Papers

We use microlocal tools to define distinguished incoming and outgoing vacuum states of the quantum theory of massive Klein–Gordon fields in non-trapping asymptotically flat spacetimes, including radiative perturbations of Minkowski space. The asymptotic vacuum states satisfy the Hadamard condition, and the incoming and outgoing particle representations are unitarily equivalent, or in other words the quantum S-matrix is well-defined. These results are based on a description of scattering of classical fields which keeps track of the asymptotic distinction between positive- and negative-frequency solutions of the Klein–Gordon equation. Our emphasis is on developing the theory without recourse to explicit asymptotics for classical waves.

We establish quantitative hypocoercivity for singular stochastic damped wave equations arising in stochastic quantization. Building on the finite-dimensional argument of Cao, Lu, and Wang [Arch. Rat. Mech. Anal. 2023], we derive a dimension-free criterion that replaces uniform semiconvexity by a log-Sobolev inequality together with exponential lower-tail bounds for the bottom of the Hessian spectrum. We verify this criterion for the two-dimensional $\Phi^4_2$ and sine-Gordon models and for the three-dimensional $\Phi^4_3$ model, through estimates on the lowest eigenvalue of associated singular random Schrödinger operators. Combined with the continuum limit established in a companion paper, this yields exponential $L^2$ convergence to equilibrium for the $\Phi^4_2$ dynamics and for sine-Gordon with $\beta^2<2\pi$. For $\Phi^4_2$, we verify that in a weak-coupling, small-mass regime, optimizing the damping yields a kinetic relaxation rate of at least order $m$. This yields a genuine acceleration over the order-$m^2$ relaxation rate of the overdamped dynamics. The lattice estimates are uniform in the discretization for sine-Gordon throughout $\beta^2<4\pi$, and for $\Phi^4_3$ at fixed volume, including regimes beyond those for which the continuum dynamics is vpresently constructed.

We measured the conversion rate from 1s orthoexcitons to 1s paraexcitons in Cu$_2$O below 1 K using a dilution refrigerator. To determine the conversion rate, we performed time-resolved luminescence spectroscopy of 1s orthoexcitons and 1s paraexcitons confined in a strain-induced trap potential. From the time evolution of the ${\Gamma}$$_3$$^{-}$-LO-phonon-assisted luminescence of 1s orthoexcitons, we obtained a conversion rate of $5.9 \times 10^7$ s${^{-1}}$ at a mixing-chamber temperature of 64 mK under an applied stress of 2.2 kbar. Between 64 and 800 mK, the conversion rate depends only weakly on temperature, and it is less than half of the value of $1.6 \times 10^8$ s${^{-1}}$ reported at 2 K under the same applied stress. The conversion rate therefore continues to decrease below 2 K, contrary to the previous expectation that it becomes nearly constant below about 1.7 K. We discuss these results in terms of the momentum distribution of orthoexcitons, which does not reach equilibrium with the lattice during the conversion at these low temperatures. These findings call for a theory that accounts for both the small magnitude of the conversion rate and its weak temperature dependence below 1 K.

The origin of hot Jupiters remains an open question. A significant fraction reside in binary or multiple star systems, suggesting that stellar companions may play an important role in shaping their present-day architectures. However, the orbits of the vast majority of these stellar companions remain poorly constrained, leaving their role in hot Jupiter evolution an open question. We present the Tracing the Influence of Distant companions on Exoplanetary Systems (TIDES) survey, a campaign to map the orbits of stellar companions in systems hosting hot Jupiters to assess the extent to which binaries play a role in hot Jupiter formation and migration. Here, we introduce our survey design and new orbital fits for the first six systems in our sample—$\tau$ Boo, WASP-2, WASP-11, WASP-76, HAT-P-14, and HAT-P-16—by combining previous observations of the stellar companions together with new Keck/NIRC2 imaging and Keck/KPIC relative radial velocities. Among these six systems, the four with the most precisely constrained orbits exhibit high eccentricities ($e \geq 0.8$), and three of these systems also display significant planet–binary misalignments ($\Delta i \geq 20^\circ$). This suggests the orbital properties of stellar companions to hot Jupiter host stars are qualitatively different than field binaries and binaries hosting inner transiting small planets. These orbital architectures are consistent with stellar companions shaping the evolution of hot Jupiters, either through high-eccentricity migration or by participating in an earlier episode of dynamical evolution that ultimately led to hot Jupiter formation. Continued orbital monitoring of the full sample will reveal whether outer stellar companions play a causal role in the evolution of hot Jupiters.

