Papers

Understanding how common dielectric substrates influence the spin transport properties of graphene is essential for advancing graphene-based spintronic technologies. Here we use a comprehensive set of numerical simulations to reveal how a SiO$_2$ substrate modifies the spin texture and governs spin relaxation in graphene. Using first-principles density matrix dynamics simulations, as well as tight-binding (TB) transport simulations, we quantify the effects of electron-phonon scattering, impurity scattering, and electrostatic disorder on the spin relaxation process. We find that a 2D SiO$_2$ substrate induces a predominantly Rashba-type helical spin texture in graphene, leading to a spin lifetime anisotropy of 1/2. Meanwhile, bulk SiO$_2$ breaks in-plane symmetry in graphene, leading to anisotropic in-plane and out-of-plane components in the spin texture, which we capture with a newly-developed TB model of graphene. Transport simulations under realistic disorder conditions reveal a spin lifetime anisotropy between 0.5 and 1, similar to what is seen in measurements of graphene spin valves on a SiO$_2$ substrate. Our results reveal a more complex picture of spin relaxation at the ubiquitous graphene/SiO$_2$ interface, beyond the standard Rashba model, providing critical insight for interpreting experiments and guiding substrate engineering for graphene spintronics.

Recent experiments on superconducting films have revealed an acoustic plasmon mode that depends critically on the superconducting transition, directly challenging the long-standing Anderson-Higgs paradigm regarding the stiffness of the plasma spectrum in superconductors. In this Letter, we provide a microscopic theoretical framework that explains this behavior and establishes the physical conditions under which classical Anderson-Higgs constraints are bypassed. We demonstrate that in films of finite thickness, the transverse redistribution of normal and superfluid charge densities enables a unique coupling mechanism to electromagnetic radiation - a feature fundamentally absent in the conventional Carlson-Goldman scenario. Our theory predicts an acoustic mode whose dispersion, temperature scaling, and dependence on film thickness are in remarkable agreement with recent experimental observations. By delineating the regime of this acoustic response, we reconcile the observed electromagnetic activity of collective excitations with the fundamental principles of superconductivity.

Gauge fields are fundamental to modern physics, but prescribed gauge configurations are often difficult to implement in artificial systems. Here, we present a general scheme for realizing arbitrary static $\mathrm{O}(N)$ lattice gauge configurations using symmetry-protected zero modes of sublattice-imbalanced bipartite units. The target $\mathrm{O}(N)$ link on each bond is encoded in the connectivity and strengths of positive microscopic couplings. By decoupling the zero-mode manifold from the remaining modes, the target gauge Hamiltonian forms an exact spectral block of the microscopic tight-binding model rather than a perturbative approximation. We experimentally demonstrate this framework in acoustic crystals through a $\mathbb{Z}_2$ quadrupole topological insulator, an $\mathrm{SO}(2)$ Hofstadter model, and an $\mathrm{SO}(3)$ non-Abelian topological insulator. Our results provide a general and accessible route to gauge-field physics in artificial systems.

In this work, we establish the quantitative unique continuation on both $n$-dimensional simplex lattice $\Delta^{(n)}_{N}$ and $\mathbb{Z}^n$ for arbitrary $n\geq 3$.

