Papers

We experimentally investigate how symmetry-protected topological order in a one-dimensional cluster state is transformed by measurement and decoherence in a five-qubit superconducting array. We first characterize the state's nonlocal string order and show that controlled dephasing selectively suppresses one symmetry sector while leaving the other robust, consistent with average symmetry-protected topological order. We then measure one sublattice in a tunable basis and show that the remaining qubits are driven between a long-range-entangled GHZ state and a paramagnetic state. When the measurement record is discarded, the conventional long-range correlator vanishes while a nonlinear fidelity correlator remains finite, providing a finite-size signature of strong-to-weak spontaneous symmetry breaking. These experiments demonstrate how conditioning, averaging, and decoherence reveal distinct manifestations of order encoded in the same underlying cluster state, and establish a superconducting-circuit setting for probing mixed-state symmetry and topology.

We present a novel framework for improving dark siren cosmology by applying a Gaussian process (GP) to the line-of-sight (LOS) reconstruction of incomplete galaxy catalogs. In the standard galaxy catalog method for inferring the Hubble constant $H_0$ from gravitational-wave (GW) dark sirens, missing galaxies are typically assumed to follow a uniform distribution in comoving volume, an assumption that discards galaxy redshift clustering information crucial for cosmological inference. We propose instead to model the LOS galaxy redshift distribution as a non-parametric function drawn from a GP realization, which is fitted to the observed incomplete catalog via a hierarchical Bayesian likelihood that explicitly accounts for the survey selection function. Applied to mock GW and galaxy catalogs extending up to redshift $z\leq0.4$, our method yields $H_0$ constraints that are on average 23% more precise than the standard homogeneous completion when using a 24%-complete galaxy catalog, and 37% more precise for an 8%-complete catalog. The largest improvement, reaching 66%, is obtained in configurations where the GP most effectively reconstructs the redshift over- and under-density features that the homogeneous completion fails to capture.

We use spatially resolved Keck Cosmic Web Imager spectroscopy to study high-surface-brightness stellar components and internal kinematics in 44 low-surface-brightness galaxies from the SMUDGes survey, including 30 ultradiffuse galaxies, spanning the red sequence, green valley, and blue cloud regions of the galaxy color-magnitude diagram. Although these galaxies appear largely smooth in survey imaging, we detect at least one cluster candidate in every galaxy. We identify clusters with nebular emission lines in 24 galaxies. They are common in blue-cloud galaxies but rare in red sequence galaxies. We identify three nuclear star cluster candidates, one of which shows nebular emission lines. Among clusters without nebular emission lines, bluer galaxies tend to have brighter cluster luminosity functions, suggesting the presence of young or intermediate-age clusters in addition to old globular clusters. This age diversity may complicate the use of photometrically selected globular cluster populations as tracers of total halo mass. We measure rotation velocities for 17 galaxies using the clusters with nebular emission lines and for 12 using diffuse stellar light. Within 0.5 effective radii, the inferred dynamical mass generally exceeds the stellar mass, although the inferred dark matter contribution varies by an order of magnitude. The variety in properties for this sample of ultradiffuse galaxies and low-surface-brightness dwarfs suggests that no single formation mechanism explains the population of low-surface-brightness galaxies.

Warm dark matter (WDM) has served as a valuable benchmark for constraining small-scale structure in the past decades. In this note, I examine what it would take for dark matter to be warm in the literal sense assumed by that benchmark, i.e., a thermal relic that decoupled while relativistic. Satisfying current constraints on the WDM mass, which approach the $\sim$10 keV scale, requires one of three possibilities. One possibility is that there were $\sim 10^4$ relativistic degrees of freedom in the thermal bath at the time of decoupling, which is far beyond what is available in the Standard Model or plausible extensions of it. An alternative is that there was a period of early matter domination whose entropy injection diluted the relic density. However, in this scenario, the perturbations would have evolved through an expansion history that was different from the radiation-dominated one assumed in deriving WDM transfer functions. The third possibility is a dark sector that was never in thermal contact with the Standard Model and was simply born colder via asymmetric reheating. All of these possibilities rely on strong coincidences, where physics that has nothing to do with WDM happens to provide the exact initial conditions assumed in a WDM cosmology. Meanwhile, WDM is often used as a proxy for models with self-consistent thermal histories that generically predict the suppression of structure formation on small scales in a way that is both quantitatively and qualitatively different from WDM. I therefore advocate for a transition to more expressive parameterizations and simulation-based methods in order to extract more useful information from the wealth of upcoming data.

