Papers

We demonstrate that exciton-phonon coupling in polar semiconductors is governed by a parity-controlled interference selection rule. By performing an exact multipole expansion of the excitonic form factor and validating it against numerical integration of hydrogenic envelope functions, we show that the long-range infrared divergence of the Fröhlich interaction is exactly canceled for elastic scattering between excitonic states of the same parity. The ground-state exciton is thereby protected from long-wavelength polar phonons by destructive electron-hole interference. In contrast, transitions between states of opposite parity exhibit constructive interference, preserving a finite, robust coupling to macroscopic polar fields independent of band-structure details. Mass asymmetry between the electron and hole activates higher-order multipole terms in the elastic channel but leaves the constructive inelastic channel essentially unaffected. The selection rule is dimensionally invariant, applying to bulk and two-dimensional systems alike, and naturally explains the anomalously weak phonon dressing observed in halide perovskites as well as the strong phonon sidebands in transition-metal dichalcogenides. Our framework provides a universal, analytically exact criterion for exciton-phonon coupling strength, offering a design principle for engineering excitonic materials with tailored phonon interactions.

The $t$-channel production of a top quark in association with a $Z$ boson, $tZq$, is measured in the trilepton channel. The measured $pp \rightarrow t\ell^+\ell^-q$ process is defined for $m_{\ell\ell} > 30\,\text{GeV}$ and includes both resonant $Z$-boson production and non-resonant dilepton production. The data collected by the ATLAS experiment in 2015 to 2018 in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13\,\text{TeV}$ are used, corresponding to an integrated luminosity of $140\,\text{fb}^{-1}$. Events containing three light leptons ($e$ or $\mu$) and two to four jets, one or two of which are identified as $b$-quark-initiated jets, are selected. The inclusive $pp \rightarrow t \ell\ell q$ cross-section with $m_{\ell\ell} > 30\,\text{GeV}$ is measured, along with the separate cross-sections for top-quark and top-antiquark production and their ratio. The inclusive cross-section is measured to be $95.2\;^{+8.5}_{-7.9}\;\text{(stat.)}\;^{+5.5}_{-5.3}\;\text{(syst.)}\,\text{fb}$ and found to be in agreement with the most advanced Standard Model predictions. Differential cross-section measurements as a function of many kinematic variables are also presented. Both absolute and normalised differential cross-section measurements are made at particle level and parton level in their respective phase spaces. The top-quark spin asymmetry is measured from the unfolded measurement of the top-quark polarisation angle as $A = 0.34 \pm 0.14 \;\text{(stat.)} \pm 0.06\;\text{(syst.)}$, in good agreement with the Standard Model prediction. The differential cross-section measurement results are interpreted in the framework of Standard Model effective field theory and limits are set on dimension-6 operators involving the top quark.

Analytical approximations to eigenvalues of parameter-dependent Hamiltonians can provide physical insight that is not readily apparent from numerical diagonalization alone. Here, we introduce an activation-selection network (ASN), a differentiable symbolic-regression architecture in which each input node learns a sparse combination of predefined analytical functions, and the trained network can be converted directly into an explicit expression. Before regression, the Hamiltonian parameters and eigenvalues are expressed as dimensionless ratios. This normalization enforces dimensional homogeneity, reduces the number of independent variables, and ensures that the extracted expressions do not depend on the choice of energy units. Using the library {0, x, x^2}, compositions across successive hidden layers generate polynomial expansions of progressively higher degree; polynomial expansions of arbitrary finite degree can therefore be obtained in principle by increasing the network depth. We apply the ASN to effective three- and four-site spin-chain Hamiltonians relevant to zero-quantum nuclear magnetic resonance. Comparisons with degenerate perturbation theory show that the extracted expressions capture the expected constant, linear, and quadratic structure. Fixed-basis least-squares models match or slightly outperform the ASN when an appropriate quadratic basis is specified in advance, while inclusion of a radial feature improves the local approximation near the degeneracy. These results establish the ASN as a differentiable framework for selecting compact symbolic representations when several functional forms are plausible, while showing that adaptive activation selection does not provide an intrinsic accuracy advantage over a suitable predefined basis.

