Papers

We study strictly positive multivariate binary distributions by separating one-body marginals from dependence. Local positive reweighting defines a dependence nucleus, completely characterized by the higher-order Walsh log-linear coefficients $J_S$, $|S|\ge2$. Any such nucleus and any strictly positive one-body marginals determine a unique joint distribution. In finite-spin Gibbs systems, these coefficients are the many-body interaction couplings.

Approximating the effective anisotropic hyperelastic response of a representative volume element (RVE) requires constitutive expressiveness, mechanical consistency, and computational efficiency. This work develops a polyconvex physics-augmented neural network (PANN) construction based on paired directional features whose orientations, stretch powers, and determinant exponents adapt to the RVE response. The features are composed with convex, componentwise nondecreasing cores, realized as an input-convex neural network (ICNN) or an input-convex Kolmogorov-Arnold network (ICKAN). The complete energies satisfy objectivity, an exactly stress-free reference, two-dimensional polyconvexity, and prescribed growth conditions by construction, and nonnegative energy is certified separately for the selected models. On a multicavity and a single-cavity periodic cell, these energies are compared with an Unconstrained energy, trained identically without the curvature and growth constraints, and with three hyperreduced projection-based reduced-order models (HPROMs), which serve as physics-based references. On the first cell, learning the features lowers the stress error sevenfold, and six features suffice on both. The constrained energies remain below one percent in stress error and in the displacement error of a tensile-coupon FE$^2$ application with a full-order reference, whereas the Unconstrained energy and the HPROMs are more accurate inside the data. Beyond the data, however, the Unconstrained energy loses rank-one convexity, and under confined compression it stops below half of the 500 MPa that the constrained energies reach. These results quantify what the guarantees cost in accuracy and what they secure beyond the data.

Frustrated magnets host rich emergent behavior because competing interactions generate dense manifolds of low-energy states. The Ising Shastry-Sutherland model is a paradigmatic setting, motivated experimentally by Ising-like rare-earth tetraborides such as TmB$_4$ and ErB$_4$, whose field-induced magnetization plateaus have motivated extensive microscopic modeling. Yet how tunable quantum fluctuations reorganize this material-motivated phase diagram remains largely unexplored. Here, we realize a transverse- and longitudinal-field Ising model on the Shastry-Sutherland lattice using a programmable Rydberg-atom array. We map its quantum phase diagram using density matrix renormalization group calculations and probe corresponding signatures experimentally in arrays containing more than 110 atoms. Beyond the established classical phases, the calculations identify two regimes absent in the classical limit and stabilized at finite transverse field: a $2/5$ filling plateau whose finite stability region emerges from a classically degenerate phase boundary and a symmetry-preserving quantum-dimer regime replacing classically selected collinear order. Experiments on finite open arrays reveal signatures consistent with these regimes across three boundary-pinning conditions, with the resulting response maps agreeing qualitatively with the calculated phase diagram. Our results establish programmable Rydberg-atom arrays as tools for exploring frustrated, material-motivated Hamiltonians and motivate searches for new, quantum-driven magnetization plateaus and quantum-dimer behavior in ErB$_4$ under a transverse field or in strain-tuned TmB$_4$.

Molecular dynamics simulations of solid polymer electrolytes require force fields that are fast enough to converge ion transport over hundreds of nanoseconds, yet accurately describe the ion-polymer interactions that govern it. Fixed-charge force fields meet the first requirement but neglect electronic polarization, an effect often approximated by scaling ionic charges using empirically chosen factors. Here we present AutoDrude, a differentiable framework that parametrizes polarizable Drude force fields directly from DFT energies, forces, and dipoles, with no empirical tuning and at only 1.20 times the cost of a fixed-charge simulation. For PEO-LiTFSI, the dipole-constrained (hard-constraint) AutoDrude model reproduces the experimental ionic conductivity as accurately as the best charge-scaled model (17% versus 16% mean absolute percentage error). We compare the polarizable forcefield to fixed charge ones models by fitting a fixed charge model. Unlike the charge-scaled models tested here, however, AutoDrude also reproduces the dilute-limit cation transference number, its increase with salt concentration, and the absence of Li-TFSI contact ion pairs at low concentration. A penalty-based (soft-constraint) variant yields a closer fit to the DFT reference yet underestimates the conductivity by up to an order of magnitude, demonstrating that closer agreement with DFT training data alone does not guarantee accurate ion transport. These results indicate that although charge scaling can reproduce ionic conductivity the explicit inclusion of polarization is necessary to capture the concentration dependence of cation transport in PEO-LiTFSI.