We predict and classify interaction-driven quantum spin Hall crystals (QSHCs), a class of states emerging at fractional filling through an interplay of topology and spontaneous translation-symmetry breaking. QSHCs form nearly degenerate manifolds whose members can realize distinct topological phases protected by time-reversal or valley $U(1)_v$ symmetry, with time-reversal acting nontrivially within the manifold. As a representative of this broad class of states we provide evidence for 9-fold quasi-degenerate $\sqrt{3}\times\sqrt{3}$ charge ordered QSHCs at $\nu = -8/3$ of twisted bilayer MoTe$_2$ near a $5^\circ$ twist. Here a $\mathbb{Z}_3$ index organizes states related by lattice translation into three time-reversal invariant states with nontrivial $\mathbb{Z}_2$ topology and three time-reversal related doublets whose individual members spontaneously break time-reversal and carry a $U(1)_v$ protected spin-Chern number. Finally, we determine the conditions that favor QSHCs over closely competing intervalley-coherent crystals.

A magnetic field applied perpendicular to the helical axis of a monoaxial chiral helimagnet compresses the spin helix into a coplanar chiral soliton lattice (CSL). We show that optically driven high-harmonic generation from itinerant electrons coupled to a frozen CSL resolves the lattice-scale structure of the localized twist, rather than the continuum soliton shape. High-order harmonics remain perturbative for the uniform helix. As the winding localizes at fixed magnetic period, they grow by many orders of magnitude and acquire a nonperturbative dependence on the drive amplitude. The growth originates from a spatially nonuniform effective hopping that turns each soliton into a localized dip in the hopping amplitude. When the degree of winding localization is held fixed, high-order intensities fall by many orders of magnitude as the magnetic period increases toward the continuum limit, where the hopping modulation is spatially smoothed. High-order harmonics thus resolve a real-space characteristic of the coplanar CSL, even in the absence of scalar chirality and an emergent magnetic field.

Correlations allowed by quantum mechanics can defy any classical explanation, with Bell nonlocality standing as their most profound and operationally powerful manifestation. While nonlocality has been demonstrated across a wide range of platforms, in many-body systems it has remained limited to ensembles of qubits, leaving the observation of higher-dimensional multipartite Bell correlations an open challenge. Here we report the observation of qutrit Bell correlations in a spin-1 $^{87}$Rb Bose-Einstein condensate via the violation of a Bell witness based on collective spin observables only. Exploiting spin-exchange collisions in an ensemble of $N \simeq 3.1 \times 10^{4}$ atoms, we generate spin-nematic squeezing of $-11.8(7)$ dB and observe a violation that surpasses the minimum bound achievable by a collection of $N$ qubits, providing direct evidence of genuine multipartite qutrit Bell correlations. Our results establish spinor Bose-Einstein condensates as a viable platform for investigating high-dimensional Bell correlations in the many-body regime, and demonstrate that coarse-grained collective measurements suffice to certify the dimensionality of quantum correlations at macroscopic scales.

The Johnson-Nyquist theory is commonly implemented by representing a conductor as a collection of independent local thermal-noise sources whose strength is determined by the local temperature. Whether this local-noise representation remains valid for electrically coupled conductors maintained at different temperatures has received comparatively little attention. We investigate this question by means of microscopic two-dimensional simulations of interacting charge carriers in conducting wires capacitively coupled. The model reproduces Ohm's law, the equilibrium Johnson noise, and vanishing correlations between detached wire segments when both wires are at the same temperature. However, when the wires are held at different temperatures, finite correlations develop between the electromotive forces generated in distant segments, leading to systematic deviations of the Johnson temperature inferred from the local-noise picture. The effect persists although the microscopic particle interactions are short-ranged and the two wires interact only through the capacitive coupling. These results suggest that the independent-local-source representation of thermal noise may not remain valid in electrically coupled nonequilibrium conductors.

