Papers

We study the Katz-Long-Moody (KLM) construction and classify exactly when the resulting braid group representations factor through Hecke algebras, for scalar braid part and semisimple free-group part, over an algebraically closed field of characteristic zero and at every convolution parameter lambda different from 1. We show that, except for one exceptional two-strand family, this property then depends only on the eigenvalues of the free-group part and is independent of lambda. Semisimplicity is a genuine hypothesis: we exhibit non-semisimple inputs, namely g = I + N with N nonzero and N^2 = 0, whose KLM quotient is nonetheless a Hecke module, realizing the permutation representation of the symmetric group. We also give an exact criterion for when the resulting representations factor through Temperley-Lieb algebras.

This paper proposes a multi ring M-APSK constellation optimization method for discrete-modulated continuous variable quantum key distribution. Unlike conventional APSK structures with fixed ring spacing and predefined ring probabilities, the proposed method optimizes the ring radius ratio and ring probability to improve the finite-size secret key rate. A method based on the Gram matrix is used to calculate the nonzero spectrum of the average state $\tau$, and fidelity is used to compare the optimized discrete average state with the Gaussian average state. The results show that the proposed structure extends the maximum transmission distance of 16-APSK by approximately 15% compared with the conventional binomial APSK structure. The optimization gain is larger for small size APSK constellations, where the average state has a larger structural gap from Gaussian modulation.

Gas-phase cluster growth by monomer addition is commonly modeled as an isothermal process. We develop a survival-limited framework in which association produces a thermally excited cluster that may dissociate before either cooling through bath-gas collisions or encountering the next monomer. A continuous-energy survival probability is first derived for an individual post-association thermal trajectory and is then marginalized over distributions of excitation energy, equilibrium energy, and monomer-arrival time using a trajectory functional. Molecular-dynamics simulations of water, silver, and gold clusters provide size-dependent caloric relationships and latent heats, while event-based Monte Carlo simulations independently test the survival formulation. Theory and Monte Carlo results agree closely. The ensemble-averaged survival probability exhibits strong and non-monotonic size dependence, with the largest thermal penalties generally occurring for the smallest clusters. Intermediate-size local maxima arise only when complete cluster-energy distributions are retained and result from competition between curvature-enhanced dissociation and the narrowing of the low-energy tail with increasing size. Surviving clusters are consequently drawn preferentially from the colder portion of the pre-collision energy distribution, and mean thermal trajectories can substantially underestimate population survival. To connect single-event survival to cumulative growth, we introduce a thermal forward-rate correction relative to an isothermal reference and incorporate it into a reversible birth–death model. Although the correction at each size may be moderate, its multiplicative accumulation can increase mean first-passage times by many orders of magnitude. The framework provides a general route for identifying post-collision stabilization as a control on gas-phase cluster growth.

We perform a complete qualitative analysis of the cosmological dynamics of Lovelock gravity in a spatially flat Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid obeying a barotropic equation of state $p=\omega\rho$. Starting from the generalized $N$-dimensional Friedmann equations written in terms of the independent components of the Riemann tensor, we reduce the dynamics to a single autonomous first-order equation for the Hubble parameter $H$, whose right-hand side is a ratio of polynomials in $H^2$ fixed by the order $n$ of the Lovelock polynomial, the number of dimensions $N$, and the coupling constants $\alpha_i$. The real roots of these polynomials determine the fixed points and the singular points of the system, which govern its asymptotic behaviour. We give a complete classification of the possible evolution scenarios, identify the attractive and repulsive fixed points, locate the "phantom intervals" in which the effective matter density becomes negative, and show that fixed points are reached in infinite time whereas singular points are reached in finite time. For $N>4$ and suitable negative couplings a qualitatively new scenario arises, which we call the "Big Shock": the universe starts from a state with finite density and finite scale factor but with an infinite rate of change of the Hubble parameter, replacing the standard Big Bang. The general analysis is illustrated for $n=1$, $N=4$ (general relativity), $n=2$, $N=5$ (Einstein-Gauss-Bonnet gravity), and $n=3$, $N=7$ (cubic Lovelock gravity).

We compute the modification to the quark-neutral pion vertex, induced by a constant and uniform magnetic field, using the Linear Sigma Model with quarks as a low energy effective theory of QCD. The vertex is modified even at tree-level since, due to the loss of translational invariance, the calculation should be carried out in configuration space, with the quark described by Ritus wave functions instead of plane waves. We also compute the one-loop vertex modification. These modifications are found for arbitrary Landau levels occupied by the quark. We illustrate the result for the case where the quark occupies the lowest Landau level. To check the result, we also compute the one-loop vertex modification using the Schwinger proper-time method with the quark occupying the lowest Landau level and find the same result as in the case where the Ritus formalism is used.

