary classes of instruments: space- and balloon-borne detectors that resolve individual elements up to sub-PeV energies, and ground-based air-shower observatories that extend the reach to beyond $10^{11}$ GeV but resolve only broad mass groups. The Global Spline Fit (GSF) is a data-driven model that combines both into a single, self-consistent description of the flux of all elements from hydrogen to nickel. The flux of four leading mass groups is parametrized by cubic basis splines, imposing smoothness but no astrophysical expectation on the spectral shape, while the energy-scale offsets of the participating experiments are cross-calibrated within their quoted systematic uncertainties as part of the fit. The model is defined at the local interstellar spectrum, with the effect of solar modulation at the lowest energies accounted for in the fit. The fit uses the most precise recent data, among them the elemental spectra from AMS-02, CALET, and DAMPE, the knee-region measurements of LHAASO, and the fluorescence-based composition of the Pierre Auger Observatory, and describes about one thousand data points with $\chi^2/\mathrm{ndf}\approx 1.3$, or 0.83 after de-weighting localized disagreements between data sets, demonstrating that the global body of cosmic-ray data is consistent once energy scales are aligned. The model delivers the flux, the mass composition, and their full covariance, along with a compact reduced representation for uncertainty propagation. We further provide the cosmic-ray nucleon flux, which differs from widely used parametrizations by 20-50% over four decades in energy. This exceeds the remaining model uncertainty several times over and has direct consequences for atmospheric neutrino and muon flux predictions.

Recent advances in intrinsic two-dimensional (2D) magnets have created a need for a unified understanding of finite-temperature phase transitions across different spin-symmetry classes. Here, we investigate finite-temperature magnetism in the classical 2D Heisenberg model using large-scale Monte Carlo simulations, continuously spanning the easy-plane, isotropic, and easy-axis regimes. We find that characteristic temperatures are strongly affected by the interplay of finite-size effects and spin symmetry, induced by magnetocrystalline anisotropy, being most pronounced in the isotropic Heisenberg regime and substantially reduced toward the easy-plane and easy-axis limits. Examining Berezinskii–Kosterlitz–Thouless (BKT) physics in the easy-plane regime, we find that the characteristic temperatures independently estimated from the magnetization and heat capacity deviate significantly from those proposed by BKT theory, but match a previously reported anomaly in the XY-model. We report that characteristic temperatures instead are correlated with the proliferation of vortex-antivortex pairs, suggesting the gain in entropy by their accelerated nucleation as the origin of the anomaly. Establishing this connection both theoretically and numerically, we argue that the thermodynamic characteristic temperature in finite easy-plane Heisenberg magnets, including the deviation from BKT theory, is subject to the interplay between finite-size spin correlations and vortex proliferation. These results clarify how experimental and technologically relevant temperature scales evolve with magnetic anisotropy, spin symmetry, and system size in finite 2D magnets.

We present GEM (Ghost Embedding Method), an open-source software package written in Python for computing equilibrium properties of strongly correlated electronic systems within the ghost-Gutzwiller approximation method. GEM provides a computationally efficient framework for studying multi-orbital lattice models. It supports zero- and finite-temperature calculations and symmetry broken phases. It is integrated with the TRIQS ecosystem, providing tools for model construction, self-consistent solution, and evaluation of physical observables. We first detail the method's theoretical formulation, then we present the software architecture, and finally we introduce some practical workflow, which also validates the implementation against established results. In particular, we illustrate the capabilities of GEM through multiorbital and finite-temperature applications and discuss its computational cost relative to more demanding quantum embedding approaches.

Near-term quantum optimizers accommodate roughly a hundred binary variables, requiring large Quadratic Unconstrained Binary Optimization problems to be decomposed into hardware-sized subproblems while other variables remain fixed. Variables are typically selected by ranking the objective changes from individual flips. We show that this rule is uninformative once the incumbent is optimal under single-variable flips: every score represents a cost, while remaining improvements depend on overlooked pairwise interactions. A second-order expansion instead yields a prize-collecting densest-subgraph selection problem, solvable greedily in time linear in the number of variables, and two solver-free bounds bracketing the improvement achievable within a selected subset. On transportation networks from Chicago and Philadelphia, our rule with 16-variable subproblems outperforms random selection with 64, demonstrating that quadrupling device capacity cannot compensate for weaker selection. Replacing geometric adjacency with road-network connectivity widens the margin by a factor of 1.6-1.9. With the selection trace fixed, varying the fraction of subproblems solved on a 120-qubit device from zero to one leaves the final objective unchanged to six significant figures. At tested hardware-accessible sizes, gains therefore arise from selection rather than the backend. Hardware feasibility is limited by coupling terms: 120-variable problems fail to compile with 7,260 terms but succeed with 5,118. Compilation scales almost quadratically with term count and dominates execution cost, reaching 1,752 seconds versus 469 seconds of quantum processing.

We present a systematic study of the ground states of pentaquark systems using the neural network variational Monte Carlo method within the constituent quark potential model. We investigate all manifestly exotic pentaquark systems with negative parity, which cannot mix with the conventional baryons through the creation and annihilation of light or strange quark pair. We exhaust 387 color, spin, and isospin configurations and identify 21 pentaquark bound state candidates with binding energies ranging from $2$ to $15$ MeV. A striking observation is that all of the bound states are shallowly bound molecular states, and a deeply bound pentaquark state does not exist. The $QQqq\bar{Q}$, $ssqq\bar{Q}$, $Qsqq\bar{Q}$ and $Qqqq\bar{Q}$ bound states are composed of a heavy vector meson and a baryon, while the $QQqq\bar{s}$ and $Qqqq\bar{s}$ bound states are composed of a $K$ meson and a heavy baryon. As a cross-validation, the ground-state energies of the unbound systems converge to the baryon–meson thresholds from above, which are consistent with the S-wave scattering states and provide a reliable baseline for the bound-state criterion. Especially, we reproduce the lowest scattering states $\eta_c N$ and $\eta_c \Lambda$ in the $qqqc\bar{c}$ and $qqsc\bar{c}$ channels respectively, where the hidden-charm pentaquark resonances were observed experimentally. We also find that all fully heavy pentaquark states are unbound. Our results provide valuable guidance for future pentaquark searches at LHCb, Belle II, and other experiments.