Photogenerated carriers in lead-halide perovskites are widely believed to move as large polarons, whose accompanying lattice distortion is thought to screen the carrier from charged defects. Three recent findings call this picture into question. First, time-resolved structural probes now measure the photoinduced lattice distortion directly; yet calculations show that thermal motion of the lattice alone can raise the carrier effective mass-an increase previously taken as evidence for polarons-so that it remains unclear whether the lattice distortion around a carrier is really a polaron. Second, the carrier-lattice coupling strengthens as the material is thinned from 3D to 2D. In the two main families of 2D perovskites, Ruddlesden-Popper and Dion-Jacobson, the carrier couples to the lattice through different channels, and their contrasting behavior is set by which coupling channel dominates rather than by lattice stiffness alone. Third, the first direct test of defect tolerance does not point to polaron screening; its authors attribute defect tolerance to the soft, disordered lattice. New transport data show that polaron screening reduces scattering between carriers, but not that it protects carriers from defects. Polaron formation, even if established, therefore does not establish polarons as the cause of defect tolerance. Separating the two requires measuring the lattice distortion as a function of excitation density, over a range spanning the low densities of a solar cell under sunlight and the much higher densities used in most ultrafast experiments. On this basis, we propose experiments that can clarify how photogenerated carriers behave in lead-halide perovskites.

We consider the matrix model of a seven-dimensional quantum space built from concentric fuzzy $CP^3$'s of increasing matrix size, and show that its continuum limit is the metric cone $C(CP^3)$ over $CP^3$, not flat $R^7$. Every ingredient is fixed before any comparison, so this geometry is a prediction rather than an input. The two geometries agree in the $s$ wave ($p=0$) but separate in the higher angular sectors (harmonics on $CP^3$ of degree $p\geq1$): in each sector tested, the spectrum of the free Laplacian converges at second order to that of the cone, and at 20480 layers the cone is matched to $1\times10^{-9}$ for $p\leq8$, whereas flat space misses by 8-18%. The free propagator converges to that of the cone at the same order, and heat diffusion reproduces the $r^6$ measure and the Bessel spectrum of the cone. The maps between neighbouring layers are obtained in closed form from the polar decomposition of the second-quantized Schwinger-boson lift, using a known operator identity, and coincide with the Kováčik-Tekel coefficient-copying prescription. For $CP^1$ the construction reduces, away from the outer boundary, to the Kováčik-Tekel fuzzy onion. Modes along the twistor fibre are exactly degenerate with the harmonics on $S^4$.

How can language models learn to optimize physical designs through experience? We introduce FracLearn, an experience-abstraction-generalization framework evaluated through a deliberately unfamiliar, Tetris-inspired fracture game. The model first proposes architectures and examines simulated fracture responses to accumulate experience. Abstraction organizes these observations into conditional principles linking reinforcement placement, crack evolution and load transfer, with supporting evidence and failure conditions. Generalization challenges the model to combine these principles in new architectures and surpass the earlier design record. Campaigns demonstrate progressive refinement and recovery through hypothesis revision, yielding a best composite score 11.0% above the experience-stage record. Fracture analyses connect improved performance to crack deflection and temporary trapping as toughening mechanisms, alongside greater residual load capacity. Learning occurs through external knowledge and decisions, without model-weight updates. This approach offers a route to scientific agents that turn computational experiments into reusable physical knowledge for materials discovery and engineering design.

In this paper, we present the first results for the one-loop decay $A \rightarrow ZZ\gamma$ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. We calculate the one-loop partial decay widths and branching ratios for both unpolarized and polarized final-state $Z$ bosons. The effects of Vector-Like Quarks propagating in the loop are also examined in our phenomenological analysis. We find that the branching ratios can reach $10^{-5}-10^{-4}$ for several benchmark points within the viable parameter space of the considered models. The contributions from Vector-Like Quarks can modify the total rates by approximately $5\%$. With the high luminosities expected at future multi-TeV muon colliders, these effects may be experimentally accessible.

Based on our previous results regarding critical exponent estimates for the 3D Ising model and scaling relations [1], we have proven that the exact value of the correlation-length exponent is $\frac{\sqrt[3]{2}}{2}$. This is in very close agreement with the most precise numerical estimates currently available. Using a group theoretical approach and some propositions of constructive geometry, we derived an exact construction of algebraic expressions for the critical exponents $\gamma$ and $\beta$. We proved that these expressions depend solely on the exact value of $\nu\,$.