We present a variational artificial neural-network (VANN) solution of $^{17}$F in a two-body $^{16}$O$+p$ potential model. The calculation uses a standard interaction from the literature as a controlled benchmark for testing whether a neural variational ansatz can reproduce not only bound-state energies and interior wave functions, but also the Coulomb–Whittaker tails that control halo and peripheral-capture observables. The reduced radial wave function is obtained by minimizing the Rayleigh quotient of the radial Schrödinger Hamiltonian with the constraints required by each partial wave. Because the variational energy can converge before the asymptotic normalization is correct, the ansatz combines a neural interior with the charged-particle Coulomb–Whittaker form. In the $s_{1/2}$ channel, the Pauli-forbidden $0s_{1/2}$ component is computed and the physical one-node branch is checked independently for forbidden-state contamination. The Coulomb–Whittaker-constrained VANN reproduces independent Numerov benchmarks for the compact $d_{5/2}$ ground state and the extended $s_{1/2}$ halo state in energy, nodes, rms radius, and overlap. The compact-state ANC agrees to within one percent, while the halo ANC differs by about $4.2\%$, within the larger numerical sensitivity of the asymptotic extraction. The continuum scattering states are obtained by standard Numerov integration with Coulomb matching; only the bound states are represented by the neural ansatz. Combined with these $p$-wave scattering states, the VANN bound states yield astrophysical $S$ factors consistent with published benchmarks and data within the accuracy of the adopted two-body model. The results demonstrate the usefulness of physically constrained neural wave functions for tail-sensitive nuclear calculations and identify the asymptotic region as the most sensitive part of the calculation.

Digital light processing (DLP) enables rapid fabrication of polymer structures, but fracture performance depends on multiple interacting processing variables, making exhaustive experimental characterization impractical. This work presents a data-efficient framework for process-fracture mapping of a DLP-printed photopolymer using Bayesian active learning and digital image correlation (DIC)-assisted Mode I fracture experiments. Four processing parameters were considered: layer angle, UV exposure time, layer height, and print temperature. Fracture resistance was quantified by the critical J-integral, $J_c$, obtained from three-point-bending tests with DIC-based evaluation of crack-mouth opening displacement and hinge-point kinematics. Beginning with two randomly selected conditions, Gaussian process regression (GPR) and a modified upper confidence bound (UCB)-style acquisition function selected 26 additional experiments, yielding 28 processing conditions with three replicates each. The final GPR surrogate reproduced the training data with $R^2=0.99$ and achieved leave-one-out cross-validation performance of $R^2=0.63$ and Pearson $r=0.81$. Surrogate-based sensitivity analysis quantified parameter effects and global contributions. One-at-a-time response curves revealed nonlinear conditional trends, while global Sobol analysis identified UV exposure time as the dominant processing variable, with first-order and total-order indices of 0.6780 and 0.7581, respectively. Based on total-order influence, the parameters ranked as UV exposure time, layer angle, print temperature, and layer height. The first-order Sobol indices summed to 0.8058, indicating non-negligible interaction and higher-order effects. These results demonstrate that Bayesian-active-learning-guided experimentation can efficiently recover process-fracture relationships and parameter interactions from a sparse experimental campaign.

We use Landau theory of phase transitions to design a magnetoelastic coupling descriptor that can identify magnetic materials on the brink of a first-order transition, where a strong magnetocaloric effect (MCE) can arise. The descriptor can be computed from electronic structure calculations and requires structural optimization in the paramagnetic state, which we model using special quasi-random collinear spin configurations. We first evaluate the descriptor for a set of known magnetocaloric materials and identify compounds in which the MCE is driven by magnetoelastic coupling. We then apply the descriptor in a high-throughput ab initio screening of magnetic L1$_2$ compounds. This search identifies the L1$_2$ cubic phases of Mn$_3$Ge and Mn$_3$Sb as materials with strong magnetoelastic coupling and potential for a large magnetocaloric response.

Physical computing systems exploit device dynamics for computation, but their gradient-based optimization is challenging: backpropagation through a digital twin suffers from a model-reality gap. On-device gradient computation could resolve this issue, and a handful of theoretical and experimental studies have proposed ways to achieve it. Yet a unifying theory identifying when a physical system can compute the gradient of its own performance has been missing. Here we develop such a unification based on the adjoint method: we identify sufficient conditions under which the adjoint field required for formally exact gradients can be generated on the same hardware that performs the computation. Linear and nonlinear systems obey fundamentally different conditions: for linear systems, damping or gain is admissible provided reciprocity is preserved. For nonlinear trajectory systems, the sufficient conditions are reciprocity of the linearized system and the existence of a time-reversal mirror. Algorithmically, the nonlinear case requires infinitesimal nudging, whereas linear systems admit a finite-amplitude experiment. We recover (quantum) Equilibrium Propagation, Hamiltonian echo backpropagation, fully forward mode training and in situ gradient methods in integrated-photonic and free-space-optical systems. Finally, we show that reciprocity is a special case of more general intertwining conditions. For linear systems, these permit exact on-device gradients in a class of non-Hermitian, non-reciprocal systems. For nonlinear trajectories, they combine with generalized time-reversal mirrors to cover, e.g., PT-symmetric equations. The framework also includes time-dependent parameters and Onsager-reciprocal dynamics, providing a unified basis for formally exact physical learning.

Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, progressively reducing active Pauli rows while adaptively emitting eligible two-qubit blocks in addition to single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It Pareto-dominates prior state-of-the-art compilers, requiring 1.17–1.58$\times$ fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87–5.67$\times$ on average.

The Covarying Coupling Constants (CCC) framework, developed to account for high-redshift JWST observations, contains a mechanism – a covarying-constant effective mass field keyed to local density – that modifies galactic dynamics without particle dark matter. We test it against the full Spitzer Photometry and Accurate Rotation Curves (SPARC) sample of 175 disc galaxies, extending an earlier study of a few objects. Working in an inverse formulation, in which each model predicts the baryonic rotation curve from the observed one, we compare CCC against Modified Newtonian Dynamics (MOND) and one- and two-parameter Navarro-Frenk-White (NFW) haloes on identical footing, using the reduced $\chi^2_\nu$. We show that the published sharp density turn-off in the earlier study is unphysical and replace it with a smooth transition – the density-space analogue of the MOND interpolating function, introducing no new parameter. One-parameter smooth-CCC then performs comparably to galaxy-by-galaxy fitted MOND (the lower $\chi^2_\nu$ in 56 per cent of galaxies, mean $\chi^2_\nu$ of 2.58 versus 2.65; the paired difference is not significant), while two-parameter NFW shows a substantially broader fit-quality distribution and a larger tail of poor or boundary-limited fits (mean $\chi^2_\nu \approx 7$). The CCC turn-off density is not universal (scatter 0.82 dex) and correlates with galaxy size, qualitatively consistent with a spherical reconstruction applied to flattened disc systems. Recast as an acceleration, however, $a_t = V_{\rm flat}^2/R_t$ has scatter 0.33 dex (on the 91-galaxy resolved subset) – matching the MOND scale $a_0$ (0.34 dex) – and comparable magnitude of order $2 \times 10^{-10}$ m/s$^2$, with its size correlation removed. Though not designed for galactic dynamics, CCC describes rotation curves as well as galaxy-by-galaxy fitted MOND.

Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution. RECAST combines learned correction within the numerical time-stepping loop with reconstruction of the corresponding fine-grid state from the corrected coarse history. We evaluate the framework on six one-dimensional PDE systems spanning transport, diffusion, dispersion, reaction, and wave dynamics, using spatial grids coarsened by factors of 8-16 and 1000-step closed-loop rollouts from unseen initial conditions. Across the test cases, RECAST remains closely aligned with the fine-grid reference solutions and reduces time-averaged relative error by approximately 50-92% compared with the corresponding uncorrected coarse-grid solvers. Additional tests show generalization to unseen PDE parameter values, while comparison with a contemporary coarse-correction architecture shows that RECAST achieves lower error and better long-horizon agreement with the fine-grid reference over 5000-step rollouts. These results demonstrate that the learned correction and reconstruction capabilities of RECAST can enable substantially coarser PDE evolution without the corresponding loss of solution fidelity, providing a proof-of-concept route toward machine-learning acceleration of higher-dimensional numerical simulations across science and engineering.