Achieving high-lying vibrational states is essential for actively controlling molecular reactions. We demonstrate vibrational ladder climbing of CO adsorbed on Pt(111) within the plasmonic tip-substrate nanogap formed in a scanning tunneling microscope, detected via tip-enhanced sum-frequency generation (TE-SFG). As the infrared pulse energy increases, hot-band peaks appear sequentially up to the 3-4 transition, indicating the stepwise population of higher vibrational states. Numerical analysis using the optical Bloch equations captures the observed energy dependence of these features. These results demonstrate the capability of TE-SFG to probe vibrational ladder climbing in surface molecular systems and suggest a promising route toward accessing high-lying vibrational states and controlling vibrational excitation at the nanoscale.

Standing transverse waves in closed coronal structures have been widely studied as a possible route to energy dissipation, with resonant absorption transferring kink wave energy to localized Alfvénic motions and the Kelvin-Helmholtz instability (KHI) accelerating the formation of small dissipative scales. However, it remains unclear whether the same mechanism applies to the open corona, given the long-standing consensus that the KHI tends to be prohibited for propagating Alfvénic waves. Within the framework of magnetohydrodynamics (MHD), we perform three-dimensional MHD simulations of boundary-driven kink waves in a gravitationally stratified open flux tube extending from the chromosphere into the corona. We find that propagating waves in open magnetic structures can also drive the system toward a turbulent state, with KH vortices clearly identifiable across the flux tube. This occurs because resonant absorption transfers energy from the propagating kink waves to azimuthal Alfvénic motions near the tube boundary, and wave reflection off the gradient of the Alfvén speed subsequently enables these boundary motions to acquire a locally standing character. Our results provide a possible answer to the long-standing question of whether and how propagating waves in open magnetic structures can generate nonlinear turbulent fine structures despite their globally propagating nature.

One-dimensional (1D) superlattices provide one simplified platform for exploring moiré physics from a low-dimensional perspective, with the ratio of lattice constants playing a role analogous to the twist angle in two-dimensional bilayers. Here, we propose a 1D $\mathcal{PT}$-symmetric bichromatic optical lattice for a weakly repulsive Bose-Einstein condensate and investigate how the interplay of dissipation and interaction impacts the lowest moiré flat band. Without interaction, we find that the lowest-band flatness induced by commensurate ratios exhibits a parity-dependent response to the $\mathcal{PT}$-symmetric imaginary potential due to the distinct $\mathcal{PT}$ pairing mechanism for the energy spectrum. For ratios with even denominators (i.e., even parities), the level attraction and thus the $\mathcal{PT}$-symmetry breaking occur within the lowest two bands, leading to a monotonic broadening of the lowest flat band, whereas odd denominators (i.e., odd parities) yield a nonmonotonic response due to the $\mathcal{PT}$-symmetry breaking within the second and the third lowest bands instead while the lowest band remains purely real. This parity-dependent phenomenon can be understood by the perturbation theory. Furthermore, by solving the Gross-Pitaevskii equation, we also find that although the weak repulsive interaction can broaden the moiré bands alone, the combined effects of interaction and imaginary potential also lead to parity-dependent behaviors. For even parities, band flattening is consistently diminished, whereas for odd parities, the imaginary potential can either enhance or reduce the degree of flattening. These results pave the way for experimental studies of dissipation and interaction effects on band flatness in moiré systems.

We present spectral measurements for 17 Little Red Dots (LRDs) and 14 blue broad-line active galactic nuclei (AGNs) at $2\lesssim z \lesssim 6$ using multi-epoch JWST NIRSpec MSA spectra from the NEXUS program, sampling rest-frame timescales of $\sim 1-3$ months. Overall, the LRD population shows significantly enhanced Balmer decrement compared with both blue JWST AGNs at similar redshifts and 56 low-redshift broad-line AGNs matched in H$\rm\alpha$ luminosity. The rest-optical continua of LRDs show little ensemble variability (rms $\lesssim 3\%$), and the total H$\rm\alpha$ emission also shows weaker ensemble variability compared with low-redshift AGNs matched in H$\rm\alpha$ luminosity and rest-frame timescales. Based on the flux uncertainties, we constrain the intrinsic H$\rm\alpha$ rms variability to be $\lesssim 4\%$ for the LRD population over these timescales. Combining our results with recent broad-line variability measurements of LRDs over yearly to decade timescales reveals a low-level white-noise pattern across all timescales, in stark contrast to the variability amplitude ($\sim 6\%$ over monthly timescales) and red-noise pattern observed in normal AGNs. These results add to the growing observational studies that suggest population-wise, LRDs have weak variability both in optical continuum and broad-line emission. Furthermore, the distinct white-noise broad-line variability pattern suggests different production mechanisms of broad-line emission in LRDs as opposed to normal AGNs, and/or different properties of the driving ionizing flux from the central engine.

