Papers

Projective representations arise naturally in physics and representation theory, and determining whether they can be linearized has been a fundamental problem. In this work, we study the analogous problem for quantum cellular automata (QCA) representations, which incorporate locality constraints imposed by a metric space $X$. Over an arbitrary field $\mathbb{F}$, we develop an obstruction theory for the linearization of QCA representations, using the algebraic $K$-theory spectrum of QCA constructed in previous work of the authors. The resulting obstructions are governed by the homotopy type of the QCA spaces, from which we extract universal obstruction classes to linearization. In the complex algebraic and unitary case, we also fully compute the homotopy types of the QCA spaces over a point, a line, and a plane.

Defect-driven phase instability critically influences the structural reliability of ultrawide bandgap oxides, yet direct nanoscale metrics linking local chemistry to structural transformation remain limited. Here, we introduce a coordination-sensitive atom probe tomography framework that quantitatively resolves reductions in local cation coordination and links them directly to defect-driven phase transformation. Using Si-doped beta-(AlxGa1-x)2O3 heterostructures with controlled Al composition (6-17%) and doping levels (10^17-10^20 cm^-3), we show that gamma-phase inclusions emerge exclusively under the combined conditions of elevated Al content and heavy Si doping. Two-dimensional compositional mapping reveals pronounced lateral Al/Ga inhomogeneity in these regions, while nearest-neighbor and radial distribution analyses quantitatively resolve a significant reduction in first-shell Ga coordination, consistent with local cation deficiency. Correlative scanning transmission electron microscopy confirms that these coordination-depleted regions coincide spatially with gamma-phase inclusions. Density functional theory further supports this mechanism, demonstrating that Al incorporation reduces monoclinic lattice stability and, in conjunction with donor-induced vacancy formation, facilitates vacancy-mediated cation rearrangement and coordination collapse. Together, these results establish coordination loss as a measurable nanoscale signature directly linked to defect-driven phase instability. This framework provides a generalizable approach for probing defect-driven phase instability in doped and alloyed ultrawide bandgap semiconductors.

Squeezed vacuum lets gravitational-wave detectors and other quantum sensors surpass the standard quantum limit, and is optimal in the loss-limited regime; phase noise breaks this optimality. Numerically optimizing the quantum Fisher information across the loss and phase-noise landscape, we identify non-Gaussian states that outperform any Gaussian state. These fall into three classes: Fock-like, cubic-phase-like, and states with discrete rotational symmetry. Limiting the average number of photons in the input state to $\bar{n}=5$, with $1-\eta = 5\%$ photon loss and 200 mrad phase noise, the non-Gaussian advantage reaches up to 2.2 dB. Furthermore, we observe that the non-Gaussian advantage can persist even when the measurement strategy is homodyne detection.

Probabilistic weather forecasting is undergoing rapid transformation with artificial intelligence (AI). In traditional numerical weather prediction, computing power can limit how well ensemble forecasts approximate the unknown statistical distribution of future states. AI models facilitate larger ensembles and are trained with probabilistic considerations, ideally leading to better uncertainty quantification. Forecasts from these state-of-the-art models are often considered well-calibrated. However, here we show that the statistical coverage of such models, the ultimate measure of calibration, can struggle, especially on extreme events. To address this shortcoming, we employ conformal prediction, a class of statistical methods that mathematically guarantees coverage under no distributional assumptions, unlike previous post-processing techniques. We apply online conformal prediction to temperature and precipitation forecasts (including extremes) of three leading global weather models, GenCast, NeuralGCM, and AIFS-ENS, ensuring calibrated uncertainty at no expense to other probabilistic metrics. This post-processing method can be applied to any forecasting model.

Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.