Quantum-selected configuration interaction (QSCI) methods use a quantum computer to identify dominant electronic configurations in the molecular ground state, while a classical computer diagonalizes the Hamiltonian within the reduced subspace spanned by those configurations. Sample-based quantum diagonalization (SQD), a leading QSCI approach, uses iterative classical post-processing to correct noisy quantum measurement to ensure that the corresponding configurations remain physically sensible. In this work, we show that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace. When classical resources are not explicitly constrained, classical uniform random sampling can reproduce SQD benchmarks as noise increases the diversity of sampled configurations. We show any fair benchmarking protocol of SQD must explicitly control diagonalization size over unique samples. We then address the problem of efficiently discovering physically relevant, energy-lowering configurations by introducing a measurement protocol based on non-orthogonal configuration interaction (NOCI). By distributing measurements across orbital bases optimized with respect to the molecular Hamiltonian, we obtain improved sample efficiency relative to measurements performed solely in the Hartree–Fock basis. Importantly, these improvements persist even under fixed classical resource budgets, demonstrating that the resulting configurations are of higher quality rather than being more numerous. Under our proposed benchmarking procedure, we establish measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.

Modular arithmetic is central to quantum algorithms for cryptographic problems, including Shor's algorithm and Grover-based cryptanalysis, with modular reduction contributing substantially to circuit cost. Pseudo-Mersenne moduli $q=2^n-c$ allow classical Crandall reduction to replace division with folding and constant arithmetic, providing a structural opportunity for more efficient quantum modular reduction than Barrett reduction. We translate this advantage into a reversible quantum setting by deriving explicit folding and normalization conditions for $2n$-bit inputs. To the best of our knowledge, this constitutes the first exact reversible quantum circuit formulation of Crandall reduction. Based on this formulation, we develop two variants: Crandall reduction-1 is designed to minimize execution cost through one-step normalization, whereas Crandall reduction-2 uses two-step normalization to support a wider range of $c$ with limited overhead. Logical resource estimates show that both variants require fewer qubits and lower T-count and T-depth than optimized folding Barrett reduction. At $n=10$, Crandall reduction-1 reduces both T-count and T-depth by approximately 46.9% relative to optimized folding Barrett reduction. Surface-code analysis further shows that, at $n=20$ under the Sparse Blossom decoder, the estimated runtimes of the two variants are 30.05 ms and 35.39 ms, respectively, compared with 53.77 ms for optimized folding Barrett reduction. These results demonstrate the practical value of exploiting modulus-specific arithmetic structure in fault-tolerant quantum circuit design.

Understanding how coherently driven quantum many-body systems redistribute energy prior to thermal equilibrium remains a central challenge in many-body physics. Here, we utilize nitrogen-vacancy (NV) magnetometry to perform micron-scale spatial imaging of room-temperature magnon dynamics in a yttrium iron garnet (YIG) thin film. We resolve a hierarchy of discrete parametric scattering events that serve as deterministic stepping stones toward thermalization. By applying a two-tone wave-mixing protocol, we first isolate the elementary four-magnon interaction and extract its coupling strength via the spatial growth of the scattering product. We then drive the system with an intense single-frequency excitation near ferromagnetic resonance, revealing that magnon-magnon interactions trigger a spontaneous, multi-generation scattering cascade. We demonstrate that in each generation, the dominant scattering channels correspond to one of the out-scattered magnons being in the slow magnon regime, reminiscent of the enhancement of optical nonlinearities in slow light systems. We capture this dynamics quantitatively using a near field magnonics framework and extract the cascade order and nonlinear coefficients directly from power-dependent frequency shifts. By revealing the multi-stage dynamical process through which monochromatic injected magnons evolve toward equilibrium, our work establishes spatially resolved magnonics as a powerful platform for visualizing non-equilibrium many-body kinetics.