Core-collapse supernovae are among the most promising yet still undetected sources of gravitational waves. A future detection would provide a direct view of the physical processes occurring deep inside a collapsing star. In this work, we investigate how networks of current and future gravitational-wave detectors can constrain the properties of rapidly rotating core-collapse supernovae using their characteristic core-bounce and early post-bounce signals. Using deep-learning techniques, we estimate the peak frequency, rotation rate, and signal amplitude from noisy detector data and compare the performance of different detector-network configurations. We find that detector networks improve both parameter recovery and sky coverage. For current-generation networks, estimation of the peak frequency is possible out to about 15 kpc, while the rotation rate remains recoverable out to distances exceeding 100 kpc. Third-generation observatories extend these distances by approximately a factor of three to four.

This work investigates the long-term evolution of the vertical structure of superthin galaxies within the framework of Milgromian dynamics (MOND). By constructing an observationally constrained model of UGC 7321, a typical superthin galaxy, we test whether its disc can maintain an extremely flattened structure in a MOND gravitational field. We also construct models with different values of the MOND depth index D_M to study how the global MOND depth affects disc evolution. We perform three-dimensional hydrodynamical N-body simulations using the publicly available code Phantom of RAMSES. In the observationally constrained model of UGC 7321, the galaxy develops a strong bar and undergoes a buckling instability during the early stages of the simulation. The bar strength then decreases gradually, and the system eventually exhibits a weak bar structure. The vertical evolution reflects the combined effects of heating induced by non-axisymmetric structures and vertical confinement in the Milgromian potential. The stellar disc undergoes only limited vertical thickening, and the disc remains largely within the superthin regime, h_z/R_D<0.1, after 5.0 Gyr. The comparison of models with different D_M values suggests that models with lower D_M values, associated in our model suite with higher baryonic masses or more compact discs, exhibit stronger vertical heating and more significant disc thickening. By contrast, models with higher D_M values, corresponding to lower masses or more diffuse structures, tend to maintain a superthin structure. Overall, the simulation results indicate that superthin discs can remain vertically thin during long-term isolated evolution in MOND, and that the long-term maintenance of superthin structures is influenced, at least partly, by the degree to which a galaxy lies in the low-acceleration regime.

Context. The near-Earth environment is continuously impacted by the solar wind and the transients embedded in it. The largest eruptions of plasma and magnetic field at the Sun are Coronal Mass Ejections (CMEs), which, upon reaching Earth, can induce geomagnetic storms and disrupt our technologically advanced societies. Aims. We aim to improve our understanding of how CMEs and CME-driven shock waves interact with the ambient solar wind, and how the resulting deformations in time and space affect the accuracy of space weather forecasting. Methods. We studied two Earth-directed CMEs, observed on December 7, 2020 and October 28, 2021. To model the solar wind and CME propagation in the inner heliosphere, we used the state-of-the-art 3D MHD model EUHFORIA with the cone CME model, focusing on the regions along the main direction of propagation (MDP) and along the Sun-Earth line. Results. The deformations of the CME and the CME-driven shock can be significant. Both CMEs propagate in a variable background wind and are structured differently even at very close angular distances. The first, in a mildly structured wind, shows its stronger deformation predominantly away from the MDP; the second, in a more complex environment, develops a strongly structured shock at very different locations, including regions close to the MDP. Conclusions. These interactions also affect the characteristics of the CME-driven shock, such as the gas compression ratio across it. CMEs observed as flank encounters at Earth can be strongly affected by the ambient solar wind, with the expected differences in the arrival time at Earth reaching up to 16 hours.

Quantum metrology, which addresses parameter estimation in quantum systems, has broad applications across science and technology. Conventional metrology protocols for multi-qubit states in the multi-parameter regime typically require highly complex quantum measurements, leading to substantial quantum-resource costs. In this work, we introduce a family of metrology protocols that use only few-qubit measurements, thereby significantly reducing the required resources. For arbitrary pure states, one of our protocols approaches the quantum Cramér-Rao bound up to an overhead in sample complexity that scales linearly with the number of qubits, irrespective of the number of parameters to be estimated. For typical Haar-random states, this overhead can be reduced to a constant. Our results build on recent advances in quantum state certification protocols with few-qubit measurements: we establish a universal connection between certification and metrology in which the precision of the certification protocol determines the metrological overhead. We also illustrate our approach through an example of Hamiltonian estimation from ground states.