Water ice is the most abundant ice in the interstellar medium (ISM). Previous studies on porous amorphous solid water (pASW) have shown that the infrared radiation field in the ISM modeled with infrared free electron laser (FEL) irradiation can result in changes in the ice towards a more ordered structure, characterized by a change in the OH-stretching vibration band. This paper aims to study the restructuring in more detail by varying the irradiation intensity and irradiation time for irradiations on-resonance with the OH-stretching, bending and libration modes. In addition, desorption of H2O is monitored during the irradiations. The research presented in this paper considers 42 infrared FEL irradiations on pASW samples deposited at two different rates, using the infrared FELs of the HFML-FELIX laboratory. Restructuring is studied using reflection absorption infrared (RAIR) spectroscopy, with a mass spectrometer monitoring the desorption of H2O in an ultra-high vacuum system. Desorption and restructuring occur in parallel, with the strongest effects observed for irradiation on-resonance with the OH-stretching vibration. Both processes exhibit two distinct regimes: an initial strong restructuring and desorption, characterized by an exponential decrease in the intensity of the desorption peaks within the first 5 s of irradiation, followed by a second regime of less efficient, yet continued restructuring and constant desorption in an extended area, involving energy dissipation through the hydrogen-bonding network. The trends in restructuring and desorption, depending on the absorbed energy during irradiation, are significantly different, suggesting separate processes. The astrophysical relevance of in particular the second regime of constant desorption and restructuring is discussed.

Photoacoustic computed tomography (PACT) combines optical absorption contrast with acoustic detection for high-resolution deep-tissue imaging. A persistent challenge is that unknown speed-of-sound (SoS) heterogeneity changes acoustic time-of-flight, causing defocusing artifacts when reconstruction assumes a uniform SoS. Existing SoS-adaptive methods either rely on calibrated acoustic priors or optimize dense physical medium models, which becomes expensive and difficult to scale in 3D. We propose PAGS, a differentiable framework for blind autofocusing PACT via speed-of-sound-adaptive Gaussian splatting. PAGS represents the initial pressure field with sparse Gaussian photoacoustic (PA) sources and replaces explicit medium recovery with a compact anisotropic path-averaged SoS (ASoS) field parameterized by spherical harmonic probes. This latent propagation field directly controls source-to-transducer arrival-time alignment, while an analytic Gaussian acoustic projection maps the source representation to transducer signals efficiently. The resulting closed-loop signal-domain optimization jointly updates the Gaussian PA source parameters and the ASoS field from measured data, without calibrated SoS priors. Experiments on simulated and physical phantom data demonstrate improved reconstruction sharpness under heterogeneous acoustic media, robustness to sparse-view sampling, and computational benefits from the analytic Gaussian projection.

Let $H_0$ be the standard discrete Laplacian on $\mathbb Z^d$, $d\geq4$, let $R_0(z)=(H_0-z)^{-1}$, and let $p'$ denote the Hölder conjugate of $p$, with $p'=\infty$ when $p=1$. We establish uniform diagonal resolvent estimates from $\ell^p(\mathbb Z^d)$ to $\ell^{p'}(\mathbb Z^d)$ by proving local Fourier-decay bounds for surface measure on the Fermi surfaces of the lattice dispersion relation. At a regular point, the decay is governed by the number of coordinate directions in which the quadratic term vanishes: after a local change of variables, these directions produce cubic one-dimensional phases, while the remaining directions are quadratic. For $d\geq5$, we prove the sharp global range \[ 1\leq p\leq\frac{2(d+2)}{d+5}. \] Away from the threshold energies, this range remains sharp in odd dimensions, whereas for even $d\geq6$ the sharp range improves to \[ 1\leq p\leq\frac{2(2d+5)}{2d+11}. \] In dimension four, we obtain uniform estimates for $1\leq p<4/3$ and an $\ell^{4/3}$-to-$\ell^4$ endpoint estimate with a square-root logarithmic loss. Matching anisotropic Knapp-type constructions give the corresponding necessary conditions. We also derive Birman–Schwinger and Kato smoothing bounds, complex-eigenvalue estimates, and improved thin spectral projection estimates.