We establish a uniqueness theorem in four-dimensional spacetime, demonstrating that a nonlinear spinor system naturally constrains the background geometry to the Kastor-Traschen spacetime, which describes dynamical, cosmic multi-black-holes. By analyzing a nonlinear field equation where the super-covariant derivative of a Dirac spinor is sourced by intrinsic fermion currents, we evaluate its integrability under two physical requirements: a phase-locking condition enforcing a real hermitian product $\overline{\psi}_R \psi_L$, and a pure-electric source condition. We show that the field equation uniquely compels the spinor to be an eigenvector of the super-covariant Dirac operator, with the eigenvalue dynamically identified as the Hubble constant of the de Sitter background. These results provide a novel geometric mechanism wherein both the cosmological constant and dynamical black hole configurations spontaneously emerge from fermion condensates.

Stellar variability has become the dominant limitation to achieving the radial velocity (RV) precision required for the detection and characterization of Earth-like exoplanets. While significant progress has been made in mitigating the effects of oscillations and magnetic activity, convective granulation and its interaction with stellar magnetic fields remain among the least understood sources of RV variability. To address these challenges, we organized the splinter session `Connecting Granulation and Magnetic Activity in Radial Velocities: The Next Breakthrough for High-Precision Spectroscopy' at Cool Stars 23. The session brought together researchers working on observations, numerical simulations, and data-driven techniques to discuss the current understanding of granulation-driven RV signals and identify the most promising directions for future progress. Through invited and contributed talks, followed by community discussions, participants emphasized the importance of combining physically motivated models with data-driven approaches, developing standardized benchmark datasets, and validating simulations against high-quality observations across a range of stellar types. The discussions also highlighted the need for coordinated observing strategies, improved characterization of individual spectral lines, and physically informed line-by-line analyses to disentangle convective and magnetic signals. This contribution summarises the scientific discussions and community perspectives that emerged during the session and outlines the key challenges that must be addressed to reach the sub-40 cm/s precision required for the next generation of RV planet searches.

We study CFT$_3$ realizations and celestial representations of the $\mathcal{L}_{\Lambda}w_{1+\infty}$ algebra. Free scalar and Dirac theories yield the same one-particle light-ray action. This action extends to the critical $O(N)$ model at $N=\infty$. At large but finite $N$, we use the light-ray algebra under its closure assumptions and check prescribed iterated limits of the frequency kernel. In the dimension-completed celestial hard-graviton representation, a closed raising subalgebra annihilates $G_3^+$ exactly. We construct two nonzero singular descendants in its induced module and prove that both vanish in the celestial realization. They implement the finite-spin condition and massless spin-two shortening of the generated highest-weight sector. The nonzero-$\Lambda$ quadratic Casimir has eigenvalue three throughout the hard family. The null descendants and low-spin Ward identities yield ordered differential–difference equations for celestial correlators.

Electromagnetic fluctuations can transfer not only energy but also angular momentum, leading to forces, torques, heat currents, and friction in out-of-equilibrium setups. In enclosing configurations, we show that if at least one of two objects is rotationally symmetric, the torque is bounded by heat transfer, since both arise from photon transfers with angular momentum $\hbar n$ and energy $\hbar\omega$. With only one object assumed to be rotationally symmetric, it may be possible to obtain a nonzero torque with reciprocal media, but nonreciprocal media are required to break the symmetry between $n$ and $-n$ and produce a nonzero torque if both objects are rotationally symmetric. We then specialize to concentric cylinders with a nonreciprocal dielectric response and use Rytov fluctuational electrodynamics to express heat transfer and torque in terms of an angular-momentum-resolved flux density, $\Phi_n(\omega)$. We also analyze the conditions for stable levitation of the inner cylinder using the proximity force approximation, in the process obtaining a new analytic formula for the normal Casimir force between dilute plates at different temperatures. Finally, to find the extracted work in a contactless engine setup, we compute the fluctuation-induced friction for a slowly rotating inner cylinder, and we find a bound between torque, friction, and heat transfer. Due to this bound, the efficiency of the heat engine remains bounded by the Carnot limit.