We obtain closed explicit formulas for the spectral determinants of the smooth hyperbolic Bolza surface and the Klein quartic. In each case, a multiplicative relation expresses the determinant of the surface in terms of determinants of singular quotient orbifolds of genera zero and one. The elliptic factors are evaluated by applying the singular Polyakov anomaly formula to explicit Belyi maps on CM elliptic curves of discriminants -8 and -7, while the genus-zero factors are evaluated by explicit determinant formulas for constant-curvature spheres with conical singularities. The same multiplicative relations hold fibrewise on the corresponding equisymmetric deformation strata and yield determinant and first-variation identities. We also prove that every compact quasiplatonic hyperbolic surface is a critical point of the spectral determinant on its Teichmüller space; in particular, this applies to the Bolza surface and the Klein quartic.

Quantitative strain mapping using four-dimensional scanning transmission electron microscopy (4D-STEM) typically requires densely sampled scans that can damage beam-sensitive specimens. We develop a physics-informed neural network (PINN) for sparse 4D-STEM strain reconstruction that embeds elastic equilibrium and Saint-Venant compatibility in the training loss through automatic differentiation. The architecture combines a coordinate-based implicit representation, sine activations with stable second derivatives, frozen residual-scale normalization, an exponential physics-weight ramp, and residual-based adaptive collocation. We apply a sine-activated residual network to an experimental $180\times400$-pixel strain map of domain-structured PbGeSnSe$_{1.5}$Te$_{1.5}$. Across $1$-$75%$ sampling ($720$-$54{,}000$ probe positions), $R^2$ for $\varepsilon_{xx}$ reaches $0.80$ at $10%$ sampling and saturates near $0.86$ by $25%$; the chevron strain-band morphology is recovered from $10%$ of probe positions. At $10%$ sampling, the PINN reduces mean absolute error by approximately $26%$ relative to compressed sensing and $22%$ relative to Gaussian-process regression. An ablation against an equal-capacity data-only SIREN shows that the PDE prior improves accuracy at extreme sparsity and consistently improves physical self-consistency, but biases the reconstruction when data are abundant. Monte Carlo dropout and mean-field variational inference provide per-pixel epistemic uncertainty maps correlated with reconstruction error. With an appropriate constitutive model, the framework is adaptable to strain mapping across diverse material systems.

Topological $K$-theory supplies the decisive stable classification principle for gapped free-fermion phases in Euclidean crystals once symmetry and stabilization are fixed. In hyperbolic band theory, by contrast, it is less decisive for the full band problem: generalized momentum sectors vary through moduli spaces, but passing to ordinary $K$-classes collapses their geometric and holomorphic variation. We distinguish kinematical holomorphy, in which complex geometry organizes the sector spaces, from dynamical holomorphy, in which that geometry informs a Hamiltonian or projector, and formulate the resulting loss as an observable-factorization problem. For a compact hyperbolic surface $X$, we prove nonfactorization in three settings: fibrewise $K^0(X)$, occupied-state $K^0(B)$, and operator-algebraic $K$-theory. The affected quantities include spectra and Higgs spectral curves, the Berry holonomy and the quantum metric, the partially filled Hall response, and the Fermi surface and nodal geometries. We also identify the quantized pairings and local charges retained by topology. Up to an explicit area factor, the Kotani–Sunada bottom-band Hessian is the Hodge inner product on $H^1(X;\mathbb R)$. Together with the integral intersection form, it recovers the homology-marked principally polarized Jacobian and hence, by Torelli and uniformization, the underlying complex and hyperbolic surface, though not a full Teichmüller marking. We also separate finite-rank sectors from the thermodynamic bulk. Locally faithful covers reproduce polynomial traces exactly and control continuous spectral observables. In arithmetic congruence towers, analytic observables converge as $O(|G_n|^{-\eta})$ for some $\eta>0$, and $C^s$ observables as $O((\log |G_n|)^{-s})$, while established coherent large-rank limits recover bulk density-of-states moments.

Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are rarely known, and symmetry discovery for SDEs has remained essentially unexplored. We introduce LieStoNet, an end-to-end, template-free framework for discovering Lie-point symmetries of SDEs directly from spatiotemporal trajectories, without prespecifying symmetry groups, templates, or canonical coordinates. Building on the seminal SDE Lie-symmetry theory of Gaeta and Quintero (1999), which formalizes Lie-point SDE symmetries and their relation to Fokker-Planck symmetries, LieStoNet learns neural surrogates for drift and diffusion from increments, then learns projectable generators by enforcing the SDE determining equations, separately regularizing for closure under Lie brackets, adherence to the Lie algebra axioms (bilinearity, antisymmetry, Jacobi), and a non-redundant independent basis. The surrogate also defines an associated Fokker-Planck equation, enabling optional discovery of its Lie-point symmetries in parallel. Across multiple canonical SDEs with known analytic symmetries, LieStoNet recovers generators consistent with the ground-truth symmetry algebra, providing interpretable symmetry discovery for noisy dynamics. Code is available at \href{https://github.com/sumit-sinha-seas/LieStoNet_Final.git}{this link}.

Considering the mass parameters as free phenomenological parameters, we investigate inflation driven by a canonical scalar field with different potentials in LQC. We find that a smaller mass value makes it easier to obtain a sufficient number of e-folds for the quadratic potential, while for the Starobinsky potential, more e-folds are obtained for larger mass values. By estimating the probability of slow-roll inflation, we find that it remains very close to unity for all considered cases. We compute the primordial power spectrum using three approaches: the dressed metric, the hybrid, and the alternative mass function approaches for the case that the kinetic energy dominated at bounce. The resulting power spectrum for both potentials and different mass values shows the same qualitative pattern in all three approaches. It is suppressed at small $k$, amplified and oscillating over an intermediate range, and nearly scale-invariant at large $k$. The approaches mainly differ in how fast the power spectrum converges to this regime, with the hybrid approach converging the fastest, followed by the alternative mass function and dressed metric approaches. We find that the pivot scale $k_\star$ is highly sensitive to the inflaton mass, changing by more than an order of magnitude for a mass variation of only a few percent. Using the tensor power spectrum at $k_\star$, we calculate the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, finding good agreement with current data. Finally, the scalar power spectra are fed into the CAMB code to obtain the angular power spectrum and compare with the Planck 2018 data and the best-fit $\Lambda$CDM model. All three approaches are consistent with data at high multipoles, while at low multipoles the hybrid approach gives the closest agreement and the dressed metric approach shows the largest deviation.

We consider the Riemann problem for a 3x3 system of conservation laws with generalized Chaplygin pressure $p(\rho,v)=-\frac{A(v)}{\rho^\alpha}$, $0<\alpha\leq 1$, where the pressure depends on an additional transported variable. We analyze the system's wave structure and classify the Riemann solutions. Whenever classical solutions consisting of shocks, rarefaction waves, and contact discontinuities fail to exist, singular solutions arise. We verify that these satisfy the conservation laws in the distributional sense within the classical Dirac delta framework, and compare them with Nedeljkov's shadow-wave construction, giving two complementary descriptions of the same singular solution. We further study admissibility via the Dafermos maximum entropy dissipation principle, with several examples showing how it selects the physically relevant solution. Lax-Friedrichs simulations illustrate the Riemann wave patterns and provide a comparison with the analytical results. To construct viscous profiles for the isolated overcompressive $\delta$-shock, we assume $\alpha\in\mathbb{Q}\cap(0,1]$ and apply the Dafermos regularization together with a spherical blow-up. Working in three directional charts, we construct the reduced singular concatenation consisting of the left outer orbit, the middle orbit on the blown-up boundary, and the right outer orbit. We then prove that, for sufficiently small positive viscosity, this singular concatenation perturbs to a heteroclinic orbit. Consequently, the isolated overcompressive $\delta$-shock is realized as the zero-viscosity limit of a family of self-similar Dafermos viscous profiles.