Sub-bandgap optical absorption in AlN between 2 eV and 4 eV is widely observed, but its microscopic origin remains contested. Using photo-induced electron paramagnetic resonance (photo-EPR) and optical absorption spectroscopy on the same samples, we demonstrate a correlation between this absorption band and the neutral charge state of substitutional carbon on the nitrogen site (C$_N$). Hybrid functional calculations of the optical absorption spectra show that a transition involving C$_N$ and the valence band occurs near 3.3 eV, which agrees well with a peak identified within the measured optical absorption between 2 eV and 4 eV. This conclusion requires the combined ability to manipulate the charge state of carbon using photo-EPR and to use first-principles calculations of the absorption line shape that account for the dispersion of the valence band and the energy dependence of the optical matrix elements.

We propose a unified framework that connects inflationary dynamics with dark matter production within a supersymmetric $U(1)_{B-L}$ extension of the Standard Model. The setup is based on smooth hybrid inflation embedded in supergravity, with a non-minimal Kahler potential ensuring control of higher-order corrections. The model involves three scalar fields: the inflaton $\sigma$, an auxiliary field $\zeta$ responsible for ending inflation, and a singlet mediator $\eta$ that links the inflationary and dark sectors. Dark matter is realized as an inert scalar stabilized by a $\mathbb{Z}_2$ symmetry and produced non-thermally via reheating dynamics. We show that reproducing the observed dark matter relic abundance imposes strong constraints on the inflationary sector, significantly reducing the allowed parameter space. As a result, the scalar spectral index is tightly constrained to $n_s \simeq 0.972 - 0.974$, consistent with current observational bounds. While the inflaton-dark matter coupling has a negligible effect on the background evolution, it induces observable modifications in the tensor-to-scalar ratio and the spectrum of primordial gravitational waves. This establishes a direct link between dark matter physics and inflationary observables.

We study the exclusive production of dileptons in proton–proton collisions as a probe of the proton charge-radius scale. Using a dipole form factor model, we compare the conventional choice of $\Lambda^2=0.71$~GeV$^2$ with PDG test scenarios corresponding to $r_p=0.8751 \pm 0.0061$~fm and $r_p=0.84087 \pm 0.00039$~fm, representative of the historical large-radius from CODATA and smaller-radius from muonic-hydrogen determinations, respectively. The sensitivity is greatest at large dilepton invariant masses and forward/backward rapidity. Fitting to the current ATLAS and CMS data within the adopted model gives $\Lambda^2 = 0.465 \pm 0.056~\mathrm{GeV}^2$, corresponding to an effective radius $r_p = 1.002 \pm 0.038~\mathrm{fm}$, which indicates non-trivial sensitivity on the proton radius scale, but is not yet a definitive solution to the proton radius puzzle. While this result depends on the theoretical model used in the calculation, it shows that exclusive dilepton production at LHC can provide complementary model-dependent information on the proton electromagnetic forms factor.

The (2+1)D U(1) pure gauge theory always exists in the confining phase, with strings of non-zero string tension giving a characteristic linear potential between static charges. This makes it a useful testing ground for quantum computing methods designed to study string dynamics of confining gauge theories. Here we implement a minimal U(1) quantum link model on a quantum computer with qubit degrees of freedom representing the dual height variables of the model. This facilitates an efficient realization of plaquette interactions and enables effective calculations of real-time dynamics that are inaccessible to traditional quantum Monte Carlo. A specifically tailored lattice geometry is chosen to match the heavy-hexagonal geometry of the IBM quantum hardware used here, minimizing non-adjacent qubit interactions. By performing quantum quenches from a simple initial string state, we probe the transverse quantum fluctuations of the string before it thermalizes. Our experimental results from digital quantum simulations, with up to 112 qubits, show good agreement with reference tensor-network calculations at short times and with thermal averages at long times. Near the phase transition, the quench dynamics exhibit large fluctuations of the initial string that extend across both spatial dimensions of the lattice. Nonetheless, our error-mitigated estimators from the quantum hardware also give accurate predictions in that regime, with noise-induced violations of local gauge symmetries comparable to finite-bond-dimension tensor-network results.