Compared with a scalar Bose-Einstein condensate (BEC), a spinor BEC supports richer phenomena because of its internal spin degrees of freedom, including topological solitons such as domain walls or skyrmions. Here, we theoretically reveal three distinct axisymmetric soliton structures formed as a circular domain wall in a spin-1 BEC, connected within fixed winding numbers. We refer to these structures as the broken-axisymmetry (BA)-skin, antiferromagnetic (AF)-skin and normal-core phases. Their occurrence is controlled by the two dimensionless parameters in the absence of linear Zeeman coefficient $p=0$: $q/\mu$, the ratio of the quadratic Zeeman coefficient to the chemical potential, and $c_s/c_n$, the ratio of spin interaction to the density interaction. The BA-skin and AF-skin phases exhibit local easy-plane magnetic order and local easy-plane spin-nematic order, respectively, while the normal-core phase is similar to a doubly quantized vortex analogous to that of a scalar BEC with a density depletion at the center. We obtain semi-analytical estimates of selected transition boundaries separating these phases by analyzing the Bogoliubov-de Gennes equation and also numerically confirm them by solving the Gross-Pitaevskii equation. We estimate the skyrmion radius using a hydrostatic approximation and compare the result with numerical solutions. We envision our results on skyrmions in a spin-1 BEC can trigger further investigation on novel soliton structures in a magnetic superfluid.

Level crossings, where two quantum energy levels intersect, are ubiquitous in quantum systems and play a central role in controlling quantum dynamics. In this study, we establish a framework that connects these level crossing structures to the ultimate precision limits of quantum metrology. By analyzing a Hamiltonian with the level crossings structure, we identify the conditions under which multiple parameters can be estimated simultaneously with maximal sensitivity near the level crossing point. We then construct a resource efficient sensing protocol based on unitary quench dynamics and Bayesian estimation, enabling high precision, low cost parameter estimation without requiring entanglement or complex control. We present a protocol whose estimation precision saturates the Holevo Cramer Rao bound, the tightest achievable precision bound in multi parameter estimation. Using the two level model and the two spin Ising model as illustrative examples, we demonstrate how the protocol can be applied to a system with level crossing Hamiltonian structure. Our findings reveal that level crossings serve as universal operating points for precision quantum metrology, offering a simple and scalable path toward practical multi parameter sensing across diverse quantum platforms.

We calculate analytic expression for the cross section up to order $(eB)^2$ for the production of a heavy quark $(Q)$ of mass $m_Q$ through the gluon $(g)$ fusion process $g+g\to Q+\bar{Q}$ in the presence of a constant weak external magnetic field $(B)$ with strength $eB \ll m_Q^2$. This is done using the weak-field expansion of the fermion propagator calculated within Schwinger's proper-time formalism. Owing to the hierarchy of scales ($m_Q^2 \gg eB$), we neglect the effects of the magnetic field on the quark and antiquark spinors in the external lines. Since the magnetic field breaks rotational invariance, the cross section becomes anisotropic and depends on the relative orientation angle $(\theta)$ between the magnetic field and the incoming gluons in the center-of-mass frame. The lowest-order magnetic correction to the vacuum cross section scales as $(eB)^2$ and is found to have $\cos 2\theta$ and $\cos 4\theta$ dependence, reflecting the breaking of rotational symmetry by the magnetic field. The cross section is maximized when the gluons propagate along the field direction ($\theta = 0, \pi$) and minimized in the perpendicular configuration ($\theta = \pi/2$). The resulting asymmetry peaks near the production threshold and falls with increasing center-of-mass energy, scaling as $(eB)^2/m_Q^4$ with the quark mass. These results provide direct, calculable signatures of the initial-stage magnetic field in relativistic heavy-ion collisions which can, in principle, be imprinted on heavy-flavour observables measured in the final state of heavy-ion collisions.

Replacing the circle by a manifold leads to current Lie algebras and their central and derivation extensions. We separate the coefficient algebra, harmonic analysis and geometric data. Differentials modulo exact forms describe central extensions; divergence-free vector fields give explicit cocycles, whose compatible derivations satisfy a stabilizer equation. Compact examples include the three-sphere and its current–Virasoro extension. We also explain the analytic qualifications for SL(2,R) and its symmetric space and the role of transported multiplication in soft geometries. The recent harmonic constructions of Campoamor-Stursberg, Marrani and Rausch de Traubenberg are compared with the cohomological work of Coquereaux, Frappat, Ragoucy and Sorba and Castellani's loop geometry and infinite-dimensional free differential algebras. A coefficient-algebra construction connects currents to higher brackets and clarifies the additional requirements of a dynamical theory. For Lie algebras of order F, central extensions obey coupled binary and symmetric F-ary conditions, with explicit examples and obstructions.