The planar Pompeiu problem, originating in 1929, and the associated Schiffer conjecture are long-standing rigidity questions linking rigid-motion integral transforms and Fourier zero sets to overdetermined Neumann eigenvalue problems. We construct a bounded simply connected noncircular domain $\Omega\subset\mathbb{R}^2$ with real-analytic Jordan boundary and a nonconstant function $u$ such that $(\Delta+k^2)u=0$ in $\Omega$, $u=1,\partial_\nu u=0$ on $\partial\Omega $ for some $k\in(31.967007261,31.967007293)$. Thus $u$ is a Neumann eigenfunction which is constant on the boundary, and $\Omega$ is a counterexample to Schiffer's conjecture. Green's identity also gives $\widehat{\mathbf 1_\Omega}(k\omega)=0$ $(\omega\in\mathbb S^1)$, so $\Omega$ fails the Pompeiu property and is also a counterexample to the planar Pompeiu conjecture for bounded simply connected Lipschitz domains. We obtain the domain as $\Omega=\phi(\mathbb{D})$, where $\phi$ is a ten-fold symmetric conformal map close to an explicitly listed polynomial of degree $301$. On the unit disc, the analytic problem becomes a cubic operator equation on real coefficient spaces, $F(g,p)=g+|p|^2(1+Kg)=0$, where $K$, expressed in a disk-polynomial basis, is an explicit inverse of the Laplacian on the range compatible with zero Dirichlet and Neumann traces, and $p=k\phi'$. Positivity of the disk-polynomial linearisation coefficients, sharp bounds for $K$, and monotone control of the infinite tails establish an a posteriori contraction near the listed polynomial in a weighted coefficient algebra, and hence an exact zero of $F$.

Protostellar outflow shocks reshape local dust properties and molecular chemistry. The L1157 outflow is an archetypal chemically rich shocked region, but the thermal dust associated with its successive shocks has remained unresolved because molecular-line contamination obscures the broadband continuum. We obtained new James Clerk Maxwell Telescope (825–906 $\mu$m) spectral-line observations and Submillimeter Array (1.1–1.4 mm) continuum observations toward L1157 B0-B1-B2, probing spatial scales from 0.4 pc to 1200 au. After removing molecular-line contamination on a pixel-by-pixel basis, we derived the dust temperature, column density, and dust opacity index from continuum data spanning 70 $\mu$m to 1.3 mm. The line-corrected continuum maps reveal the dust distribution across successive shocks. The dust opacity index ($\beta\approx1.8$–2.3) indicates that grains have not grown to millimeter sizes throughout the shocked regions. Combined with previous $\rm NH_3$ observations, we find that the dust emission resolves into compact clumps along the precessing jet, whereas gaseous $\rm NH_3$ peaks at the shock fronts, reaching abundances of $\sim10^{-5}$ relative to $\rm H_2$, even where the 0.85 and 1.3 mm dust emission is detected at only 3–5$\sigma$. Our newly developed physicochemical shock model shows that $\rm NH_3$ forms predominantly on grain surfaces and is released by shock-induced sputtering, with the highest abundances occurring where post-shock re-adsorption remains inefficient. These results establish spatially resolved dust continuum imaging as a direct observational probe of grain evolution and provide new observational constraints on dust-gas interactions in protostellar shocks.

Transition metal dichalcogenide moiré heterobilayers with type-II band alignment provide a versatile platform for layer-polarized generalized Wigner crystals, in which strong Coulomb interactions drive charge ordering at fractional lattice fillings. With a finite interlayer band offset, an out-of-plane electric field can tune layer-resolved moiré bands through resonance and enable controllable interlayer hybridization. Although hybridized Mott insulators have been previously demonstrated, whether fractional charge-ordered states can survive such hybridization remains elusive. Here we drive an H-stacked MoSe2/WS2 moiré heterobilayer through a type-I-to-type-II band-alignment transition and realize layer-hybridized Mott insulator and generalized Wigner crystals. For fillings below one electron per moiré cell, tunneling delocalizes electrons and modifies Wigner crystallization. However, above one electron per cell, Coulomb repulsion overcomes tunneling and favors layer-separated occupation, stabilizing stronger charge-ordered states. These results establish electrically tunable hybridized moiré heterobilayers as a powerful platform for engineering correlated charge order and exploring fractional Chern phases and emergent magnetism.

High-quality entangled states of photons underlie quantum information science (QIS) applications across communication, sensing, and computing. In many discrete-variable photonic QIS architectures, large application-ready states (e.g., cluster states, repeater graph states) are constructed via fusion measurements on small entangled seed states, of which Bell states are the fundamental example. The quality of seed-state generation therefore sets a baseline for application performance, making it crucial to understand this process under realistic error mechanisms, particularly in integrated photonics experiments. In this work, we analyze five heralded schemes for generating event-ready photonic Bell states, contrasting their heralding probabilities, fidelities, and error robustness. We develop a hierarchy of error models, progressing from an analytically tractable lumped-loss model to realistic heralded single-photon sources with multiphoton emission errors and finally to integrated frequency-bin implementations with architecture-dependent loss. Across these models, we find that schemes based on higher-order multiphoton interference provide superior fidelity robustness in low-loss implementations, while lower-photon-number schemes can be preferable when probabilistic sources or lossy beamsplitters dominate the resource cost. Our results provide design guidance for integrated discrete-variable quantum photonics, with particular relevance for frequency-bin architectures where active beamsplitter loss can determine the optimal resource-state-generation strategy.