Diamond hosts optically active point defects central to quantum technologies, yet the carbon self-interstitials introduced during growth and irradiation compete with them and form new defects whose configurational landscape is poorly charted, as subtle energy differences govern the competing minima and pathways. Here we build an interstitial-focused dataset by active learning and benchmark three machine-learning interatomic potentials – GAP, NEP and the equivariant MACE – against density functional theory for energies, forces and migration barriers. MACE reproduces the reference energetics and relative stabilities, whereas the others can misorder the ground states. Annealing molecular dynamics with the validated potentials uncovers a series of previously unreported carbon interstitial clusters, from di- to octa-interstitials – several introducing in-gap states of interest as colour centres – and shows that their metastability is governed by kinetically accessible pathways rather than energetic ordering. These results chart the interstitial defect landscape and accelerate defect discovery for quantum technologies.

We present a complete classification of concave kite central configurations in the planar 4-body problem with three equal masses. There are two different types of central configurations when the fourth mass lies inside or outside the triangle formed by the other three. Using a rigorous computer-assisted analytical method and a fixed coordinate system, we show that the central configurations in each case form a one-parameter family and obtain a complete classification of these configurations. In addition, we rigorously show the existence and types of the bifurcation points in the reduced space. We also provide two numerical global bifurcation pictures in the entire planar 4-body configuration space as the mass ratio varies from $0$ to $+\infty$, including symmetric and asymmetric concave central configurations with three equal masses.

Fault-tolerant quantum computation requires the coordinated action of three distinct systems: classical control logic, quantum hardware, and classical error decoders. Current scheduling models treat logical operations as atomic, hiding the fact that these subsystems operate sequentially and spend significant time idle. We present a pipelined execution framework that decomposes each logical operation into its component stages i.e. Control, Execute, and Decode. Building on this, we discuss some speculation strategies that allow successor operations to begin processing before their predecessors have completed decoding. We evaluate our framework on several common benchmarks and show that pipelining with speculation reduces total pipeline steps by 20-40% compared to a no-speculation baseline. The most aggressive strategy consistently outperforms conservative alternatives, even though partial rollback is needed at times, because the per-rollback penalty is small relative to the parallelism gained. We further show that speculation facilitates load balancing by distributing work more evenly across the heterogeneous subsystems of a fault-tolerant quantum computer, converting idle time into useful computation while also saving on execution time.

This experimental work explores the flow field around a three-dimensional expansion-compression geometry on a slender cone at Mach 5 and 8 using high-frequency pressure sensors, high-framerate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\circ$ cone geometry has a hyperbolic slice acting as an expansion corner which is then followed by a $30^\circ$ finite-span compression ramp. The freestream Reynolds number was varied so that the boundary layer approaching the expansion corner was either laminar, transitional or turbulent. At laminar or early transitional conditions, the separation shock locks onto the expansion corner and the separation region encompasses most of the slice, with the separation shear layer flapping at a preferred frequency. As Reynolds number is increased, the separation shock moves downstream onto the slice, the separation bubble shrinks, and the shear layer flapping frequency increases while its amplitude drops. In all cases, large-scale low-frequency breathing motions are observed. The strong relaminarization across the expansion corner at Mach 8 prevents the shock/boundary-layer interaction from reaching truly turbulent conditions and fundamentally changes its behavior on this non-canonical geometry.

We study the problem of emergency operation center placement in disaster response, where a minimal number of hubs must be selected to ensure timely coverage of all affected locations. This task can be formulated as a minimum dominating set problem on a graph encoding reachability within a target response time. We propose a hybrid quantum-classical approximation framework that leverages neutral-atom quantum computers as independent set samplers. Candidate dominating sets are constructed from both small maximal independent sets and complements of large independent sets, and are subsequently refined via a lightweight classical procedure. We benchmark the approach on synthetic instances and realistic case studies, and implement it on the Fresnel quantum processor by Pasqal, solving instances of up to 100 nodes. Our results show that quantum-generated samples, despite hardware noise, enable near-optimal solutions of the placement problem. Overall, our results demonstrate that neutral-atom devices operating in analog mode can already be used to tackle graph optimization problems for real-world applications.