The Indian Dark Matter Search Experiment (InDEx) operates superheated droplet detectors with tetrafluoroethane ($\mathrm{C_2H_2F_4}$) as the active target at the Jaduguda Underground Science Laboratory (JUSL), and has so far probed dark matter (DM) through nuclear recoils at operating temperatures at which the target is insensitive to electron recoils. In this work, we consider six operating temperatures, $T=45$–$70\,^\circ\mathrm{C}$ in steps of $5\,^\circ\mathrm{C}$; the corresponding Seitz thresholds range from $0.61\,\mathrm{keV}$ down to $26.8\,\mathrm{eV}$. The ionization response of the $\mathrm{C_2H_2F_4}$ target is computed in the isolated-atom approximation from Roothaan–Hartree–Fock wavefunctions. The projected $90\%$ confidence-level upper limits on the DM–electron scattering cross section are derived for a dark-photon-type mediator in both the heavy- and light-mediator limits, for a benchmark exposure of $10^3\,\mathrm{kg\,days}$ under the zero-background assumption. For the lowest threshold, $E_{\rm th}=26.8\,\mathrm{eV}$ at $T=70\,^\circ\mathrm{C}$, the search probes DM masses down to $\sim 12\,\mathrm{MeV}$, with the $90\%$ confidence-level limit reaching $2.7\times10^{-41}\,\mathrm{cm}^2$ near $m_\chi\simeq100\,\mathrm{MeV}$ for the contact interaction and $3.0\times10^{-37}\,\mathrm{cm}^2$ near $m_\chi\simeq83\,\mathrm{MeV}$ for the long-range interaction. The electron channel thus extends the reach of InDEx to sub-GeV DM masses, down to $\mathcal{O}(10\,\mathrm{MeV})$, providing a complementary probe of low-mass dark matter alongside its nuclear-recoil program and enhancing sensitivity to DM candidates coupling predominantly to leptons.

Large language models (LLMs) hallucinate numerical values when generating high-stakes meteorological text, posing risks for weather communication. We present AFDBench, an AI meteorologist that generates professional Area Forecast Discussions (AFDs) by reasoning through structured AI weather forecast data from Google's WeatherNext 2. We introduce AFDBench, the first benchmark for evaluating generative meteorological reasoning, comprising 7,732 expert written discussions from 13 National Weather Service (NWS) offices paired with real AI weather forecast inputs, and three complementary metrics: Met-Align (numerical accuracy), Style-Align (professional dialect adherence), and Input-Grounding (fidelity to source weather data). Zero-shot evaluations reveal that open-source LLMs achieve low Style-Align (~0.33) and moderate Input-Grounding (~0.88), failing to write in the professional NWS register or faithfully use their input data. We apply Group Relative Policy Optimization (GRPO) with domain-specific rewards targeting temperature accuracy, synoptic correctness, and format compliance. On 1,033 held-out samples from two unseen NWS offices, GRPO nearly doubles Style-Align from 0.318 to 0.619 and improves Input-Grounding from 0.881 to 0.940, demonstrating that reinforcement learning teaches a 7B-parameter model to write like a professional meteorologist and faithfully interpret AI weather data.

Scalar-induced gravitational waves (SIGWs) probe primordial curvature perturbations beyond cosmic microwave background scales, while primordial black holes (PBHs) probe the rare tail of the same statistics. We ask whether SIGW morphology can reveal scale-dependent primordial non-Gaussianity. We adopt the internal-leg separable kernel, $\mathcal F_{\rm NL}(\mathbf{k};\mathbf q,\mathbf{k}-\mathbf q)=\bar f_{\rm NL}f(q)f(\lVert\mathbf{k}-\mathbf q\rVert)$, and compute Gaussian, reducible, and connected contributions through $\mathcal O(\bar f_{\rm NL}^{4})$ in the second-order tensor-source approximation. We compare persistent power-law running with a UV-matched tanh weight that saturates at high scalar momentum. Across narrow, finite-width, asymmetric, and multi-slope scalar spectra, running produces more than amplitude renormalization. Power-law running shifts the scalar support sampled by non-Gaussian convolutions, generating peak displacement, asymmetric shoulders, and persistent ultraviolet deformations. The tanh template instead produces a transition-localized modification and approaches a momentum-independent ultraviolet plateau. Analytical estimates of the perturbative hierarchy, weighted slopes, log-normal saddle displacement, peak shifts, and infrared scaling explain the trends and the enhanced sensitivity of the $\mathcal O(\bar f_{\rm NL}^{4})$ sector. For localized sources with finite weighted moments, smooth running preserves the leading $k^3$ infrared behavior up to logarithmic corrections. Since the PBH mass scales as $M\propto k^{-2}$, preferential high-wavenumber weighting conditionally favors lower PBH masses in a narrow-support interpretation. Peak position, spectral curvature, shoulders, and ultraviolet slopes are diagnostics for PTAs, LISA, and third-generation observations, providing finite-order templates for primordial interactions on otherwise inaccessible scales.