We combine N-body dust-trail generation with a fast nodal-encounter forecast and apply the model to the Leonid returns of 2031-2035. The dominant error is neither the ejection physics nor the encounter machinery but the parent trajectory at the moment of ejection: a back-integration of 55P/Tempel-Tuttle places the pre-1700 ejection sites more than 1 au from the fitted apparition solutions. We therefore anchor the ejection sites, not the dust, to the JPL Horizons ephemeris. Anchoring removes an age-proportional bias in the modelled nodes and, for the first time in this model, reproduces the classical attribution of the 2001 and 2002 storms to the 1767 trail, with peak times accurate to 1 and 40 min. A second systematic is not a property of the parent: a forecast read from a stored dataset holds each node where the snapshot left it, while the real node moves a median 1.2e-2 au in 0.12 revolutions. Two frozen snapshots of the same trail disagree by as much, so each year uses its own epoch-matched dataset. A completeness audit – every encounter the model predicts, not only the nominated ones – over-predicts the 1932 trail eighteenfold. We predict two comparable maxima on 2034 November 18, zenithal hourly rate ~1.4e3 at 03:30 UT from the 1932 trail and ~1.2e3 at 23:45 UT from the 1733 trail, with ~1.4e3 in 2033 and ~650 in 2035. Which dominates is a direct observational test of the trail-density term.

Multicritical phenomena play a central role in quantum many-body systems, yet their microscopic origin in light–matter platforms remains largely unexplored. Here we investigate a generalized two-mode quantum Rabi model with independently tunable rotating- and counter-rotating-wave couplings. We demonstrate that anisotropy lifts the parent U(1)-symmetric superradiant manifold with a gapless Goldstone-like mode by phase locking the complex superradiant order parameter. This phase-locking mechanism provides the common microscopic origin of the coordinate- and momentum-like soft-mode instabilities, the emergence of symmetry-related two- and four-triple-point multicritical topologies, and the corresponding thermodynamic responses. Within a unified Bogoliubov framework, we further show how the dominant soft mode is redistributed between the two symmetry-related instability channels, thereby determining the multicritical phase structure. The resulting phase boundaries are determined by collective soft-mode softening and coincide exactly with the mean-field instability conditions. We further show that the multicritical topology is directly encoded in the full quantum ground-state energy and its response functions, establishing a unified connection between phase topology, competing collective excitations, and thermodynamic observables. Our results identify competing soft-mode channels as the microscopic origin of tunable multicriticality in strongly coupled light–matter systems.

We present a conditional latent generative framework for parametric rarefied flows that separates neural-field representation, latent transport, and frozen physics adaptation. Neural-field auto-decoders compress discrete-velocity cavity solutions and direct simulation Monte Carlo cylinder solutions into shared coordinate decoders. Train-only principal-component charts support conditional flow matching (FM) and diffusion without a deterministic condition-to-latent backbone, and structured low-rank adapters correct selected decoder outputs while the upstream pipeline remains frozen. On two steady benchmarks, the frozen pipelines interpolate out-of-sample conditions with cavity kinetic relative $L_1$ errors at the $10^{-5}$ level and cylinder per-field area-weighted RMSEs of 0.038 (density), 0.041 (temperature), and below 0.01 (velocities). For the cavity, physics adaptation reduces the matched-grid Bhatnagar–Gross–Krook diagnostic by 28.65% while preserving field accuracy; for the cylinder, the analytic wall map enforces no-penetration exactly and, jointly with the learned FM adapter, reduces the inlet violation to 0.277 and the global mass-balance ratio to 0.963 of the frozen values with negligible field-error change. A five-seed controlled comparison with deterministic condition-to-chart multilayer perceptrons shows that, although the generative pipelines do not surpass the compact MLP in point accuracy on these single-valued steady problems, the results validate sampling-based conditional transport on the shared representation as an effective steady surrogate, with a natural route to multivalued or stochastic solution families.

Tidally locked exoplanets orbiting M dwarf stars are prime targets in the search for habitable worlds, yet their complex climate dynamics challenge conventional models of habitability. We homogeneously estimated the liquid-water habitability of exoplanets with the highest up-to-date Earth-similarity index. We modified the climate model PLASIM to apply it to tidally locked exoplanets across a range of parameters. We systematically classified and compared potentially habitable exoplanets and selected among the ones featuring the highest Earth-similarity index in the conservative sample of the Habitable Wolds Catalog, both relative to each other and as a function of atmospheric pressure. Our analysis revealed three main climate regimes: Snowball, Hot, and Eyeball planets-the latter having a warm and habitable substellar region with T > 273 K and a localized hydrological cycle. Although surface temperature generally increases with pressure, Eyeball planet climates remain stable in a wide pressure range. Complex atmospheric dynamics govern the behavior of the climate, highlighting the need for detailed climate simulations to guide future observations.