Neopentane-derived plastic crystals undergo order-disorder phase transitions accompanied by exceptionally large entropy changes, making them attractive solid-state materials for thermal energy storage and barocaloric cooling. Yet it remains unclear whether the microscopic nature of this entropy change is an intrinsic property of each compound or can be understood generally and tuned systematically through molecular design. Here, we use classical molecular dynamics simulations of neopentyl glycol (NPG), pentaglycerine (PG), and pentaerythritol (PE), validated against experimental transition temperatures, enthalpy changes, and phase diagrams, to show that the character of the phase-transition entropy undergoes a complete inversion as the hydrogen-bond connectivity of the molecule increases: orientational disordering dominates in NPG, whereas lattice vibrations dominate in PE and become remarkably robust against pressure. PG occupies a balanced intermediate regime in which the orientational, conformational, and vibrational channels contribute comparably. This inversion reflects two coupled microscopic mechanisms: a growing low-frequency gap between the phonon densities of states of the ordered and disordered phases as the hydrogen-bond network densifies, and an increase in molecular symmetry that progressively suppresses orientational disordering. Because the vibrational channel is substantially less sensitive to pressure than the orientational one, hydrogen-bond density emerges as a practical, chemically accessible design handle for tailoring not only the magnitude but also the pressure robustness of the caloric response in hydrogen-bonded plastic crystals, with direct implications for the search for new barocaloric and thermal-energy-storage materials.

Boson sampling with array of on-demand single photons (discreet variable Fock states) as resource states provides distinct advantages in complexity scaling compared to single photon resource states mimicked by the states (continuous variable) generated in nonlinear photonics. Recent progress in realization of regular ordered array of mesa top single quantum dots (MTSQDs) enabling on-demand generation of many photon resource states with high single photon purity and indistinguishability [1,2] has opened the possibility of implementing chip-scale Boson sampling with single photons. An important question towards scale up of such circuits is how the dephasing and decay timescale of individual on-demand single photons affect the final probability distribution of the N-photon entangled state. In this work we report a framework that provides direct link between the physical sources of decoherence to the outcome of multiphoton correlation measurements. We explicitly incorporate the symmetrization of the N-photon states while accounting for the shape of the individual wave packets and dephasing. Using this framework, we show predictive estimates of the probability of generation of a 4-photon NOON state using an optical circuit initialized with 4 identical single photon wave packets, mimicking the emitted photons from MTSQD single photon sources reported in [2]. Specifically, we show how the probability of generating various 4-photon entangled states depend on the two-photon interference visibility which is determined by the pure dephasing timescale in relation to the radiative decay timescale. The results provide quantitative guidelines to measure 4 photon and higher number of entangled photon states generated in an optical circuit with on demand single photon sources and provide a link between physical processes such as temperature and the output state of the quantum optical circuits.

The 3He(alpha,gamma)7Be reaction takes place in several distinct astrophysical scenarios. First, in solar hydrogen burning, 3He(alpha,gamma)7Be controls the competition between the pp-I chain, on the one hand, and the pp-II and -III chains, on the other hand. Its rate directly affects the solar model predictions for the well-measured 7Be and 8B solar neutrino fluxes, which can in principle be used as solar thermometer. Second, in Big Bang nucleosynthesis, 3He(alpha,gamma)7Be is the main production channel for primordial 7Li, the decay product of 7Be. Finally, the reaction is believed to produce radioactive 7Be in astrophysical novae. The cross section of this reaction has been studied previously using different methods, namely 7Be activation, 7Be recoil detection, and in-beam {\gamma}-ray detection. The latter studies have in many cases been performed with just one detector in close geometry. Here, for the first time a comprehensive measurement of the 3He({\alpha},{\gamma})7Be {\gamma}-ray angular distribution is reported. Altogether 22 high-purity germanium detectors were used, arranged at 27-145 degrees angle with respect to the beam direction. Data were taken at 442-1213 keV center-of-mass energy. In addition, one data point for the astrophysical S-factor was obtained with the activation method. The angular data are compared with the predictions from a hybrid theoretical approach, where the E1 transitions are modeled using a cluster-based effective field theory (EFT) while the M1 and E2 transitions within an EFT-inspired framework. Good agreement is found, if the interference among these multipolarities is taken into account in the theory.