Electric field noise produced by the surface of ion trap electrodes reduces the fidelity of quantum computing operations. Despite decades of investigation its microscopic origins remain unclear. Here, we measure electric field noise at trapping locations along the symmetry axis of a linear surface Paul trap. We find that noise levels vary by three orders-of-magnitude in one 600$\,\mu$m section of the trap. Optical and scanning electron microscope images show micron-sized particles close to the trapping locations with the highest noise levels. We find that modeling the particles as a lossy dielectric with a effective loss tangent $\tan\theta=0.33(0.06)$ describes the magnitude of the noise, as well as its spatial and frequency dependence. Our observations may explain the large variation of reported noise levels in literature.

The growth of a thin film of a high-entropy AlCoCuFeNi alloy on a silicon (100) substrate was studied using molecular dynamics modeling. The simulation was carried out using the embedded atom model to describe the interactions among Al, Co, Cu, Ni, and Fe atoms. The interaction between Al, Co, Cu, Fe, Ni atoms and the Si substrate was modeled using the Lennard-Jones potential, while the interaction between silicon atoms was described using the Stillinger-Weber potential. The total simulation time was 50 ns. It was found that small clusters were formed at the first stage of deposition and that crystallization started after approximately 5 ns of simulation, when the characteristic cluster size was about 2 nm. At the end of the simulation, after 50 ns of modeling, the simulated film contained face-centered cubic, body-centered cubic, hexagonal close-packed, and amorphous phases. Analysis of the radial distribution function made it possible to determine nearest-neighbor distances and estimate the lattice parameters of these phases.

We argue land-sea contrast is an important driver of spatial patterns of observed surface temperature and atmospheric circulation trends, including the negative Inter-Decadal Pacific Oscillation (IPO)-like tendency across the Pacific basin. Observed and modeled trends display an overall decline in sea level pressure over the faster-warming land, with a spatial pattern that resembles the seasonal cycle and modeled response to land heating. Coupled historical forcing climate model simulations underestimate the land-sea warming ratio. It is only in the early response of abrupt CO2 quadrupling climate model simulations that climate models are able to recreate the observed land-sea warming ratio, in which case a negative IPO-like sea level pressure trend and surface warming pattern over the Pacific comparable to observed trends are seen. We propose that some discrepancies between observed trends and those predicted by climate models are explained by the underestimation of the land-sea warming ratio by climate models.

The long-term evolution of planetary systems around solar-type stars is governed by the interplay between stellar expansion, tidal interactions, and mass loss during the red giant branch (RGB) and asymptotic giant branch (AGB) phases. However, tidal dissipation efficiencies and AGB mass-loss rates both remain poorly constrained, leading to significant uncertainty in predicting the fate of planetary systems, in particular, that of the Earth orbiting the ageing Sun. We reassess the survival of the Earth and the inner Solar System planets during the entire evolution of the Sun, focusing on the impact of updated tidal dissipation prescriptions and varying AGB mass-loss rates. We modelled the orbital evolution of the Earth using stellar evolution tracks for a solar-mass star. We compared these results with outcomes obtained using previously published and commonly adopted tidal prescriptions, and we explored a range of AGB mass-loss rates. We find that the predicted fate of the Earth is highly sensitive to the tidal model and the assumed mass-loss rate. Based on updated tidal dissipation prescriptions, Earth survives the RGB and AGB phases of the Sun. In contrast, the use of earlier tidal dissipation prescriptions leads to engulfment during the AGB phase. Furthermore, low AGB mass-loss rates result in engulfment, and vice versa. Using the observed mass-loss rates of the AGB star L2 Pup as a proxy for the Sun's future AGB mass-loss rate results in the survival of the Earth during the AGB phase when combined with our tidal dissipation evaluation. Given the current observational uncertainties in AGB mass-loss rates, the ultimate fate of the Earth remains uncertain, highlighting the need for improved constraints on the late-stages of stellar evolution. However, considering observational proxies for the Sun during the AGB phase, it is likely that the Earth will survive the Sun's giant phases.