Predicting the products of ionic-liquid impacts on extractor surfaces is important for electrospray-thruster lifetime analysis, yet available atomistic methods require a compromise between chemical fidelity and computational cost. Reactive force fields enable high-throughput sampling but do not explicitly resolve electronic charge redistribution and may miss relevant reaction pathways during impact, whereas mixed quantum–classical density-functional-theory molecular dynamics (DFT/MD) can capture charge redistribution and neutral-product formation at substantially higher computational cost. Pretrained atomistic foundation models have recently emerged as a potential route toward DFT-like chemical fidelity at considerably lower cost. Here, we benchmark two pretrained machine-learning interatomic potentials, MACE-MP-0 (medium) and MACE-POLAR-1, against DFT/MD and ReaxFF for geometry optimization of 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF$_4$) and for 10-100 eV impacts on a model Au extractor surface. The models reproduce several collision outcomes observed in DFT/MD, including ionic dissociation, high-energy covalent fragmentation, and, in particular, HF formation through neutralization-like chemistry that is not captured in the ReaxFF simulations. In the computational-performance benchmark, MACE-POLAR-1 and MACE-MP-0 (medium) completed each 2~ps trajectory in 5.12 and 2.54~min, respectively, corresponding to wall times approximately four orders of magnitude shorter than the DFT/MD reference under the reported benchmark conditions. These results support pretrained machine-learning potentials as a practical intermediate-cost approach for chemically resolved electrospray-impact simulations and motivate targeted fine-tuning with DFT data for broader applications in electrospray-thruster and electric-propulsion modeling.

Observationally, blue horizontal branch (BHB) stars are defined as hot stars occupying a characteristic region between the extreme blue horizontal branch and RR Lyrae variables in the Hertzsprung-Russell diagram. Most of them are interpreted as stripped core-helium-burning stars, but the role of binary interaction in their formation remains unclear. Here, we report the discovery of a metal-rich BHB star in a 0.82628-day binary system (Feige 64) comprising a $0.35\pm0.03\,M_{\odot}$ BHB star and a likely $1.26\pm0.17\,M_{\odot}$ white dwarf (WD). The BHB star has an effective temperature of $15{,}524\pm310$ K and a luminosity of $39.7\pm4.1\,L_{\odot}$. Stellar evolution modelling indicates that it is a helium-shell-burning star produced through the common-envelope channel, retaining a hydrogen-rich envelope that is more massive than previously thought for low-mass stars. This finding provides direct evidence for binary interaction in the formation of BHB stars, offering a fresh perspective on interpreting this emerging population.

We investigate the exact dynamics of first-order system–bath coherence induced by excitation exchange in bilinear bosonic models. By solving the linear Heisenberg equations, we obtain the exact evolution of system and bath operators and evaluate the first-order coherence between the system mode and the collective bath mode directly coupled to it. We analyze how this coherence depends on initial occupations, coupling strength, spectral width, and detuning, showing that its buildup and oscillatory behavior are closely related to excitation exchange and reservoir memory. We further examine controlled coherence dynamics under leakage-elimination-operator inspired modulation of the system frequency. The results show that random modulation can suppress excitation leakage and maintain finite and relatively stable coherence fluctuations at long times. These results clarify the evolution and control of first-order system–bath coherence in settings where a localized bosonic mode is coupled to a structured bosonic reservoir.

The work of Baverez, Guillarmou, Kupiainen, and Rhodes [BGKR24] is the starting point of this paper. It shows that analytic changes of boundary parametrizations act differentiably on Liouville amplitudes, with derivative given by Virasoro operators and a scalar anomaly term. We compute this scalar term. Its holomorphic part is a Schwarzian boundary integral, which gives a geometric explanation of the Virasoro central term. We then derive local Ward identities on disks, annuli, and pairs of pants. They give finite recursions for descendant matrix coefficients. From these recursions we recover the polynomial factorization of normalized pair-of-pants coefficients. In the annular zero-weight limit, we recover the Shapovalov form. For a pair of pants with two incoming boundaries, we recover the formal chiral vertex-operator coefficients. We also give a geometric proof of smoothness in the bulk insertion points and derive the genus-zero arbitrary level BPZ equations for degenerate bulk insertions.