The staggered order parameter of the gapped XYZ spin-$1/2$ chain follows from the eight-vertex solution, but in elliptic variables that fix the Hamiltonian couplings only implicitly. We derive a closed form for the coefficient governing the leading quadratic response of the spontaneous staggered magnetization to the XY anisotropy at fixed longitudinal anisotropy in the gapped antiferromagnetic regime. Starting from the Baxter–Kelland–Jimbo–Miwa–Nakayashiki polarization formula, we show that at fixed longitudinal anisotropy both the modular nome and the crossing-parameter variable of the formula move with the XY anisotropy, and that the motion of the crossing-parameter variable reverses the sign of the expansion at fixed elliptic variables. The coefficient is a rational term plus a Lambert series. It is strictly negative and bounded above by a rational function of the longitudinal anisotropy, to which it is asymptotic in the Ising limit. At the isotropic point it diverges as the inverse five-halves power of the distance to that point, and since the Lambert sum has an asymptotic expansion with exponentially small remainder, the subleading terms of the divergence also follow in closed form. When the XY anisotropy vanishes as the five-fourths power of the distance to the isotropic point, the ratio of the perturbed to the unperturbed order parameter tends to a Gaussian in the scaling variable, and the quadratic truncation is controlled when that variable is small. A fourth-order perturbative calculation in the spin chain, with no input from the eight-vertex solution, reproduces the leading strong-coupling behaviour, and infinite-DMRG calculations at four anisotropies in the gapped regime are consistent with the closed form.

Altermagnetism, as a novel magnetic paradigm, not only possesses a zero net magnetic moment, but also exhibits a substantial nonrelativistic spin-splitting effect. Currently, developing a simple and experimentally feasible method for designing altermagnets is eagerly pursued. Moreover, achieving 100% spin polarization along certain directions in valence or conduction bands for altermagnets remains challenging. To address these issues, based on a tight-binding model, we propose a viable chemical strategy for constructing organometallic altermagnets by using ambidentate ligands. Furthermore, in these organometallic altermagnets, direction-dependent 100% spin polarization along the [110] direction in band edges can be induced via the coexistence of altermagnetically spin-split dispersive and flat bands, where the flat band suppresses electron transport in one spin channel and the dispersive band enables conduction in the other spin channel. Then, via first-principles calculations, a screening of 90 two-dimensional ambidentate-ligand based square organometallic lattices leads to the identification of three altermagnetic materials, namely Fe(taz)2Cl2 (taz = 1,2,4- triazine), Co(app)2Cl2, and Fe(app)2Cl2 (app = 1,4-azaphosphinine), all of which possess 100% spin polarization along the [110] direction in valence bands, as well as notable piezomagnetic behavior. This study paves the way for achieving direction-dependent fully spin-polarization in altermagnetic materials.

We introduce coset lifted product (CLP) codes, a family of quantum LDPC codes that combine the protograph structure of lifted product codes with the coset action of Aydin, Tamo, and Barg \cite{AydinTamoBarg2026}. Given a finite group $G$, a subgroup $H \le G$ that need not be normal, a protograph $A$ over $\mathbb F_2[G]$, and a protograph $B$ over $\mathbb F_2[N_G(H)]$, the two protographs act on the cosets $G/H$ from the left and from the right to produce quantum CSS codes. Further, for groups of odd order, we give an explicit formula for the dimension as a sum over the irreducible representations $\rho$ of $G$ of hypergraph product dimensions. A search over $14,843$ pairs $(G,H)$ with $H$ restricted to be non-normal and $120 \le n \le 400$ yields certified codes that exceed the best published value of $Q=kd^2/n$ at check weights $6,7$ and $9$, i.e., we obtain $[[360,20,20]]$ at $w=6$, a $[[360,24,20]]$ code at $w=7$, and codes $[[252,16,18]]$ and $[[288,16,20]]$ at $w=9$. Our search also produce high-distance codes with parameters $[[168,10,14]], [[240,8,20]]$ at $w=6$ and $[[216,8,18]]$ at $w=7$.