The flow of moderately dense (n {\approx} 10^{11} cm^{-3}) hydrogen plasma with high electron temperature (T_{e} {\approx} 30 - 35 eV) and plasma potential (V_{p} {\approx} 100 V), expanding towards an expansion chamber (EC) from an ECR plasma source is investigated using Langmuir probes (LPs) and Ion Energy Analysers (IEAs). The LPs reveal presence of a second ionization zone (SIZ) a few centimetres from the ECR zone, indicating very short ionization mean paths, which are confirmed theoretically. The SIZ gives a density boost, produces a double layer, DL ({\Delta}V_{DL} {\approx} 106 - 40 V) and a warm electron population after the DL (n_{w}/n {\approx} 0.04 - 0.10, T_{w} {\approx} 40 - 60 eV). IEA measurements conducted at two sites (z_{1} {\approx} 5 cm, z_{2} {\approx} 10 cm) reveal ions with energies in the range {\approx} 65 - 8 eV at pressures {\approx} 1 - 8 mTorr. DL formation is explained in terms of the SIZ and warm electron generation is analysed in detail.

We formulate a non-local, field-theoretic description of phase fluctuations and topological transitions in two-dimensional (2D) superconductors by generalizing the local only-phase Popov action to a framework utilizing non-local fractional operators. By replacing the standard spatial Laplacian with the Riesz fractional Laplacian $-(-\nabla^2)^{\alpha/2}$ (where $1<\alpha<2$), we prove that the vortex-antivortex interaction transitions from logarithmic confinement to a stronger power-law confinement of the form $V(r)\propto r^{2-\alpha}$. Through a generalized Kosterlitz-Thouless energetic-entropic analysis, we demonstrate that this non-local confinement strictly suppresses thermal vortex proliferation. Because the non-local operator safely places the system outside the strict domain of validity of the Mermin-Wagner restriction, this power-law confinement natively stabilizes true long-range order at finite temperatures. Finally, by constructing a gauge-invariant fractional action, we formulate a fractional London equation. This approach yields a real-space power-law kernel that maps directly onto the anomalous Pippard limit of superconductors with long coherence lengths, providing a unified phenomenologically motivated framework for non-local electrodynamics.

Background. Aircraft-wildlife collisions are a documented aviation hazard. The FAA National Wildlife Strike Database is the main public source of U.S. reports, but raw extracts are large and rarely released as versioned aggregates. Methods. We convert the public FAA Access export (STRIKE_REPORTS) to SQLite, define a report as damaging when DAMAGE_LEVEL is one of M, M?, S, D, and fold rows into open aggregates (year, airport, species, aircraft, animal family) via hierarchical SPECIES_ID prefixes. We analyze all civil reports and a commercial subset (AC_MASS 3-5). Rates are per reported strike, not per flight hour, so every rate is conditional on a report having been filed. Trend statistics use complete incident years 1990-2025; cross-sectional facets cover the full seed, incident years 1990-2026. Results. Numbers are locked to the 2026-07-04 freeze. Reported strikes in 2025 reach a series high (24,458 total; 901 damaging). Species that dominate strike counts are not those with the highest damage rates: perching songbirds account for 41.1% of identified strikes but damage aircraft in 1.5% of reports (95% CI 1.4-1.6), whereas deer account for 0.7% but damage aircraft in 81.8% of reports (95% CI 79.8-83.7). Airports ranked by total strikes (led by Denver Intl) diverge from rankings by damaging strikes (led by Sacramento Intl); across the 452 airports with at least 50 reports, volume and conditional damage rate are negatively rank-correlated (Spearman rho = -0.44, p < 0.001); large stations plausibly capture minor events more completely, so this is not a hazard ranking. The share of reports labeled damaging declines over decades, consistent with improved reporting of minor events, while absolute damaging counts peak in 2025. Conclusions. Versioned open aggregates and a documented damage-rate analysis enable independent reuse; released under CC BY 4.0.