To resiliently and sustainably meet our future energy demand, photovoltaic (PV) modules must be deployed across a broad and diverse range of geographical regions with varying operating conditions. As these conditions strongly affect both performance and optimal system design, a dedicated PV-specific climate classification can be of great use. In this work, we develop a climate classification framework tailored to PV applications using a variety of machine learning (ML) techniques. Building on previous studies, our approach incorporates both energy yield, and for the first time, also the module lifetime with climate dependent degradation. We generate an interpolated dataset containing twelve input features and two target variables (i.e. energy yield and module lifetime). Feature importance analysis shows that annual global horizontal irradiation and ambient temperature are the most influential predictors. The most accurate regression model achieves root mean square errors (RMSE) of 0.007 MWh for energy yield and 1.5 years for lifetime prediction. The calculated feature importance scores are then integrated into a hierarchical clustering framework, resulting in 6 primary climate clusters (Tropical, Desert, Continental, Temperate, Boreal, and Polar) and 15 corresponding subclusters. Our analysis shows that the low temperature continental climate offers the highest discounted lifetime energy yield. These results can support a wide range of applications, including PV module optimization, system siting decisions, and comparative performance studies.

Pressure anisotropy and off-diagonal pressure stresses are ubiquitous and play important roles in collisionless/weakly collisional plasmas. The Chew-Goldberger-Low (CGL) MHD model is often used; however, it can lose hyperbolicity when the pressure anisotropy or plasma beta becomes large, making it hard to develop approximate Riemann solvers. An alternative approach is to use the 10-moment MHD equations, but their eigenmode analysis is also difficult, which similarly hinders the development of less-diffusive Riemann solvers. This paper presents a new energy-consistent finite difference scheme for 10-moment MHD designed to operate over a broad range of plasma beta. The proposed scheme extends the 10-moment MHD model using the energy-consistent finite-difference approach developed for conventional MHD. Nonlinear filtering is applied to all six independent components of the pressure tensor, and the kinetic and magnetic energies dissipated by the filtering are explicitly transferred to the diagonal pressure components under an equipartition assumption to maintain consistency with the total energy balance. The proposed scheme is validated against seven test problems in the isotropic limit, the gyrotropic limit, and without isotropization/gyrotropization. The results demonstrate the expected spatial convergence and total energy behavior, reproduce the linear growth rate, and yield pressure tensor structures qualitatively consistent with theoretical expectations and previous simulations, spanning plasma beta values from $10^{-10}$ to $10^{10}$. The proposed scheme provides a promising framework for large-scale simulations of collisionless plasmas across widely separated plasma beta regimes and opens a path toward applications such as solar wind turbulence and plasmoid-mediated reconnection.

The rare-earth peak ($A\sim164$) is a prominent feature of the $r$-process, and previous theoretical studies suggest that it is possibly linked to local nuclear structural effects. However, the nuclear level density (NLD), a physical quantity directly reflecting these properties, has been largely overlooked compared to other structural properties such as nuclear masses. To address this, we perform $r$-process simulations across three astrophysical scenarios using neutron-capture rates derived from six distinct NLD models. Our results reveal that microscopic models yield systematic deviations in NLD relative to phenomenological ones, leading to critical impacts on nucleosynthesis. Specifically, systematic NLD differences in even-$A$ nuclei redirect the nuclear flow, accelerating the early formation of the rare-earth peak and temporarily enhancing its magnitude. This underlying structural shift also fundamentally alters the $r$-process sensitivity to the neutron-capture rate, effectively eliminating its dependence on the odd-even nature of protons. Overall, these findings demonstrate that the internal nuclear structure encoded within NLDs can collectively induce a global redirection of the nucleosynthesis pathway, highlighting the critical need for self-consistent microscopic inputs in future simulations.

The origin of white dwarf magnetic fields is an open question. Furthermore, such fields play a vital role in the evolution of interacting binary stars. Here we present a study of white dwarf fields in so called pre-polars (or low accretion rate polars, LARPs , i.e. magnetic cataclysmic variables, where the mass losing secondary star is not in Roche lobe contact, but the systems experience accretion via stellar wind. Such systems play a crucial role in understanding the magnetic braking and the angular momentum evolution of close binaries. We aim to identify a set of wind-accreting pre-polars amongst our sample of nine candidate systems. We also attempt to measure the white dwarf magnetic fields and study the accretion geometry associated with wind-accreting pre-polars. We have obtained optical circular imaging photopolarimetry and circular spectropolarimetry of the targets. These are used to model the cyclotron emission and to estimate the white dwarf magnetic field strengths. We find that at least in four out of our nine candidate systems, we can confirm the magnetic nature of the white dwarf. Out of these, One system, ZTF J1737+4013, appears to be an eclipsing polar. Furthermore, ZTF J2220+0721 and ZTF J2353+4153 appear to be very strong candidates for wind-accreting pre-polars (or LARPs), with the fourth, ZTF J0056+4926, showing strong variable $H_{\alpha}$ emission, atypical of pre-polars. However, the emission could be related to the strong activity of the donor star, dominating the optical spectrum. One system, ZTF J0504+2145, is likely a novalike CV. The exact nature of the other systems remains unclear.