The two main traditional player statistics used in soccer are goals scored and assists, with an assist credited when a player's pass immediately leads to a teammate scoring. Attributing credit solely to the player who makes the final pass before a goal fails to account for the contributions of multiple players in the buildup to the goal. Consequently, traditional statistics provide only a limited view of player involvement. In this paper, we use multivariate Hawkes processes (MHPs) to model timestamped sequences of passes and shots, which form continuous-time networks. MHPs provide a branching mechanism where an event (a pass or shot) can be generated as a child of a previous event, which allows us to quantify each pass's contribution to a subsequent pass or shot. This approach distributes credit across multiple passes within an attacking sequence, making it applicable across a wide range of situations. Building on this framework, we propose expected goal involvements (xGI), a metric that measures a player's involvement in creating goal scoring opportunities based on their passes. This metric identifies players who play key roles in creating goal scoring opportunities even if they do not make the final pass, offering a more comprehensive measure of attacking involvement and player performance.

The integration of two-dimensional Ti3C2Tx MXenes into Halide Perovskite (HaP) optoelectronics has shown immense potential for enhancing device performance, yet the fundamental chemical interactions within the precursor ink (a critical stage determining the final material state) remain largely unexplored. This study presents a comprehensive investigation into the chemical stability and surface evolution of Ti3C2Tx MXenes when exposed to the individual and combined components of a model methylammonium lead iodide (MAPbI3) solution. By combining detailed X-ray Photoelectron Spectroscopy (XPS) analysis with Density Functional Theory (DFT) calculations, we decouple the complex interactions between MXenes and the ink constituents. We demonstrate that elemental iodine (I2) and polyiodides (In-) act as aggressive oxidizers, triggering rapid degradation and dissolution of the MXene flakes. Conversely, lead iodide (PbI2) induces a slower oxidation process driven by the strong adsorption of Pb2+ ions onto oxygen terminated sites. In stark contrast, methylammonium iodide (MAI) exhibits a stabilizing effect: it adsorbs onto the MXene surface via hydrogen bonding, effectively passivating the flakes and retarding degradation. In addition, our results reveal that the sequence of precursor addition governs the MXene surface state, requiring extra caution, but also enabling further tunability. These findings provide a critical view on how MXene integration with materials, in general, and HaP in particular, should be perceived, providing a fundamental for their rational engineering.

Lymphangions, the valved muscular segments of lymphatic vessels, pump lymph against an adverse pressure gradient. Current models resolve this pumping in one vessel, a short chain or a regional network, and whole-body human models are passive. We extend the passive whole-body network of a companion static study to the active regime on the same anatomical graph, with intrinsic contraction, dynamic valves and a respiration-gated venous outlet on every vessel. Without fitting the waveform or the contraction amplitude, the network settles into a bounded pumping cycle at the lymphovenous junction, at a clinical pressure of 7.5 to 12.3 mmHg and a drainage of 35 to 50 mm^3/s. Respiration adds a swing of 1 to 2.5 mmHg at the junction and contraction about 1 mmHg inside the duct. Pressure generation is limited more by load than by drive, and no single contraction amplitude fits every vessel. Raising the subclavian venous pressure from 3 to 15 mmHg lifts the deep cervical node from 8.6 to 21.1 mmHg at the weakest drive, a transmission of 1.04 that falls to 0.78 at the strongest, so contraction buffers cervical drainage against venous pressure. The same solver gives the human cervical outlet pressure that cerebrospinal-fluid drainage models prescribe.

Multiterminal Josephson junctions (MTJJs) extend conventional two-terminal Josephson physics to devices defined by multiple superconducting phases, where rich phenomena have been predicted. However, in conventional MTJJs, superconducting transport is often dominated by local coupling between neighboring leads, obscuring physics that goes beyond simple connectivity. Here, we realize a multiterminal Josephson network in a graphene Hall bar geometry with micron-scale dimensions, enabling substantial nonlocal coupling between distant terminals. Our key observation is a pronounced negative differential longitudinal resistance (NDLR) in the four-probe response near switching currents, while no such feature appears in two-terminal measurements. We reproduce the NDLR response with a network containing the interplay between two distinct forms of nonlocality: nonlocal Josephson coupling, which determines the switching sequence of the superconducting network, and nonlocal normal-state conductance, which redistributes current after different regions switch. Our results highlight the potential of the emergent NDLR for characterizing superconductor–semiconductor hybrid systems and for nonlinear circuits. Further, this Josephson Hall bar geometry provides a platform for exploring the interplay between mesoscopic superconductivity and many-body ground states in graphene-based heterostructures.