The Aragats High-Altitude Research Station (3200 m a.s.l.) combines meteorological, atmospheric electric, and particle flux measurements, providing a unique setting for investigating thunderstorm ground enhancements (TGEs) and recent environmental variability. We analyze one-minute observations from 2012 to 2025, first focusing on the meteorological and electric-field conditions controlling TGEs and then on trends in air temperature and daytime solar radiation. From an archive of 610 TGEs, a quality-controlled subset of 284 events with particle flux enhancements larger than 10 percent was selected. Comparisons of May, August, and October show that strong near surface electric fields alone are insufficient for frequent TGEs. May combines strong-field conditions with low cloud bases and shows a pronounced inverse relation between TGE occurrence and cloud-base distance. Thus, TGE occurrence is jointly controlled by thundercloud electrification and cloud-to-detector distance, while the recent warming tendency cannot be attributed to increased measured short-wave radiation. The annual mean air temperature shows a statistically significant positive trend, whereas daytime solar radiation shows a significant negative trend. Thus, warming at Aragats cannot be explained solely by variations in solar radiation.

Kepler's first two laws state that a planet moves on an ellipse with the Sun at a focus and sweeps out equal areas in equal times (constant areal speed). In the Principia, Newton showed how these laws connect to universal gravitation. Since then, the equivalence between orbital laws and force laws has remained a central topic in celestial mechanics. We present fully geometric proofs, built from explicit Euclidean straightedge-and-compass constructions, of this equivalence in both directions. The proof system combines finite-step constructions, tangent and triangle geometry, affine transport, local displacement ratios, conic invariants, and several hodograph realizations. Within this broader framework, one contribution is to use the auxiliary circle as the primary hodograph proxy in configuration space rather than the directrix-circle normalization of radius 2a. Our emphasis is a Principia-style argument that avoids differential equations while remaining close to Euclidean methods.

We present FESOM2-JAX, a Python re-implementation of the Finite-volumE Sea ice-Ocean Model (FESOM2) in JAX. The model retains the unstructured-mesh, cell-vertex finite-volume formulation of the original, runs unchanged from a laptop CPU to 256 GPUs, and is end-to-end differentiable. FESOM2-JAX is a code shadow of the Fortran model: a projection onto the Python ecosystem, translated with large language models and verified kernel by kernel against the original. It is built to lower the barrier to experimentation, from new numerics and parameterizations to gradient-based calibration and hybrid physics-machine-learning components, while remaining close enough to the original so that what is developed in the shadow can be transferred back. In a 1958-2019 hindcast at 1$^{\circ}$ equivalent resolution with identical physics and forcing, the mean states of the JAX and Fortran versions differ from each other by two orders of magnitude less than either differs from observations, and the two runs agree for six decades in global temperature, salinity, heat content, and sea ice. The complete 1$^{\circ}$ configuration fits on a single GPU, a node of four GH200 superchips integrates $\sim$113 simulated years per wall-clock day, and meshes of up to 7.4 million surface vertices ($\sim$5 km) scale to 128 GPUs. What limits the model is communication rather than arithmetic. What the shadow adds to the original is the gradient: a single reverse-mode pass through the full time loop returns the sensitivity of a model diagnostic to a parameter at every mesh vertex, verified against finite differences. To our knowledge, FESOM2-JAX is the first global ocean-sea-ice model of CMIP-class complexity written natively in a differentiable framework, and the first on an unstructured mesh.

The aeroacoustic resonance of round supersonic jets impinging on concave surfaces is investigated using compressible large-eddy simulations, vortex-sheet modelling, and Powell's feedback-loop analysis. The choked jets operate at an ideally expanded Mach number of $1.56$ and a Reynolds number of $6\times10^4$. Six geometries are considered: two flat plates at $L/D=2.08$ and $2.58$, where $L$ is the nozzle-to-wall distance and $D$ the nozzle exit diameter, and four Gaussian concave surfaces of fixed depth and indentation spread $\sigma\in\{0.4,0.8,1.6,4.0\}$. As the indentation narrows, the primary-tone amplitude increases by up to $23\,\mathrm{dB}$ relative to the flat-wall reference at $L/D=2.6$, together with larger wall-pressure fluctuations and moments. A Powell-Tam source-transfer budget attributes this amplification to increased Mach-disk source amplitude and more efficient return of the upstream feedback wave to the nozzle. The stronger upstream-propagating waves are consistent with acoustic focusing by the concave wall. For the helical cases, the measured frequencies and radial eigenfunctions agree closely with the guided jet mode predicted by the vortex-sheet model, supporting its role in closing the upstream feedback path. The same selection is recovered for concave and flat walls alike, so this tone is governed by the shear-layer profile of the equivalent ideally expanded jet rather than by the wall geometry. The axisymmetric frequencies, by contrast, coincide with no guided-mode branch and appear instead to follow Powell's classical loop-length criterion. The results identify distinct frequency-selection mechanisms for helical and axisymmetric screech and demonstrate that wall curvature provides effective control of screech amplitude and surface loading.