We investigate the melting dynamics of an ice disk subjected to an external oscillatory flow using two-dimensional direct numerical simulations, in the absence of buoyancy, varying the flow amplitude and its oscillation frequency. We identify two distinct regimes governed by the interplay between advection and diffusion within the boundary layer. For slow oscillations, the melting process is well described by an effective steady flow, where a description based on classical forced convection is applicable. For fast oscillations the melting time increases significantly and approaches the diffusion limit regime, as a result of the oscillatory flow being unable to renew the fluid within the oscillating boundary layer, causing cold meltwater to accumulate near the interface and reducing heat transfer.

Few planetary systems form in isolation. Rather, interactions in their birth environments may sculpt their architectures or drive them into unstable configurations. Here we study the role of environmental perturbations in triggering dynamical instabilities leading to hot Jupiter formation in dense clusters, focusing on whether the elevated occurrence rate of hot Jupiters in the open cluster M67 can be explained through flyby-induced high-eccentricity migration. We develop a hybrid method for modelling the secular and tidal evolution of planetary systems under external perturbations by passing stars using a combination of analytic and numerical approaches. We evolve 10,000 realizations each of systems with either a single planet, two planets, or a planet and a stellar companion for $\sim$4 Gyr in an M67-like cluster, comparing outcome statistics against a control sample without flybys. In single- and two-planet systems, the rate of flyby-induced hot Jupiter formation is negligible. However, in systems with an initially isotropically oriented stellar companion, the cluster environment boosts hot Jupiter formation by a factor of $\sim$2, accompanied by a factor of $\sim$3 increase in the rate of planets undergoing tidal disruption. Based on observationally motivated estimates of primordial populations, our hot Jupiter yields are consistent with both field and M67 occurrence rates, provided the primordial wide binary fraction among solar-type stars is close to $\sim$50 per cent, binary-driven high-eccentricity migration is the dominant formation pathway, and a substantial fraction of tidally disrupted systems survive as hot Jupiters through partial mass loss.

Chemical interactions between the hydrogen-dominated envelopes and silicate-rich interiors of sub-Neptunes likely play a key role in shaping their atmospheric structure, mass-radius relations, and upper atmosphere composition. While atmospheric abundances and structure deeply influence each other, many existing models have either considered the effects of chemical interactions without the structural implications or have modeled the envelope structure using oversimplified chemical networks. In this work, we introduce Rocky Raccoon, a coupled chemical equilibrium-atmospheric structure model. This model incorporates Mg, Si, O, C, and H species and produces self-consistent atmospheric chemical and thermal profiles for sub-Neptune envelopes, treating multi-species condensation for the first time. We find that the condensation sequence of magnesium silicates above a magma ocean is determined by the basal magma composition. We show that these condensation sequences drive the upper atmospheric composition to two endmembers: high oxygen abundances in the underlying melt produce compositions rich in oxygen-bearing volatiles (sub-solar C/O) and higher mean molecular weight atmospheres with $\mu \sim 4$ amu, while oxygen-poor melts produce lower mean molecular weight atmospheres dominated by methane and silane (super-solar C/O). The transition between the two regimes is abrupt and depends on melt properties like Mg/Si ratios and oxygen abundances. The different condensation sequences also lead to different thermal profiles, as deep convection is inhibited over different regions due to varying molecular weight gradients. Further experiments and simulations are key to resolving critical uncertainties in the condensation sequences and the corresponding significant impacts on sub-Neptune composition and thermal structure.