While AI has shown remarkable promise in atmospheric and meteorological forecasting, accurately simulating other components of the Earth system with AI remains an active frontier. We present DLESyM-Ocean, a Deep Learning Earth System Model that simulates global present-day sea ice and upper ocean conditions. Unlike conventional probabilistic models optimized via diffusion objectives or losses such as continuous-ranked probability score, DLESyM-Ocean is trained using a patch energy score loss. When driven by atmospheric forcing, DLESyM-Ocean produces a well-calibrated, spatially coherent, and skillful ensemble of sea ice and upper ocean conditions with minimal bias relative to reanalysis products. DLESyM-Ocean is stable when autoregressively run for multi-year simulations and produces a climatology and variability with minimal bias compared with reanalysis. We evaluate case studies including a recent sea ice extreme, a severe marine heatwave, the 2023 El Niño transition, and the 2023 spike in global mean temperature. In all of these case studies, DLESyM-Ocean produces realistic surface and subsurface trajectories and ample ensemble diversity in response to common atmospheric forcing, suggestive of learned autoregressive ocean dynamics. When coupled with other Earth system components, such as the atmosphere, the computational efficiency of DLESyM-Ocean makes it a promising tool for subseasonal to seasonal forecasting.

Electrical tuning of intersubband-polaritonic metasurfaces cannot be fully identified from reflectance alone because intensity obscures the complex pole–zero dynamics governing critical coupling. We establish a field-consistent multiscale analysis that connects self-consistent Schrödinger–Poisson quantum states, complex rigorous coupled-wave spectra, and constrained one-port temporal coupled-mode theory across 21 electric fields. A single zero-field complex calibration fixes the shared photonic and phase-delay baseline, after which the effective coupling is the only field-dependent fitted parameter. The model reproduces the full-wave spectra with a complex-amplitude RMSE of 0.0255–0.0288 and is independently cross-checked through microscopic residue and overlap calculations. Complex poles describe internal polariton hybridization, whereas reflection zeros expose the external radiative–dissipative balance. The quantum-confined Stark effect drives the lower- and upper-polariton zeros through the real-energy axis in opposite directions, yielding two branch-resolved critical-coupling transitions that agree with direct full-wave cross-checks.

We present a four-component multireference second-order perturbation theory (4C-MRPT2) within the small tensor product distributed active space (STP-DAS) framework. The formulation is compatible with the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), and Dirac-Coulomb-Breit (DCB) Hamiltonians, and inherits the memory-efficient and massively parallel STP-DAS algorithm, enabling perturbative treatments over very large external spaces. Benchmark calculations on noble-gas and group-13 atoms demonstrate that 4C-MRPT2 efficiently recovers all-electron dynamic correlation while providing new insight into relativistic correlation effects. The calculations show that the Breit contribution to the correlation energy increases rapidly with atomic number and reaches approximately 4% of the total correlation energy for Xe. The method also shows that second-order correlation energies are only weakly dependent on the choice of multiconfigurational reference orbitals, and that frozen-core and frozen-virtual approximations substantially reduce computational cost with minimal loss of accuracy.

The spontaneous emission factor - often known as the e̱ta} factor - is an important quantity in the description of quantum well lasers, influencing both the threshold power as well as the general shape of the light in-light out (L-L) curve. Past work on modelling multiple quantum well (MQW) nanowire laser devices has typically assumed that the e̱ta} factor is a constant parameter that can either be estimated or fit in a post-hoc manner. However, the e̱ta} factor can be derived from the transitions between valence and conduction bands in semiconductor quantum wells, together with knowledge of the cavity modes. Here we investigate the dynamic nature of the e̱ta} factor for MQW nanowire lasers, and show how it can be computed. We also examine the dependence of the spontaneous emission rate and spontaneous emission factor e̱ta} on the charge carrier density, quantum well thickness, and composition, and discuss the impact on laser threshold and operation.