In this report, 15 variants of nine parametric models for non-directional ocean wave spectra are reviewed. They are compared against observation-based spectra created by taking spectra measured by moored buoys, binning by wind speed, and averaging. Surface Stokes drift (SSD) and Stokes drift profiles are computed using the model and observation-based spectra, and these are compared. This 'parametric wave model' strategy for estimating Stokes drift is contrasted with other methods for estimating Stokes drift, such as using spectra from a dynamical wave model. Advantages and shortcomings are reviewed. One practical application for Stokes drift profiles is in ocean circulation modeling. Here, the information is used to compute wave-enhanced mixing ('Langmuir turbulence'). We present examples of such cases, in the context of a global ocean model, tested in two modes (coupled and uncoupled) and with two types of forcing (Stokes drift approximated using wind speed and Stokes drift computed using a full ocean wave model). A more comprehensive review of the uncoupled tests with the full ocean wave model can be found in a separate report, Fan et al. (2026). We evaluate simple Stokes drift models that use wind speed and/or wind stress but do not require a dynamical wave model. We find some are sufficiently accurate for routine prediction of SSD. A subset of these models can also predict Stokes drift profiles (via parametric spectra), but none are accurate in this role. The SSD values computed from a very large drifting buoy dataset are compared with the total drift calculated using positional change of the same buoys. The SSD is roughly 25% of the total drift, consistent with expectations based on 'rules of thumb'. However, the scatter is large, indicating that such rules have predictive skill only in the mean sense.

The lymphatic system returns 2 to 3 L of interstitial fluid per day to the venous circulation and drains the central nervous system. Most models of lymph transport describe one lymphangion or a short chain, so they cannot show how body-wide topology, calibre hierarchy and the venous outlet set pressure and flow. We build a passive steady hydraulic model on an anatomically derived graph of the human lymphatic system, with 1010 vertices and 1126 edges expanded to 89,060 sub-edges. Radii follow a Murray cube law, derived both from minimum work and from wall-shear-stress homeostasis. Pressure and flow follow from nodal hydraulic balance over Hagen-Poiseuille conductances, with an exponential wall law, hysteretic valves, Starling leak, node retention and a Windkessel outlet. Active contraction is off, and only the inflow scale is calibrated. Two quantities that are not fitted land in clinical range at the same operating point. Radii fall inside the vessel-class range, from 1.50 mm in the thoracic duct to 0.16 mm in the cervical collectors, and pressures stay below the 50 mmHg cuff scale on all sub-edges. About 49% of the gross load is removed before the outlet, nearly independent of the outflow scale and of the outlet parameters. On the route that drains the central nervous system, 30% of the superficial cervical load reaches the vein, at 10 to 18 mmHg along a segment that cervical-scale models replace with a prescribed outlet pressure. The model is a passive whole-body baseline for contraction-driven and clinical extensions.

The growing diversity of two-dimensional (2D) materials has expanded opportunities in electronics, energy technologies, catalysis, and optical applications. Within this landscape, understanding how corrugated architectures accommodate metallic bonding and influence the stability and properties of monoelemental niobium sheets remains an open research direction. Here, we propose a corrugated niobene nanosheet, denoted c-Nb, and investigate its structural, energetic, vibrational, mechanical, electronic, and optical properties using density functional theory simulations. The optimized structure adopts a centrosymmetric P-3m1 symmetry, with six atoms per primitive cell and a geometrical thickness of 4.279 Angstrom. Its cohesive energy of -6.03 eV/atom indicates strong binding relative to isolated atoms, although bulk BCC Nb remains energetically favored by 2.49 eV/atom. The absence of imaginary phonon frequencies along the investigated high-symmetry path and the positive-definite in-plane stiffness matrix support dynamical and mechanical structural stability. Despite its pronounced corrugation, the nanosheet exhibits isotropic in-plane elasticity, with Young's and shear moduli of 43.66 N/m and 13.66 N/m, respectively, and a Poisson's ratio of 0.598. Electronic states near the Fermi level are dominated by Nb 4d orbitals, establishing multiband metallicity. These findings identify a corrugated structural candidate that combines strong cohesion, elastic compliance, and metallic electronic behavior, extending the structural diversity of monoelemental 2D metals and providing a basis for further exploration of niobium nanosheets in electronic and ultraviolet-responsive systems.

Electronic properties of materials depend both on band energies and quantum geometry of electronic states. We relate bonding indices to the quantum geometric tensor (QGT), showing how chemical bonding dictates the momentum-space texture of bands, bridging chemical and physical descriptions of solids. We show the QGT decomposed into the three center bond index, weighted by their oriented area. Resolving these contributions by orbital pair reveals the donor–acceptor character that distinguish ionic, covalent, hypervalent, and metavalent bonding. We identify the bonding pattern for topology in materials: noncollinear three center bonds, which are the source of Berry curvature in solids. Bond fluctuation can be directly linked to electromagnetic response by resolving their energy spectrum, opening a quantitative route towards the design of physical properties of materials from bonding motifs.