In particle physics, discovery claims conventionally require an observed significance exceeding $5\sigma$. However, the interpretation of a $5\sigma$ result depends critically on the testing procedure, namely whether the hypothesis is tested at a single pre-specified point in parameter space or by scanning over a range of possible signal locations. This distinction gives rise to the look-elsewhere effect, a concept that is widely used but often interpreted as a simple penalty for scanning. In this work, we reinterpret the look-elsewhere effect as a correction for procedural inconsistency arising when the null distribution is generated under one procedure while the test statistic is evaluated under another. Within the framework of hypothesis testing, we examine its implications and clarify the distinct roles of the look-elsewhere effect in binary and peak-search scenarios. In particular, we show that binary test is robust against the look-elsewhere effect, whereas peak searches require an explicit correction for the search over signal locations. Using a moderate trial factor of approximately 26, calibrated from the ATLAS Higgs search, we show that a $3\sigma$ global significance of peak search can correspond to approximately $4\sigma$ significance of the binary test for the same value of the observed test statistic. This reformulation provides a clearer statistical interpretation of the look-elsewhere effect and offers a more coherent framework for understanding significance claims in particle physics.

We study the Ising model on $\mathbb{Z}^d$ with $d\geq 4$ and derive near-critical bounds on the truncated two-point function $\langle\sigma_0;\sigma_x\rangle_{\beta,h} := \langle\sigma_0\sigma_x\rangle_{\beta,h} - \langle\sigma_0\rangle_{\beta,h}\langle\sigma_x\rangle_{\beta,h}$ at parameters $\beta\leq\beta_c$ and $h\geq 0$. As a corollary, we obtain that the associated mass (or exponential decay rate) is equal to \begin{equation*} \max\bigl((\beta_c-\beta)^{1/2},h^{1/3}\bigr)^{1+o(1)}, \end{equation*} where $o(1)$ tends to $0$ as $(\beta,h)$ tends to $(\beta_c,0)$. The proof combines the corresponding result at $h=0$, recently established by Duminil-Copin and Panis, with an interpolation argument inspired by Aizenman and Fernández and carried out via the random current representation of the model.

The design of disordered point patterns with desirable properties is an exciting and ongoing research endeavor, with applications ranging from materials to computer science. A successful approach in recent years has been the optimization of point patterns through a loss function that enforces properties in their Fourier-space representation. Yet, these methods have so far strictly been limited to flat Euclidean space, precluding their use in the contexts of coatings of curved surfaces for photonics, or of sampling of curved manifolds for instance. We introduce FaSHIoNPOp, an algorithm that relies on fast non-uniform spherical harmonics transforms, to enforce pair correlations in point patterns on the sphere with an $O(N \log N)$ complexity in $N$ the number of points. Having demonstrated its performance, we showcase applications of FaSHIoNPOp, ranging from the generation of hyperuniform structures on the sphere for sampling and physical applications, to the design of gyromorphs (disordered structures with maximal scattering power at a given frequency) on the sphere. We additionally show that FaSHIoNPOp can be combined to both global constraints like centrosymmetry, with applications to the design of more isotropic $3d$ gyromorphs, and local real-space constraints like pair repulsion. Our work paves the way for optimal sampling and coating design on curved manifolds, with many applications across physics, materials and computer science.

The topology of the electronic structure for an avoided crossing and a conical intersection (CI) is different and is characterized by the presence of the geometric phase in the electronic wavefunction in the latter. Using the linear Jahn-Teller model, we show that an avoided crossing can be created from the conical intersection while preserving the nontrivial topology of the latter by adding a Pauli $\sigma_y$ term to the Hamiltonian. Analogously to solid state systems, we derive a half-integer topological invariant as the integral of the Berry curvature over the CI nuclear branching space. We investigate the influence of electronic topology on chemical dynamics by conducting fewest-switches surface hopping simulations and find distinct hopping rates on identical eigensurfaces but with different topologies. Our work extends the influence of topology on molecular excited state dynamics beyond the Berry phase that can be practically realized through electron-nuclear and spin-orbit coupling.