We first construct general saddles of the five-dimensional gravitational supersymmetric index with $S^1\times\mathbb{R}^4$ asymptotics, carrying an arbitrary number of electric charges and Gibbons-Hawking centers. We then uplift the three-charge configurations to type IIB supergravity, obtaining solutions asymptotic to $S^1\times \mathbb{R}^4\times S^1\times {\rm K}3$, carrying D1-D5-P charges. Upon taking a decoupling limit, these solutions yield asymptotically Euclidean AdS$_3\times S^3\times {\rm K}3$ candidate saddles of the dual CFT$_2$ elliptic genus. We focus on the two-center saddles, which involve three integers specifying an orbifold action. Depending on these integers, the saddles may or may not possess a Euclidean horizon, and may be smooth or exhibit orbifold singularities. We give the on-shell action of these two-center saddles in the appropriate ensemble and establish a precise match with the Farey-tail expansion of the elliptic genus at the level of saddle-point actions. The horizonless saddles are the Euclidean version of fractional spectral-flow solutions previously discussed in the literature, corresponding to $({\rm AdS}_3\times S^3)/\mathbb{Z}_k$ orbifolds. The black hole saddles are modular images of the horizonless ones. They generalize the well-known ${\rm SL}(2,\mathbb{Z})$ family of BTZ black holes by placing it in the background of the $\mathbb{Z}_k$ orbifold. We also consider the asymptotically AdS$_3\times S^3$ solutions arising as decoupling limit of five-dimensional black ring and black lens saddles, provide their on-shell action and confirm that they do not contribute to the D1-D5 elliptic genus.

This study shows that the usual time evolution operator can act as a U(1) gauge transformation on the initial wavefuntion. When considering the spin freedom in the system, the time evolution operator corresponds to a non-Abelian SU(2) gauge transformation for spin-1/2 particles and a SU(3) gauge transformation for spin-1 particles. If we adopt the adiabatic approximation in the magnetization dynamics of a ferromagnetic system driven by a spin-polarized current, a temperature-dependent non-Abelian thermal gauge potential will appear. We can employ a temperature-dependent Landau-Lifshitz-Gilbert (LLG) equation to describe the magnetization dynamics in the semi-classical limit, a linear approximated solution for this equation is given analytically.

Ultralight bosonic fields can form macroscopic clouds around rotating black holes, whereas the existence of analogous stationary fermionic condensates is strictly constrained by their intrinsic spin. Here we establish a complete geometric and kinematic framework to resolve the stationary bound states of massive Dirac fields on Kerr and Kerr-Newman backgrounds. By mapping the Kerr-Dirac system to a globally integrated sourced radial problem, we strictly isolate the boundary constraints dictated by horizon causality. The angular sector reveals a fundamental topological distinction: because the azimuthal quantum number is strictly half-integer, the regular boundary branches prevent the local field density from vanishing on the rotation axis. Consequently, rotating fermionic clouds inherently form globally filled, oblate geometries, in stark contrast to the hollow toroidal structures characteristic of scalar condensates. Crucially, our radial indicial analysis unveils the exact mathematical origin of the absence of synchronized Dirac hair. Precisely at the kinematic synchronization locus, the Frobenius matrix of the Dirac operator is non-defective and entirely devoid of logarithmic divergences. Without these singular branches to be selectively excised by boundary regularity, the physical burden of existence falls entirely onto the causal flux barrier, which strictly trivializes the zero-source amplitude. This synchronization veto demonstrates that a black hole's capacity to support macroscopic stationary fields is governed not merely by superradiant kinematics, but by the profound interplay between local horizon causality and quantum spin statistics.