When an agent leaves a spatial network, its replacement removes old contacts and may transport population to a new location. The frequency of replacement alone therefore does not determine how turnover changes spatial organization. We study diffusing agents joined by persistent attractive contacts, with the total pull on each agent bounded. At fixed population, successors appear at the departure position, within a surrounding disk, or anywhere in the system. We ask whether small differences between dense and dilute regions grow or fade. The theory separates an exactly calculable diffusion and replacement contribution from an approximate attraction contribution obtained by averaging the contact network. Paired simulations find similar attraction contributions under the three rules at all nine sampled wavelengths. Changing only the replacement location reverses the broadest tested pattern: it grows with replacement at the departure position but fades under both displaced rules. An independent radius scan traces this change from growth to decay. Under displaced replacement, intermediate wavelengths grow between sampled long and short scales with decay. Rates measured in the earliest finite window are compatible with the prediction at long and intermediate wavelengths; discrepancies are already present at short wavelengths. Replacement distance thus helps determine which spatial density contrasts are initially amplified.

Variational quantum algorithms utilize parameterized circuits many times during training, at new parameter values, over batches of data, and with gradients. Pauli propagation approximates the expectation values of such circuits classically by evolving the observable in the Heisenberg picture as a truncated sum of Pauli strings. We present PADO-Pauli, a GPU engine for Pauli propagation that compiles a circuit and its observables once into sparse matrices in which each rotation angle contributes only a cosine and a sine factor, so every later evaluation reuses the compiled program. It evaluates batches of parameters and data inputs embedded as rotation angles. By default its gradients come from a vector-Jacobian product registered with PyTorch's automatic differentiation, so they flow through the angles to any classical layer that produces them. PADO-Pauli also provides truncation by Pauli weight and coefficient size, and noise channels. Zero-filtering removes terms that do not contribute to an expectation value in the all-zero reference state and makes the batched forward pass about 1.5 times faster. Compared to cuPauliProp on an NVIDIA A100, PADO-Pauli evaluates up to 10 times faster on 4 to 12 qubits and uses up to 3.1 times less memory on 16 qubits. We check its accuracy against exact statevector simulation up to 28 qubits. These features make PADO-Pauli a practical toolkit for training variational quantum algorithms, including quantum machine learning models.

We investigate the thermal phase structures and kinematics of atomic hydrogen (H I) gas in the Draco nebula to clarify how infalling H I evolves toward cold atomic and molecular clouds. Using the DHIGLS H I 21 cm data, we apply the Regularized Optimization for Hyper-Spectral Analysis (ROHSA) algorithm to decompose the emission into spatially coherent Gaussian components, and classify them as warm neutral medium (WNM), lukewarm neutral medium (LNM), and cold neutral medium (CNM). We identify two kinematically distinct WNM components: WNM1 near $-3$ km s$^{-1}$ and WNM2 near $-30$ km s$^{-1}$. The LNM forms a broad velocity bridge between two WNMs, whereas the CNM is concentrated within a narrower intermediate velocity range. CO emission is also confined to this interval and is associated with CNM-rich regions. The H I mass fractions are $\sim 41\%$, $\sim 23\%$, $\sim 17\%$, and $\sim 19\%$ for WNM1, WNM2, LNM, and CNM, respectively, with the LNM and CNM together accounting for $\sim 36\%$ of the total H I mass. No comparably independent WNM component is recovered at intermediate velocities, although a weak broad component may remain unresolved. The observed phase structures are consistent with a dynamically compressed multiphase interaction layer in which compression increases the gas density, shortens the radiative cooling time, and drives the evolution from WNM through thermally unstable gas toward the CNM. The present interaction may both create new CNM, and further compress or grow pre-existing dense structures. Our results provide the missing link between previous evidence for dynamical interaction and molecular cloud formation in Draco, and identify CNM formation as a key step in transforming gas accreting toward the Galactic disk into cold atomic and molecular clouds.