For $N\ge2$ and $\beta>0$, consider the canonical 2D Coulomb gas ensemble \begin{equation} \mathrm{d}\mathbb{P}_{N,\beta}(Z) =\mathsf{Z}_{N,\beta}^{-1}e^{-\beta|Z|^2/2} \prod_{i<j}|z_i-z_j|^{\beta/N}\mathrm{d} Z \qquad\text{on }\mathbb{C}^N. \end{equation} The factor $N^{-1}$ in the pair exponent places the ensemble at the diffusive, or high-temperature, scale. We prove that, for every fixed inverse temperature $\beta>0$, this Gibbs measure satisfies a logarithmic Sobolev inequality (LSI) on the closed Dirichlet-form domain generated by collision-free compactly supported smooth functions, with a positive constant independent of $N$. The LSI constant may be chosen uniformly when $\beta$ ranges over a compact subset of $(0,\infty)$. A second main result establishes Poincaré and logarithmic Sobolev inequalities for planar Gaussian measures weighted by finite products of positive powers of distances to points, with constants depending only on the total variance of the underlying Gaussian measure and the total exponent, not on the number or locations of the points. To prove the full labeled Poincaré inequality, we decompose variance into permutation-invariant and label-dependent parts, controlled respectively by a weighted $\bar\partial$ estimate and by relative-coordinate conditioning with random transpositions; separately, one-site logarithmic Sobolev inequalities, a conditional entropy inequality, and a repulsive partition estimate give a defective logarithmic Sobolev inequality. Rothaus tightening combines the resulting full labeled Poincaré inequality with the defective logarithmic Sobolev inequality. The two main theorems on their stated closed form domains and all results used in their formal proofs, including those from the literature, have been formalized in Lean 4.

The emergence of Galactic PeV astronomy makes photon–photon ($\gamma\gamma$) absorption an increasingly important component of gamma-ray data analysis. In this work, the Galactic Photon Survival Probability (GPSP) atlas is presented as the first Galactic framework describing gamma-ray survival probabilities over the full parameter space $P(l,b,d,E_\gamma)$ between 1 TeV and 10 PeV. The atlas is constructed using two independent GALPROP-based interstellar radiation field (ISRF) models, allowing direct assessment of ISRF-related systematics, and is released in a FITS format compatible with standard analysis frameworks. A novel gamma-ray survival phase space representation is introduced, extending 1D survival profiles into a 2D energy–distance framework that visualizes Galactic transparency and gamma-ray horizons. Using the full atlas, Galactic transparency and Galactic plane survival maps are constructed. These reveal that Galactic opacity is highly structured, with enhanced attenuation along spiral-arm tangent directions in the $\sim$100–300 TeV regime, while attenuation becomes nearly isotropic and cosmic microwave background (CMB) dominated near PeV energies. The framework naturally accommodates attenuation calculations for extended and diffuse sources. The atlas is further extended to subluminal Lorentz invariance violation (LIV) scenarios through the GPSP-LIV atlas, incorporating LIV-modified pair production kinematics and cross sections. Sources emitting in the 2–3 PeV regime beyond gamma-ray horizons are identified as promising targets for probing LIV effects. Finally, practical applications are presented for the Galactic Center PeVatron and the Cygnus X-3 regions. The GPSP and GPSP-LIV atlases establish a publicly available foundation for studies of Galactic PeVatrons, diffuse gamma-ray emission, and fundamental physics searches in the emerging era of Galactic PeV astronomy.

The classical radiation-pressure instability predicts strong thermal variability in luminous black-hole accretion disks, whereas most disk-dominated X-ray binary soft states remain comparatively stable. We examine whether net vertical magnetic flux can weaken this instability through its contribution to the radial stress. The stability depends not only on the equilibrium magnetic stress but also on how that stress changes during a thermal perturbation. We write the local stability condition in terms of the logarithmic heating response, $q_+<q_{+,\rm crit}$, which avoids specifying how the turbulent stress is divided into reference and net-flux components. For the illustrative closure $\delta=\zeta\sqrt{\bpol\btor}/\alpha$, $\etad=-d\ln\delta/d\ln H$ describes the response of the fractional stress correction, while $\Gnf=d\ln W_{\rm nf}/d\ln H$ describes the response of the additional net-flux stress itself. For an accretion disk around a $10M_\odot$ black hole at $R=20\rg$ and $\Mdot=0.5\MEdd$, we adopt fixed local mass flux on the thermal timescale, $(\gamma,\gp)=(1,0)$, and $d\ln\zeta/d\ln H=0$. Marginal stability then occurs at $\bpol^{\rm crit}=0.0176$ for $\zeta=1$ and $0.1338$ for $\zeta=0.25$. These thresholds depend on the adopted stress closure and field-response prescription and should not be interpreted as universal magnetic-pressure fractions. Fixed-$B_z$ equilibrium sequences, using a separate relation for the variation of $B_\varphi$ between steady states, show that increasing vertical field narrows the thermally unstable accretion-rate interval but does not eliminate it for either $H/R<0.1$ or $H/R<0.2$. The relevant quantity for stabilization is therefore the thermal response of the stress associated with net vertical flux rather than the vertical magnetic-pressure fraction alone.