In this work, we revamp the democratic mixing matrix (DM) by adding a perturbation term such that the mixing angles derived from it are compatible with the NuFIT 6.1 and recent findings from the Jiangmen Underground Neutrino Observatory (JUNO). To do this, we have incorporated perturbation term in the elements of the mixing matrix such that it does not lose its unitarity. Thus, the democratic mixing matrix, once ruled out by the experimental evidences from T2K, Double Chooz, and Daya Bay, can be modified with rotational perturbation in the (1,2), (1,3), and (2,3) sectors and additional real parameters added in each element of DM. Finally, we analyze the allowed and disallowed textures in light of the JUNO findings.

A recent study has discovered a highly polarized millimeter continuum source called Punctum located at the central region of NGC 4945 which doesn't fit any known category. Apart from the radio detection at $\approx 100$ GHz, there is no identified counterpart to Punctum in other radio, infra-red, optical, and X-ray bands. All available potential models, including magnetar, supernova remnant and microquasar, cannot provide satisfactory explanation for the exceptionally high polarization of $\sim 50$% and large luminosity in mm band $L_{\rm mm} \approx 2\times 10^{35}$ erg/s within a small size $<2$ pc shown in Punctum. In this article, we discuss the possibility that Punctum is indeed a primordial black hole (PBH) with a dark matter density spike. We show that the synchrotron radiation due to the electrons and positrons produced from dark matter annihilation can satisfactorily explain the observed properties of Punctum and we can effectively obtain the annihilation cross section $\langle \sigma v \rangle \sim 10^{-33}$ cm$^3$/s using our developed analytic framework. Furthermore, if the Punctum PBH mass is $\sim 10-100M_{\odot}$, the preferred dark matter mass range is $m_{\rm DM} \sim 10-1000$ MeV.

Quantum skyrmions are topological structures that have garnered significant interest due to their demonstrated robustness and versatility across diverse optical platforms. However, existing approaches for their generation are limited to producing pre-determined two dimensional qubit states with a single topology. Here we create multi-dimensional topological states by introducing a non-local interaction between high-dimensional photonic entanglement and a metasurface, where the topological transformation induced by the metasurface is made non-deterministic by the probabilistic nature of the interfacing entangled state. Within this framework, we demonstrate that individual quantum states can host multiple co-existing topologies that are only revealed upon measurement, allowing for their parallel transport within distinct spatial mode channels. We confirm this by revealing the rich topological landscape within our modified Hilbert space while controlling the desired output topology by orbital angular momentum (OAM) projections on one of the entangled photons, producing multiple non-local polarization-OAM entangled states characterized by distinct topological classes, all from a single metasurface device. Our results reveal new capability when structured high-dimensional entanglement is interfaced with structured matter capable of coupling photonic degrees of freedom, establishing a new pathway for the compact generation of complex quantum states.

Codeword-stabilized quantum codes give a unified graph-state description of stabilizer and nonadditive quantum error-correcting codes. Although each individual CWS word state is stabilizer, coherent superpositions of different word states can be nonstabilizer. We develop a CWS-adapted magic-witness framework that isolates this codeword coherence and converts it into certified lower bounds on robustness of magic. The main result is an exact reduction of the stabilizer threshold of a natural CWS coherence witness to a finite-geometric problem over the classical CWS word set. For general weighted superpositions, the threshold is computed by enumerating affine intersections and affine-quadratic phases. For equal-weight superpositions, the phase optimization collapses, and the threshold is determined entirely by how many CWS words can lie in affine flats of each dimension. Thus a quantum optimization over stabilizer states becomes a classical affine-incidence problem. This reduction yields a fixed-parameter algorithm, an analytic lower bound for an infinite union-stabilizer family, and exact rational certificates for several standard nonadditive CWS examples. The framework also clarifies why exact enumeration fails for large structured families and identifies the remaining task as an affine-intersection problem. The result provides a geometric mechanism by which nonlinear CWS word sets generate certifiable magic.

Topological Euler insulators emerge in multiband systems with real Bloch Hamiltonians and wavefunctions. Their fragile topologies are characterized by the Euler class of degenerate bands and protected by the $PT$ or $C_2T$ symmetry in two dimensions, which go beyond the tenfold $K$-theory classification of topological matter. In this work, we extend the conception of topological Euler insulators to non-Hermitian systems and propose a theoretical framework to unlock their nontrivial Euler topology. Focusing on two-dimensional, three-band non-Hermitian lattice models with symmetric Hamiltonians, we formulate a comprehensive description of their topological Euler bands, entanglement spectrum and bulk-boundary correspondence. Three typical models of non-Hermitian Euler insulators are constructed and investigated explicitly to illustrate our theory. Unique topological phase transitions and anomalous edge-band overlaps with non-Hermitian origins are further identified. Our study establishes the presence of topological Euler bands in non-Hermitian systems and unveils their intriguing physical characteristics, thereby broadening the existing territory of topological matter in non-Hermitian open systems.