We revisit the traditional type~I, II, and III seesaw mechanisms in the presence of a complex scalar field charged under a global $U(1)$ symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axionlike particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyze two matching orders: first removing the radial mode and then the seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode, and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured nonunitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number-breaking scale, of the order of $1$–$10$~TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is, thus, falsifiable even when the new states lie far beyond experimental reach.

We characterize minimizers in Gamow's liquid drop problem.

Message-passing decoders are among the most promising candidates for scalable quantum error correction, yet their behavior in the low-error-rate regime remains poorly understood under realistic circuit-level noise. In this work, we introduce a systematic framework for identifying the graph structures that govern decoder failures and for using them to predict the resulting error floor. We apply exhaustive trapping-set enumeration directly to the detector error model of a bivariate bicycle code and test all low-weight fault configurations supported on the resulting structures. This converts the analysis of extremely rare logical failures into a finite structural search, avoiding the prohibitive cost of direct Monte Carlo simulation. We evaluate the framework on three iterative decoders with substantially different architectures and decoding heuristics. Remarkably, for RelayBP, the resulting prediction accurately reproduces the simulated error floor; for the others, it remains within the same order of magnitude. Despite their differences, leafless elementary trapping sets capture a substantial part of the low-weight error-floor contribution for all three decoders. Moreover, each decoder admits failures caused by fault configurations well below the correction capability implied by the circuit-level distance, revealing a substantial gap between code distance and practical iterative-decoding performance. These results establish trapping-set analysis as a practical framework for predicting error floors, exposing the structural weaknesses of iterative decoders, and guiding the joint design of decoding algorithms.

Atmospheric reanalyses combine observations with model forecasts using complex data assimilation systems. We test whether a differentiable weather model permits a simpler and more accurate method based on a long-window four-dimensional variational data assimilation (4D-Var) formulation that omits the conventional background-error term. The method uses automatic differentiation to find optimal NeuralGCM initial conditions that minimize the misfit to real surface-pressure observations distributed across overlapping windows of two to seven days, assuming no model error. Cycling at 6-hour intervals for three months beginning 1 January 2015 yields a stable reanalysis with smaller error relative to ERA5 in 500-hPa geopotential height than the Twentieth Century Reanalysis version 3 (20CRv3), which uses an ensemble Kalman filter to assimilate the same observations. Every window produces smaller errors than 20CRv3, with analysis error for the four-day window approximately 55% smaller than for 20CRv3. At the end of the four-day window, which does not benefit from future observations, error remains approximately 38% smaller than 20CRv3. Analyses degrade slightly beyond four days, which we attribute to the increasing importance of model error.

Classical cable theory neglects magnetic induction, Lorentz forces, and transient electromagnetic (EM) currents, limiting its accuracy for action potential propagation in branched neuronal geometries. We develop a coupled Maxwell-cable framework that integrates finite-difference time-domain (FDTD) solutions of Maxwell's equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo dynamics, including magnetic gating, EM transmembrane currents $I_{\text{EM}}$, and quantum corrections for thin segments. Controlled simulations in asymmetric and symmetric axonal bifurcations show that inductive effects lower the critical branch radius for conduction failure and break symmetry in identical daughter branches under transverse magnetic fields. We introduce an EM-corrected geometric ratio $GR_{\text{EM}}$ that revises branch-point impedance matching and captures size-dependent axial current imbalances. Parent axon conduction velocity deviates significantly from the $\sqrt{d}$ scaling law when EM feedback and quantum effects are included, leading to early blockage at large diameters. Overall, quasi-static models underestimate EM corrections to speed, waveform, and transmission fidelity; our framework offers a multi-physics tool for electrodynamic signaling in complex neuronal architectures.