We theoretically investigate the optical spin-injection response in different stoichiometric configurations of graphane and fluorographene using density functional theory. Our goal is to determine which configuration yields the strongest degree of spin polarization. The results show that the fluorographene zigzag configuration yields the best degree of spin polarization response (${\cal DSP}^{\mathrm{z}}$), with 98% spin polarized electrons at the band edge and over a wide range of excitation photon energies. In contrast, other graphane and fluorographene configurations achieve a ${\cal DSP}^{\mathrm{z}}$ of roughly 83–100%, but only within a limited photon-excitation energy range. In structures with low spin-orbit coupling, the degree of spin polarization is close to 100% over a wide range of photon energies. For higher spin-orbit coupling, this strong response appears, but only in a narrow photon energy region. Additionally, under the band-resolved decomposition scheme, the contributions of different band-to-band transitions to the ${\cal DSP}^{\mathrm{z}}$ spectrum are identified by summing only the selected valence and conduction bands. Our findings show that almost the entire ${\cal DSP}^{\mathrm{z}}$ spectrum of the fluorographene zigzag configuration comes from transitions that involve only the top valence band, which is a mixture of C–p and F–p states.

We perform a comprehensive analysis of a charged parent freeze-in dark matter model, focusing on scenarios where the Universe reheats to a temperature comparable to or lower than the mass scales of the theory. In such configurations, dark matter production is Boltzmann-suppressed, allowing for stronger couplings between dark matter and the Standard Model thermal bath while still reproducing the observed relic abundance. We emphasize the non-trivial interplay between the reheating temperature, the mediator and dark matter masses and the coupling strength. We show that tracking the number density evolution of both dark matter and the mediator is essential to obtain reliable predictions, including unexpected behaviors such as the mediator non-equilibration due to fast decays. Lastly, we explore the phenomenological implications of this scenario, updating constraints from LHC searches and lepton flavour-violating decays and highlighting the complementarity of these searches in probing the cosmologically viable parameter space.

We study a $q$-deformed extension of Brans-Dicke gravity in a spatially flat Friedmann-Lemaître-Robertson-Walker space-time. The deformation enters through a coupling function that modifies the effective gravitational strength and leads to generalized Friedmann equations. In the matter-free sector, we obtain exact analytic solutions for the scale factor and the Brans-Dicke scalar field, and recast the scalar contribution as an effective fluid. We show that the corresponding equation-of-state parameter and the deceleration parameter are constants and depend only on the Brans-Dicke coupling $\omega$ and the deformation function, allowing the scalar sector to mimic radiation-, matter-, or dark-energy-like behavior for a restricted region of parameter space.

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive. To address this, the chapter surveys state-of-the-art SciML methods for building efficient surrogate models, including linear reduced-order techniques based on Singular Value Decomposition (such as Dynamic Mode Decomposition) and nonlinear neural network approaches like Physics-Informed Neural Networks (PINNs) and $\beta$-Variational Autoencoders ($\beta$-VAEs). It first covers the authors' work combining these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. It then presents two new contributions: surrogate modeling of turbidity currents via PINNs, and the extraction of disentangled nonlinear modes from thermal flows using $\beta$-VAEs. Governing equations and representative benchmarks, including lock-exchange flows and Rayleigh-Bénard convection, illustrate these methodologies. The chapter is intentionally long, covering both the mathematical and physical foundations of coupled fluid flow and the computational aspects of state-of-the-art modeling. Overall, it demonstrates how SciML enables fast, accurate approximations of complex coupled systems within the specific data regimes and modeling assumptions considered, while substantially reducing computational cost relative to full-order simulations. Broader capabilities such as real-time prediction and uncertainty quantification remain active research directions whose feasibility depends strongly on the problem at hand.