The double-indexed geometric phase (DIGP) based on a family of Poincaré spinors was formulated to extend the Pancharatnam phase, commonly used to describe the evolution of the polarization state in an optical system relative to a reference polarization state. Analytical results establish the symmetries of the DIGP under reversal of the index $p\in\mathbb{R}$ for the latitude on the Poincaré sphere, the phase change induced by reversal of the index $q\in\mathbb{R}$ for the longitude on the same sphere, and the periodic dependence on $q$. For closed loops on the Poincaré sphere, the DIGP can be interpreted geometrically through a $p$-dependent mapping of both geographic coordinates and the associated solid angle subtended at the center of the sphere. Although the geometric phase is usually applied to compare two plane waves propagating in the same direction in free space, the DIGP is expected to contain information when comparing two non-co-propagating plane waves, as demonstrated by specular reflection by a planar thin film and far-zone scattering by a three-dimensional object. DIGP maps for specular reflection and transmission by thin films resolve Bragg phenomenons, Fabry–Pérot resonances, structural chirality, anisotropy, and defects with detail not evident in reflectance and transmittance maps. A map of direction-dependent DIGP for plane-wave scattering by a three-dimensional object may reveal strong polar and azimuthal structure absent from the map of differential scattering efficiency. Principal component analysis indicates that a collection of DIGP maps, all calculated from the same set of polarimetric measurements, form a coordinated data family rather than a collection of independent observables. The DIGP concept offers a complementary framework for polarization-state-resolved characterization and inverse scattering.

The nonlinear differential equation, which describes changes of membrane's density in the process of propagation of active potential along a nerve, has been studied. Depending on values of dispersion terms of that equation, forms and possible existence of exact periodic and solitary solutions were considered.

Development of spontaneous coherence is one of the hallmarks of bosonic condensation in a variety of physical systems, such as cold atoms, confined photons, and hybrid light-matter quasiparticles like exciton polaritons in semiconductors. While spatial coherence is well understood once a steady-state condensate has been established, its temporal evolution as the condensate forms is largely unexplored. Here, we explore the dynamical formation of a non-equilibrium, driven-dissipative exciton-polariton condensate through both time-resolved experiments and numerical modeling. Our study reveals that the spatial coherence is established through two distinct stages. The early-time stage is interaction-driven and features transient oscillations in spatial coherence. This stage is followed by a steady-state regime characterized by a spatially-uniform high degree of coherence that extends over the entire size of the system and persists over time. These stages of spatial coherence development occur in both free flowing and confined exciton-polariton systems that undergo a quench - rapid growth of the condensate starting from two different initial settings. Our study offers a deep insight into the process by which long-range spatial coherence is established in a non-equilibrium bosonic condensate.

We present sequential 12-18 and 18-26 GHz radio-band ($Ku$, $K$) VLA observations of the 22 Myr dM1e star AU Mic. We detect two flares and two marginal events over a total of 3 contiguous hours on source, resulting in a radio flare rate of $\sim$1 flare hour$^{-1}$. While this rate is consistent with previous $Ku$-band observations, both flaring ($<$1 mJy) and quiescent ($\sim$0.4 mJy) flux densities are significantly lower. Furthermore, the quiescent spectral shape here is distinct, allowing for unique constraints on the radio-emitting sources of AU Mic. The time-averaged quiescent spectrum is best described by gyrosynchrotron radiation with a peak around 17 GHz and an optically thin spectral index of $\alpha \approx -0.6$. We estimate that the source regions have magnetic field strengths of $\sim$1 kG and cover a fraction of $<$0.5% of the stellar surface, yet the instantaneous total electron kinetic energies are $\sim$10$^{28}$ erg. The power-law index describing the distribution of electrons with energy derived from the spectral index, $\delta \approx 2$, implies a near-continuous injection of electrons. This could arise from micro-flares that occur over the surface of AU Mic that sustain the radio radiation. One clear flare per band occurs, with decay-to-rise $e$-folding time ratios of $3 - 4$, indicating magnetic trapping of the electrons. The $Ku$-band flare is optically thick during the rise and peak times, indicating a peak frequency above 18 GHz. Together, these quiescent and flaring characteristics suggest that continuous, unresolved micro-flaring and magnetic trapping dominate the non-thermal radio emission of active M-dwarf coronae.