This work systematically evaluates the capability of generative large language models (LLMs), specifically GPT-4o, to support the full design, simulation, and optimization workflow of low-dropout (LDO) linear voltage regulators. The study covers four core design phases: pre-design specification mapping, transistor-level circuit topology generation, SPICE simulation guidance, and post-simulation performance fine-tuning, with an extended investigation into the integration of magnetic inductive components within the LDO signal path. GPT-4o autonomously proposes a single-stage differential-pair error amplifier architecture with thin-oxide MOS transistors, provides sizing guidance for the PMOS pass element, and recommends passive compensation networks to secure closed-loop stability. The LDO testbench adheres to low-voltage portable electronics specifications: an input range of 0.8-1.2 V, tunable 0.7-1.1 V output, maximum 250 mA load current, and integrable output capacitance below 10 nF. Transient and small-signal AC SPICE simulations validate LLM-assisted circuit implementations, quantifying settling time reduction via compensation capacitors and verifying adequate phase margin across operating bandwidth. A key novel extension explores three distinct inductor placement schemes, input-side supply filtering, out-of-loop LC output filtering, and inductive loading embedded within the feedback divider, rooted in Maxwell's electrodynamic principles and MOSFET small-signal device physics. Comparative Bode and output impedance analysis reveals that inductors inserted inside the feedback path introduce resonant complex poles, severe gain peaking, and degraded phase margin, while inductors placed external to the feedback sensing tap preserve regulator stability while suppressing high-frequency electromagnetic interference.

Nonlinear stabilization is indispensable for discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws, yet it typically disrupts the delicate error structure required for superconvergence analysis. Consequently, existing theory has largely been restricted to linear or semi-discrete schemes lacking oscillation control. This paper bridges this gap by proposing a Runge–Kutta (RK) aligned oscillation-eliminating (OE) DG framework that restores the superconvergence properties. By synchronizing the pseudo-time step in the OE procedure with the cumulative RK stage coefficients, we unlock a cancellation mechanism for low-order interface errors that is inaccessible to standard OEDG formulations. We rigorously prove that this fully discrete scheme achieves $(k+2)$-th order superconvergence to a tailored projection of the exact solution for linear conservation laws in both one and two dimensions, while maintaining the non-oscillatory shock-capturing capabilities of the original method. Moreover, we establish a general guiding principle for designing a class of OE-type DG schemes that exhibit such superconvergence. Key theoretical innovations include the construction of stage-aligned correction functions to compensate for nonlinear OE sources and the discovery of a two-dimensional projection operator that preserves outflow-edge averages, a property essential to close the discrete shift estimates. Numerical experiments confirm the predicted superconvergence rates and demonstrate that RK alignment preserves the parameter-free robustness of OEDG for problems with strong discontinuities.

The deuterium fractionation of molecules in starless cores is sensitive to their dynamical histories, which recent magnetohydrodynamical simulations have shown to be extremely varied. The deuterated isotopologues of formaldehyde (H$_2$CO) and methanol (CH$_3$OH) probe deuterium fractionation in simple organic molecules. This complete survey targets 11 low-mass starless cores in the small, quiescent Barnard 10 (B10) region of the Taurus Molecular Cloud. The cores were observed using the 12m Arizona Radio Observatory telescope with a 100% detection rate in transitions of o/pH$_2$CO, HDCO, pD$_2$CO, A/E-CH$_3$OH, and CH$_2$DOH and the dense gas tracer N$_2$H$^+$. The HDCO and pD$_2$CO column densities and deuterium fractions are not correlated with those of the grain-surface deuteration tracer CH$_2$DOH, indicating significant gas-phase formation of deuterated formaldehyde. The observed deuterium fractions do not correlate with evolutionary indicators (e.g. core central density) or physical conditions (e.g. core mass). We also find that cores within the northwestern filament have lower deuterium fractions than cores of similar densities in the other two filaments. These could indicate differential core evolution both between and within entire filaments. Comparing the deuterium fractions of the B10 sample to published sources across different evolutionary stages suggests the inheritance of D$_2$CO from starless cores, although more surveys of organic deuteration are needed to conclusively determine inheritance.