Molecular spectra observed in the interstellar medium are commonly analyzed using non-local thermodynamic equilibrium models, which requires accurate state-to-state collisional rate coefficients. Close-coupling calculations become prohibitively expensive for transitions from highly excited rotational states, therefore available datasets are often truncated at low initial states and temperatures; and since each new system also requires an accurate ab initio potential energy surface, many detected molecules have no collisional data. We employ two machine learning strategies to predict rotational state-to-state rate coefficients of molecules included in the train set beyond the range of initial states and temperatures computed so far, and predicting those of a molecule absent from training and validation sets. Feed-forward neural networks are trained on state-to-state de-excitation rate coefficients of 24 linear molecules colliding with para-H2. Scheme 1 includes all systems in the train+validation set, with 70%, 80%, and 90% initial-state boundaries and a 90% temperature boundary. Scheme 2 is trained on 22 systems described only by transition and molecular properties, and predicts two excluded systems, CS and CF+, whose astrophysical impact is explored with non-LTE calculations. For the 90% boundary, Scheme 1 predicts 99.4% of the test transitions within a factor of 2, and no prediction deviates from the reference value by more than a factor of 4.7. This model was used to complete 18 datasets. Scheme 2 reproduces the rate coefficients of two excluded systems within a factor of 3 for more than 92% of their transitions. Both schemes provide near-instantaneous complements to close-coupling calculations: Scheme 1 extends the range of a molecule already included in the training set with high accuracy, while Scheme 2 gives a reasonable first estimate for a molecule that has not been studied.

Predictive synthesis concerns the prospective modeling of how a targeted structure can be realized. The synthesis of metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) intrinsically involves a multidimensional space of interdependent variables, posing a challenge for bench chemists to parameterize and predict. In this Perspective, we discuss the evolution from chemical-intuition-driven experimentation toward the integration of artificial intelligence (AI) and machine learning (ML) in the laboratory. By virtue of prior knowledge, uncertainty, and experimental failure in determining what should be attempted next, we envision predictive synthesis progressing from static recipe recommendation toward real-time control and transferable principles of framework formation. In this context, the significance lies in transforming trial-and-error practice into a means of measurable chemical reasoning, thereby accelerating crystalline materials discovery and advancing synthetic chemistry.

In this note, we study a broad class of time-dependent and irreversible dynamics for quantum spin systems in both finite and infinite volume. We develop a simple and flexible strategy for expanding commutators of the form $[A,\tau_{s,t} \, B]$ in terms of self-avoiding paths of sets, where $A$ and $B$ are local operators and $\tau_{s,t}$ is the Heisenberg time evolution. This adaptive Dyson expansion requires no backwards time evolution and is thus also applicable to irreversible dynamics. Furthermore, we discuss how such an expansion directly implies Lieb-Robinson bounds. A central feature of our result is that the obtained Lieb-Robinson bounds are independent of any Hamiltonian and dissipative on-site terms of the generator.

The star formation efficiency per free-fall time ($\epsilon_{\rm ff}$) quantifies how efficiently giant molecular clouds (GMCs) convert gas into stars and is often observed to be orders of magnitude lower than expected for free-fall collapse. Observers typically estimate $\epsilon_{\rm ff}$ by mapping far-infrared (FIR) dust emission to infer gas surface densities ($\Sigma_{\rm gas}$) and counting embedded protostars, assuming simplified lifetimes and masses. Using the fiducial STARFORGE radiation-magnetohydrodynamics simulation of an $M_{\rm cl} = 2\times10^4 M_\odot$ GMC that self-consistently models star cluster formation and stellar feedback, we generate synthetic FIR observations and apply the same methodologies used in GMC surveys to investigate this discrepancy. We present the first $\epsilon_{\rm ff}-\Sigma_{\rm gas}$ analysis in a fully feedback-regulated GMC simulation that resolves the formation of stellar systems. Our synthetic measurements reproduce the low observationally inferred efficiencies, showing that feedback-regulated star formation naturally produces $\epsilon_{\rm ff} \sim 1-3\%$ without requiring extreme initial conditions. We also find that $\epsilon_{\rm ff}$ varies strongly over a GMC's lifetime, suggesting that much of the observed scatter reflects evolutionary sampling rather than intrinsic cloud-to-cloud differences. Finally, by comparing observational and simulation definitions, we show that methodological assumptions introduce systematic biases, with a transition near $\log \Sigma_{\rm gas} \approx 2.3 M_\odot {\rm pc}^{-2}$ that depends on resolution. Above this threshold, the smoothing of dense structure increases both the inferred free-fall time and enclosed gas, with the latter dominating and suppressing $\epsilon_{\rm ff}$. Below the threshold, the discrepancies are primarily driven by star formation rate assumptions.