The blowup equations of Huang, Sun and Wang are bilinear relations satisfied by the refined topological string partition function of a local Calabi–Yau 3-fold. We prove the blowup equations for the local Hirzebruch surfaces \(\operatorname{Tot}_{\mathbb F_\ell}K_{\mathbb F_\ell}\), \(0\leq\ell\leq2\), as identities of torus-equivariant symmetrized \(K\)-theoretic stable pair invariants; for \(\ell=2\) the invariants are localized indices. The proof identifies the stable pair vertex sum, after division by the fibre contribution, with the equivariant Euler characteristic of \((\det\mathcal V)^\ell\) on the moduli space of framed rank \(2\) sheaves on \(\mathbb P^2\). The blowup formulas of Nakajima–Yoshioka for framed sheaves then yield the unity and vanishing equations. For local \(\mathbb P^2\) we obtain the blowup equations conditionally on two explicitly stated conjectures. We also state the Huang–Sun–Wang conjecture for general local Calabi–Yau 3-folds in the language of stable pairs, and formulate stable pair conjectures for the local rational elliptic surface involving the \(E_8\) lattice.

Synthesis planning for inorganic materials requires predicting both synthesizability and viable routes by linking microscopic thermodynamic stability with macroscopic synthesis methods, precursors, and processing conditions. Here, we develop an interpretable Physics-Informed Retrieval-Augmented Generation Language Model (PIRAG-LM) for end-to-end inorganic crystal synthesis planning. We construct a material-centered Structured Synthesis Knowledge Base (SSKB) containing route-level records for 13,820 experimentally synthesized inorganic crystals. PIRAG-LM retrieves historical precedents using chemical, structural, and thermodynamic similarity, then employs a structured LLM reasoning module to propose routes, precursors, and processing conditions and assess thermodynamic feasibility, kinetics, and accessibility. It achieves 91.4% accuracy in synthesis-method prediction, compared with 72.1% for the LLM alone, and generalizes to materials reported after the knowledge cutoff. Because the framework relies on retrieval rather than parametric memorization, its performance can be improved by expanding the SSKB without retraining the language model. Guided by PIRAG-LM, we experimentally synthesize five new compounds: BaMo0.3In0.7O2.95, BaNb0.4In0.6O2.9, Hg[B(CN)4]2, CoCo(CN)6, and SrNb2Fe2(PO4)6, via solid-state and solution routes. These results demonstrate an interpretable machine-learning approach that helps bridge computational materials discovery and experimental realization.

Following the work by Rowan et al., I found that a large fraction of systems presented as triple/quadruple stars are in fact only blends. After careful inspection of 225 candidate systems from Rowan et al., I found that one-third of them are, in fact, only blended signals of two different eclipsing binaries, well separated from each other on the sky. Their typical angular separation is dozens of arcsec, reaching up to more than 100 arcsec for some targets. This is probably due to relatively large TESS pixels and insufficient cross-checking of all available catalogues and photometric data. I present a list of 76 confirmed blends with their correct identification and respective periods. Such a high fraction (33.8 per cent) of reported false-positive systems should be taken into account in future studies, when reporting to new discoveries of doubly eclipsing candidates.

Frequency-to-time mapping (FTTM)-based photonics-assisted spectrum sensing enables wideband spectrum monitoring for applications such as cognitive radio and electronic warfare. However, FTTM-based photonics-assisted spectrum sensing approaches involve trade-offs among analysis bandwidth, temporal resolution, and frequency resolution. Although channelization has been introduced to alleviate these trade-offs, the limited number of available channels in previously reported systems constrains further improvements in overall performance. Here, we propose a photonics-assisted dual-comb channelization architecture for broadband frequency measurement and time-frequency analysis. The system employs a stepped-frequency pump based on stimulated Brillouin scattering (SBS) to generate an optical filter comb and adopts a single-laser design for the pump, probe, and reference paths to enhance frequency stability while reducing system complexity. Experimental results show a 48-GHz analysis bandwidth in the 16-channel configuration and 52 GHz in the 20-channel configuration, together with microsecond-scale temporal resolution and a frequency resolution better than 80 MHz. The proposed architecture therefore offers a practical and reconfigurable solution for real-time wideband spectrum sensing.