Neuroevolution Potential (NEP) is one of the most efficient machine-learned interatomic potential frameworks for large-scale atomistic simulations. However, its original training strategy remains computationally demanding, limiting systematic exploration of model architectures and training protocols. Here, we present TorchNEP, a PyTorch-based implementation of NEP that combines analytically derived gradients, adaptive optimization, and a two-stage training strategy. TorchNEP accelerates training by more than two orders of magnitude while maintaining full compatibility with existing NEP models. We further show that the improvement in predictive accuracy primarily originates from the two-stage training protocol rather than the optimization algorithm itself. Across diverse benchmark datasets, TorchNEP consistently improves force and stress predictions while maintaining comparable or improved energy accuracy. Benchmark evaluations on elemental and alloy systems demonstrate enhanced predictive performance for both atomic configurations and key materials properties. Furthermore, we show that increasing model complexity does not necessarily improve predictive performance despite reducing training errors. Overall, TorchNEP provides an efficient and flexible training framework for developing more accurate and robust machine-learned interatomic potentials.

The expansion of the FIFA World Cup to 48 teams in 2026 introduces structural challenges in tournament design. To populate a 32-team knockout bracket from 12 groups of four, the current FIFA rules select the eight best third-placed teams using a global ranking across all groups. This global coupling creates several major problems: a combinatorial explosion of 495 possible bracket configurations; a fundamentally biased and unequal selection of third-placed qualifiers; lack of a clear path for group winners; vulnerability to collusion and ranking manipulation; and no guarantee of same-group separation beyond the first knockout round. We propose a simple unified solution called the four-section bracket (FSB) rule: split the 12 groups into four sections of three groups. All group winners, runners-up, and the two best third-placed teams in each section advance. Group winners remain in their home sections as local anchors, while lower-ranked qualifiers are transferred to other sections according to a fixed, symmetric rule. This structure guarantees same-group separation until the semifinal, protects the top eight group winners with a predictable knockout path, and reduces bracket complexity from 495 configurations to just one invariant topology per section, recovering the symmetry of the traditional 32-team format. We show substantial improvements in competitive fairness and scheduling predictability.

Server-aided Bell-state networks with sequential local encoding are an established approach to mediated key distribution. Against this background, we study a Loop-Back architecture in which two source-free, detector-free users transform the same traveling qubit. Alice privately samples $r\in\mathbb{Z}*2^2$, prepares $|\beta_r\rangle$ over the complete Bell basis, retains one qubit, and uses $r$ as the reference for the returned pair. A deterministic Pauli-composition mode, $U*{\mathrm{eff}}=U_2U_1$, serves as a reference to prior serial-unitary protocols. The main extension instead uses the two same-axis settings $R(\pm\alpha)$ and a reference-versus-complement Bell test. Opposite rotations cancel, whereas equal rotations add, so $P(C\mid\mathrm{disagreement})=0$ and $P(C\mid\mathrm{agreement})=\sin^2(2\alpha)$. At $\alpha=\pi/8$, agreement is certified with probability $1/2$, and the overall conclusive-key probability is $1/4$ for unbiased choices. The same event supplies one shared raw-key bit. For the Pauli mode, a one-qubit Pauli twirl hides either user's factor from an endpoint mediator that may prepare an arbitrary qubit–ancilla state and choose the final measurement, provided the other Pauli is uniform and the traveler is inaccessible between users. The rotational guarantee is narrower: common-sign privacy holds only for the prescribed Bell source and coarse-grained instrument. A polarization implementation can normalize the private reference to the singlet and use a beam splitter with verified two-photon detection; loss produces a third, discarded outcome. The proposal is theoretical and does not claim composable security or experimental validation.

We revisit flavor oscillations in vacuum in terms of the propagation time of intermediate states. In the limit of a long propagation time (or distance), degenerate intermediate states exhibit oscillatory behavior, as described by the Jacob–Sachs (or Grimus–Stockinger) theorem within wave-packet quantum field theory. By explicitly evaluating the relevant integrals using the saddle-point method, we derive an extended expression for the flavor-changing amplitude that remains valid even for shorter propagation times. We show that oscillations occur only when the propagation time exceeds a threshold set by the energy uncertainty of the external wave packets and by the decay width of the propagating particle. For shorter propagation, the intermediate particle behaves as a purely virtual state, in the sense that it cannot propagate over a macroscopic distance. Although a direct experimental test of the transition from virtual to real propagation is challenging, since it typically occurs at microscopic scales, our result implies that the Jacob–Sachs theorem holds to higher accuracy than previously expected, even at short propagation times. Our formalism applies not only to neutrinos but also to other propagating particles, and future improvements in energy resolution may make this threshold observable.