We report a comprehensive muon spin rotation and relaxation (muSR) study of the hexagonal 6H-perovskites Ba3LnRu2O9 (Ln = Gd, Ho) to investigate the role of rare-earth anisotropy in the magnetic ground state of 4d-4f coupled systems. Ba3HoRu2O9 exhibits two successive magnetic orderings at TN1 = 46 K and TN2 = 10 K, leading to a complex magnetic ground state, whereas Ba3GdRu2O9, with Gd3+ (L = 0) S-state ions, shows primarily single magnetic ordering at TN = 14.5 K. Zero-field (ZF) and longitudinal-field (LF) muSR measurements reveal markedly different magnetic behavior despite their structural similarity. Ba3HoRu2O9 displays a multi-scale inhomogeneous magnetic state characterized by two-component exponential relaxation, broad local-field distributions, incomplete LF decoupling, and persistent spin dynamics. The muSR results identify two characteristic magnetic energy scales near 46 and 10 K, associated with correlated Ru-Ho interactions and quasistatic magnetic ordering, respectively. Redfield analysis further demonstrates strong local magnetic fields and distributed spin fluctuation timescales, confirming magnetic inhomogeneity. Machine-learning-assisted muon-site and dipolar-field calculations show that the broad field distribution naturally arises from muons sensing distinct coexisting magnetic domains at different structural sites. In contrast, Ba3GdRu2O9 exhibits a comparatively homogeneous antiferromagnetic ground state below 14.5 K, with Gaussian relaxation consistent with a narrow static field distribution. These results establish that the rare-earth ion in Ba3LnRu2O9 is a powerful tuning parameter, driving the ground state from homogeneous to complex, multi-scale inhomogeneous behavior through competing 4d-4f magnetic interactions.

The strong Szegő theorem and the Fisher-Hartwig formula describe the asymptotic behavior of determinants obtained by restricting translationally invariant operators to large finite regions. In particular, Szegő's theorem states that, beyond the leading extensive contribution to such a determinant, there is a universal finite correction, $\sum_{r>0} rV_rV_{-r}$ where $V_r$ are the Fourier coefficients of the logarithm of the symbol. Although this formula appears throughout analysis and mathematical physics, the origin of its quadratic form and of the weight $r$ is often obscured in its standard analytic derivations. We develop an elementary picture in which the strong Szegő term arises from boundary leakage: paths contributing to the matrix exponential leave the finite interval and subsequently return. Counting the shortest such excursions immediately produces the factor $r$. We then show that an isolated boundary contributes exactly one half of the strong Szegő correction, while the two boundaries of a long interval decouple. For finite-range matrices this gives a rigorous and intuitive elementary derivation of the asymptotics, with extensions to sufficiently rapidly decaying interactions. A complementary free-fermion argument provides a physical interpretation of the same cancellation mechanism. Numerical examples illustrate the asymtotics in the well controlled regime, the Fisher Hartwig logarithmic correction. The boundary formulation does not itself require translation invariance and therefore suggests natural extensions to disordered systems, higher dimensions, and symbols with internal matrix structure. To illustrate this we numerically go beyond the formal applicability region of the Szegő formula, considering slow decay and disordered cases, and showing in some cases a robustness of the approach even for slowly decaying but disordered potentials.

Neural crest cells (NCCs) provide a well-established system for investigating collective migration during embryonic development and exhibit migratory behaviors with parallels to cancer invasion. Previous studies establish roles for co-attraction, contact inhibition of locomotion, polarity persistence, and tissue confinement in guiding NCC migration. However, it remains unclear whether NCC migration in confined environments occurs through spatial restriction alone or also through a repolarization response induced by contact with boundaries of confinement. By developing a computational model that couples self-generated chemical transport with contact-mediated repolarization and mechanical interactions, we show that cell-boundary contact can reorient cell polarity and sustain directional migration under confinement, whereas no persistent collective direction emerges without confinement. Moreover, suppressing contact-mediated repolarization from non-permissive confinement boundaries while preserving the mechanical interactions prevents sustained directional migration, suggesting that spatial restriction alone is insufficient in the model. Together, these findings establish an experimentally testable mechanism through which self-generated chemical signals and contact with confining tissues jointly regulate collective guidance of NCCs. These insights provide a basis for investigating developmental migration defects and potential strategies to regulate collective tissue invasion.