We characterize all maximally charged black hole spacetimes in $3+1$ dimensions. More precisely, given any initial data set $(M,g,k)$ saturating the mass-charge inequality that satisfies the charged dominant energy condition, we show that $(M,g,k)$ must arise from an isometric embedding into a Majumdar-Papapetrou spacetime.

The $GW$ approximation is the standard tool for quasiparticle predictions in materials, yet its regime of validity in correlated systems remains poorly quantified, because ab initio vertex corrections are computationally prohibitive. Using exact diagonalization of the half-filled extended Hubbard model on finite rings as a numerically exact reference, we construct the corresponding model-space $GW$ theory on the identical Hilbert space and quantify its error as a function of local ($U$) and non-local ($V$) interaction strength. We find that the required vertex correction changes character across the phase diagram: in the weak-coupling regime the effective vertex $\Gamma_{\rm eff} < 1$, reflecting the suppression of RPA charge fluctuations by exact short-range correlations, whereas in the Mott regime $\Gamma_{\rm eff}$ grows monotonically (to $\sim 3$ at $U=8t$ for $N=6$), reflecting the local dynamical self-energy structure required to open the Hubbard gap. Vertex corrections in the electron-hole (polarizability) channel are shown to worsen the gap error, indicating that reproducing the Mott gap requires dynamical self-energy structure rather than improved screening. For $V=0$, static COHSEX is accidentally exact at a single crossover $U^* \approx 3.5\,t$; finite $V$, through non-local Fock exchange, splits this point into a double-crossover window that collapses toward weak coupling. Even at the crossover, however, the exact spectral function retains Hubbard-band structure that no static functional reproduces, so gap agreement does not imply functional accuracy. These results yield quantitative diagnostics for the reliability of $GW$ in correlated materials.

We report the use of DFT computation and mathematical models to predict the nonlinear dielectric polarization (P^{NL}) and nonlinear susceptibility coefficients (\chi^{(2)}_{IJK}) of organic materials based on their crystal structures. We apply this computation approach on single-component crystals, co-crystals and ionic crystals found through data mining the Cambridge Structural Database. We verify these computational results with experimental terahertz (THz) generation efficiencies for known THz generators, demonstrating consistency between the measurements and the computed values. Several mined structures show similar or larger PNL values compared to state-of-the-art THz generation crystals DAST, OH1 and BNA, suggesting great potential for their use in nonlinear optical (NLO) applications. Importantly, we also compared the resulting model of nonlinear optical tensor components with commonly-used simplifications of nonlinearity, showing that the comprehensive approach should be the standard method to evaluate the nonlinear optical properties of single-crystalline materials.

In a recent breakthrough, Yamakawa and Zhandry (J. ACM 2024) constructed a proof of quantumness in the quantum random oracle model (QROM) in which the quantum prover samples a codeword preimage of a publicly computable function H. They conjectured that given any H, a successful prover must sample their preimage from a high-entropy distribution over possible answers. If true, this would give a certifiable randomness protocol in the quantum random oracle model. As partial evidence for their conjecture, Yamakawa and Zhandry proved the security of their certifiable randomness protocol assuming the Aaronson-Ambainis conjecture. We prove the security of the certifiable randomness protocol of Yamakawa-Zhandry unconditionally, without relying on the unproven Aaronson-Ambainis conjecture, against low query-depth quantum adversaries: specifically, adversaries that make up to o(\log \lambda) adaptive quantum queries to the random oracle.

Twenty-five years of RHIC operation have produced a uniquely diverse dataset, which enables a broad physics program. This contribution highlights recent STAR results in four areas: exotic-state searches and ultra-peripheral collisions; the onset of quark–gluon plasma (QGP) signatures in small systems; radial flow and its fluctuations; and polarization and spin correlations.