The electronegativity equalization principle provides a simple framework to describe charge redistribution, yet its conventional formulation is limited to a first-order description based on chemical potential equalization. In this work, we introduce 'multi-equalization,' a generalized framework that extends this concept by incorporating higher-order responses within Conceptual Density Functional Theory. This approach represents molecules as sets of flexible electron density partitions, allowing different electronic descriptions (e.g., atomic densities or localized orbitals) to be treated within a unified formalism. We demonstrate that correlations between energy and density derivatives with respect to the number of electrons lead to the simultaneous equalization of multiple descriptors, including chemical hardness and Fukui indices. A constructive algorithm is introduced to determine the optimal density partitions satisfying these multi-equalization conditions. This scheme provides a consistent description of both global charge transfer and local reactivity, overcoming the intrinsic limitations of traditional electronegativity equalization models. Notably, the inclusion of density response functions enables local hardness equalization, introducing spatial resolution into reactivity descriptions. Under multi-equalization, local reactivity descriptors become constrained functionals of the global electron density. This framework establishes a deeper connection between charge equalization models and formal density functional theory, offering a theoretically grounded route toward improved predictions of molecular reactivity.

Solar eruptive events are generally believed to involve magnetic flux ropes (MFR), formed either in the pre-eruptive phase of the event or during the eruption itself. These MFR eruptions exhibit significant complexity and variations due to the interplay of the physical mechanisms involved, in particular magnetic reconnection and ideal instabilities. This work considers the effect of the background magnetic field on the nature of eruptions with pre-existing MFRs. We used a new MHD model to simulate the whole MFR eruption process, including the pre-eruptive stage and the initiation. Three simulations were performed, all of which used an identical bipolar active region, but with different background magnetic fields in the three cases. The simulations resulted in two successful eruptions (CMEs) and one failed eruption (a confined flare). We analyzed the energetics and the acceleration of the MFR in detail, and found a transition to a rapid exponential rise phase in two of the simulations. We also calculated the criterion for the torus instability and the timing of the breakout and flare reconnections. Our results show that the rapid exponential rise phase is likely due to breakout reconnection. We conclude that a background field antiparallel to the active-region field lowers the magnetic free-energy threshold for eruption; but, does not guarantee a successful eruption. We also found that an antiparallel background field leads to faster flare reconnection, but of shorter duration. Our findings underscore the importance of the background magnetic field in understanding CMEs.

We study the problem of deciding, given a mechanism to prepare a quantum state $\rho$ and a value $\varepsilon > 0$, whether there is some non-identity Pauli matrix $P$ such that $|Tr(P \rho)| \geq \varepsilon$. We consider that the state $\rho$ is described as the result of tracing out some of the qubits of a pure state prepared by a circuit $C$, and we assume the promise that either there is a Pauli matrix satisfying the stated condition or, instead, that for all non-identity Pauli matrices $P$ it is the case that $|Tr(P\rho)|\leq \varepsilon/2$. The problem is in $QCMA$, and we prove that if it belongs to $BQP$ then $NP \subseteq BQP$. The result is obtained through a reduction from the minimum-weight code problem, and it holds even when $\rho$ is assumed to be a pure state (i.e. when no qubits are discarded) and $\varepsilon$ is constant. This resolves an open question regarding the existence of efficient tomographic procedures to find the largest coefficients of a quantum state in the Pauli basis: namely, they do not exist under the standard hypothesis $NP \nsubseteq BQP$.

A variety of experiments are operating or planned to search for displaced decays of light long-lived dark sector particles. In case such a state is discovered, the next step is determining its quantum numbers. We identify an angular observable, reconstructible solely from the decay products' four-momenta, that exhibits an anisotropic distribution for vector bosons from light meson decays and an isotropic distribution for scalars. We demonstrate that searches at DUNE, SHiP and FASER2 will be able to identify the mediator spin in sizable regions of yet unconstrained parameter space.