We calculate the spectrum of gravitational waves generated by a cosmological magnetic field with a narrow-band power spectrum. For a spectrum narrowly peaked at a comoving wavenumber $k_c$, we find that the gravitational wave signal peaks at $2k_c$ and has a sharp cutoff at this scale. We apply this result to an ultralight dark matter model of magnetogenesis operating around recombination, in which an axion-photon coupling generates a helical magnetic field by parametric resonance. We determine the conditions for the resulting gravitational waves to enter the frequency range of pulsar timing experiments. Although the required frequency can be reached for sufficiently large coupling, the corresponding amplitude is below the experimental sensitivity for physically allowed energy densities of the magnetic field. We generalize this conclusion to models of magnetogenesis operating at other epochs, estimating as $T \simeq 160 \mathrm{MeV}$ the temperature of a magnetogenesis process assumed to be the source of the stochastic gravitational wave background suggested by pulsar timing arrays. We place the lower bound $T \gtrsim 1$-$10 \mathrm{MeV}$ on such viable models.

Theory predicts that H I emission from photoionized clouds should lie close to the Case B limit established by Menzel and Baker, and observations of nearby nebulae have largely confirmed this expectation. However, recent observations of more distant high-redshift systems have revealed a small fraction with striking departures from Case B. What additional physics might be at work in these objects? This paper is part of a series exploring the physical processes that can produce such departures. In Paper I (D26), we show that Case B remains remarkably robust over a broad range of physical conditions, consistent with observations of nearby nebulae. Here, we explore one additional ingredient: a soft, non-ionizing radiation field. Such a continuum can strongly perturb the Balmer spectrum. The largest effects occur for radiation fields resembling log(Teff K)\sim 3.2-4.2 blackbodies, where photoexcitation from the metastable 2s level alters the hydrogen level populations and subsequent radiative cascade. The resulting Halpha/Hbeta and Hgamma/Hbeta ratios follow a different trajectory from dust reddening, allowing the two effects to be distinguished using multiple Balmer lines. In unresolved systems, a cool source located near the line-emitting gas may provide an additional radiation field distinct from the hot stars responsible for ionization. Balmer decrements may therefore carry information about otherwise hidden components of the radiation field surrounding the emitting gas.

Bilayer graphene (BLG) is a unique electronic material offering electrostatic tunability of its band gap. Here, we study how charge disorder in the dielectric environment modifies band-edge states by binding electrons and holes to Coulomb centres, taking into account the in- and out-of-plane dielectric response of Bernal bilayers. We apply this framework to (a) hBN-encapsulated medium-size-gap BLG used for gate-defined quantum dots, and (b) BLG under double n/p ionic gating. In hBN/BLG/hBN, we find that single remote charges produce only weakly bound states, with binding energies generally small compared with the BLG gap. Under ionic gating, we find that the bound states are too large to be trapped by individual ions – localisation arises from fluctuations in the ion density, whose magnitude is limited by Coulomb charging energy at the freezing temperature $T_f$ of the ionic configuration. Thus, in both regimes, charge disorder does not produce deep midgap states, with the bound states remaining closer to the conduction and valence band edges.

Turbulent conjugate heat transfer (CHT) in pipes with azimuthally non-uniform heating is studied theoretically and numerically with a focus on low-$\mathrm{Pr}$ fluids. While the influence of the solid properties is well documented for uniform heat flux, their effect under azimuthally non-uniform heating has not been explored systematically. We address this gap by combining spectral analysis of the problem – which reduces arbitrary boundary conditions to a discrete set of azimuthal wavenumbers – with well-resolved numerical simulations of thermally and hydraulically fully developed turbulent pipe flow at $\mathrm{Re}_\tau \approx 180$ for $\mathrm{Pr} = \{0.025, 0.71\}$, representative of liquid metals and air. Two principal results emerge: (i) the global Nusselt number is independent of the azimuthal heat-flux distribution and exhibits only a minor dependence on the solid properties, resolving an open question for low-Prandtl-number fluids; (ii) CHT nevertheless strongly affects the azimuthally resolved mean temperature at low $\mathrm{Pr}$, where azimuthal conduction in the solid homogenises the interface heat flux, and governs the level of temperature fluctuations through the effusivity ratio (thermal activity ratio) $K$. Finally, an analysis of the turbulent Prandtl number $\mathrm{Pr}_{t}$ shows a strong anisotropy, particularly near the wall, and a dependence on the azimuthal wavenumber.

This manuscript demonstrates that the Schwarzschild and Kerr metrics can be derived fundamentally from the Einstein Equivalence Principle (EEP) without explicit reliance on the Einstein field equations. We show that the EEP implies a gravitational stretching of length in the direction of acceleration, a spatial counterpart to time dilation. In the static case, this effect yields the constraint $g_{00}g_{11}=-1$, from which the Schwarzschild solution is recovered by taking the Newtonian limit. For the stationary case, we employ oblate spheroidal coordinates and construct a physically motivated tetrad to implement the EP, introducing gravity through three unknown functions. By applying the EEP-induced constraints and showing that the principle requires the preservation of the spacetime volume determinant ($g = g_0$), the system is reduced to a single unknown function that yields the Kerr metric. These results suggest that classical tests of General Relativity are, at their core, fundamental validations of the EEP. We further argue that the EEP leads naturally to Unimodular Gravity, implying that the existence of the cosmological constant is a direct consequence of this foundational postulate.

A recent preprint by OpenAI resolved the spherical fermionic Laughlin spectral-gap conjecture for the full $V_1$ interaction by a Fock-space inequality: $H_Q^2\ge \gamma H_Q$ on the lowest-Landau-level Fock space for all large flux $Q$ and every $\gamma$ below $0.0461673\ldots$, so that the gap above the Laughlin state at filling $1/3$ is at least $1/25$. That proof, with its original constant, has also been formalized in Lean. We show that the same argument supports a much larger constant. Two sharper estimates, a product-twirl bound for the three-body tail and a staircase price for the four-body allowance, raise the constant above $0.0601$ without changing the original certificate. Treating the auxiliary operators as the variables of a semidefinite program (SDP) and enlarging the finite set of orbital modes on which they act then gives $H_Q^2\ge\gamma H_Q$ for every $\gamma<\gamma_*=0.2190037845063196\ldots$, certified by exact rational arithmetic. Consequently the gap above the Laughlin state is at least $1/5$ for all sufficiently large spheres, and the untruncated planar $V_1$ Hamiltonian has positive spectrum bounded below by $\gamma_*$, uniformly in particle number and angular momentum. A heuristic extrapolation of the SDP optima suggests that auxiliary operators of the present form can give at most about $0.222$, while exact diagonalization of finite systems places the true gap near $0.4$. A larger family of auxiliary operators could push the bound further towards the true gap, and the SDP formulation makes such families easy to test. The proof of the improvement and the SDP search were completed by the AI model Claude Opus 5.5 (Anthropic) under the author's direction.

Strong light–matter interactions have attracted significant interest in physical chemistry due to the potential for modifying molecular processes by hybridizing with cavity photons and forming polaritonic states. However, for a disordered molecular ensemble within an optical cavity capable of supporting multiple photon modes, theoretical understanding of multimode polaritons remains incomplete, particularly regarding whether and how distinct photon modes are mutually coupled through molecules. In this work, we generalize the collective mode expansion formalism to incorporate multiple photonic modes and show that spatial and orientational disorder in the light–matter coupling strength (originating from dipole orientation fluctuations and photonic field inhomogeneity) can mediate cross-mode coupling. This disorder-induced coupling allows for energy transfer to otherwise unexcited photon modes through a mechanism termed disorder-induced multimode activation (DIMA). Using an effective one-dimensional Fabry–Pérot cavity as a test system, we demonstrate that the cross-mode energy transfer through DIMA can be controlled by changing the molecular layer thickness and the optical properties of the mirrors. Furthermore, we show that DIMA is robust against weak energetic disorder. This mechanistic understanding lays the foundation for a systematic control of multimode photon coupling using disorder-induced effects.

Quantum LDPC codes promise to reduce the overhead of fault-tolerant quantum computation, but their practical use requires efficient logical gates, measurements, and access to non-Clifford resources. Here, we develop a complete set of computational primitives for La-cross hypergraph product codes. For a subclass of these codes, we show that seed automorphisms together with fold-transversal gates generate the full logical Clifford group up to Pauli corrections. We further prove that every rank one logical operator admits $D$ pairwise disjoint physical representatives, enabling parallel gauging and a space–time tradeoff for logical measurements. Finally, we construct an addressable surface code interface for injecting externally prepared resource states into selected logical qubits. Together, these results establish La-cross codes as a simple, low-connectivity generalisation of surface code computation, retaining analogous computational primitives while providing a complete Clifford+$T$ instruction set across multiple encoded qubits.