Conventional theoretical descriptions of moiré superlattices, epitomized by the Bistritzer–MacDonald continuum model, are fundamentally constrained by low-energy Dirac cone approximations and first-shell interlayer coupling truncations. While successful for small-angle twisted bilayer graphene near charge neutrality, these frameworks fail to provide universal analytical solutions for strained lattices, high-energy band behaviors, or arbitrary commensurate geometries. Here, we establish a unified, approximation-free analytical formalism for generalized moiré systems based on three pillars: (i) a rigorous two-dimensional-to-one-dimensional supercell cyclic mapping, (ii) exact block-circulant diagonalization of intralayer Hamiltonians, and (iii) quasi-degenerate Löwdin perturbation theory centered on arbitrary energy degeneracy points across the full spectrum. Unlike traditional schemes anchored to the Dirac point, our approach enables systematic perturbative expansions around any band crossing, unifying the characterization of low-energy flat bands with high-energy degeneracies. We demonstrate that this framework perfectly recovers the Bistritzer–MacDonald model in the low-energy limit while extending its reach to heterostrained systems and high-energy regimes. By incorporating high-order interlayer coupling shells, we reveal an intrinsic scale self-similarity in moiré lattices and predict the emergence of higher-order magic angles and tunable flat bands driven by secondary degeneracies. This work eliminates the long-standing lack of universal analytical tools for diverse moiré platforms, providing a full-spectrum theoretical foundation for band engineering and the exploration of exotic correlated and topological states in van der Waals heterostructures.

We present the first targeted Einstein Probe (EP) X-ray observations of any planetary nebula (PN). Using the onboard Follow-up X-ray Telescope (FXT), we detect X-ray emission within the central region of IC 1297. The spectral analysis yields a plasma temperature of $kT = 0.086^{+0.054}_{-0.058}$ keV ($T\sim1.0 \times 10^{6}$ K), characteristic of shocked wind bubbles in PNe, whereas there is no evidence that its Wolf-Rayet central star emits X-rays. The absorption-corrected X-ray luminosity in the 0.3–2.0 keV energy band is $L_{\mathrm{X}} = 2.8 \times 10^{32}$ erg s$^{-1}$, also consistent with a hot bubble. At an adopted distance of $\sim3.8$ kpc, IC 1297 is the most distant X-ray emitting PN found to date, opening up a new observational window on hot-bubble formation and evolution. It is also among the most luminous known X-ray-emitting PNe. Our results demonstrate the capability of the EP FXT for detecting and characterizing faint, extended X-ray sources in the soft X-ray band for distant PNe, extending the known spectral properties of detectable X-ray emitting PNe. We also compiled the X-ray properties of all 41 known Galactic XPNe, finding a clear correlation between distance and X-ray luminosity that reflects an observational bias toward detecting the brightest sources at large distances. The compilation also shows a separation in X-ray luminosity between hot bubbles powered by H-rich and [WR]-type central stars, with the latter reaching luminosities up to an order of magnitude higher. The ten most luminous XPNe all host [WR]/PG 1159 central stars.

Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.

Chiral perturbation theory is a power tool for studying the low-energy strong interactions. In the conventional chiral expansion, according to the power counting rule, the higher-order corrections for physical observables are expected to decrease order by order as the chiral dimension increases. However, most previous study of $\pi K$ scattering lengths by different references showed that the $\mathcal{O}(p^6)$ correction to the scattering lengths is anomalously large and even exceeds the $\mathcal{O}(p^4)$ one. It poses a serious challenge to the convergence of chiral expansion. In order to explore the underlying origin of this phenomenon, the contributions of two-loop diagrams, one-loop diagrams and tree diagrams for the $\pi K$ scattering amplitude are detailed analyzed. The reducible two-loop integrals, sunset integrals and vertex integrals from the $\mathcal{O}(p^6)$ order all violate the power counting rule. The sunset and vertex integrals can be largely canceled numerically, but not enough. Furthermore, $\pi K$ scattering is compared with $\pi\pi$ scattering, which seems not violate the power counting rule. The analysis indicates that $\pi\pi$ scattering contains a higher symmetry, although each $\mathcal{O}(p^6)$-order part also violates the power counting rule, but the violation is much smaller than the one from $\pi K$ scattering. Large kaon mass also makes a contribution to the power-counting breaking, but it is not a major origin. Hence, it needs to pay more attention to the many-loop low-symmetry diagrams in future work. These diagrams may give large contribution and cannot be ignored.

We prove that the simulated annealing algorithm efficiently samples from the Sherrington-Kirkpatrick model at inverse temperature $\beta < 1$ to an arbitrary inverse polynomial accuracy in total variation.

Clouds and disequilibrium chemistry shape the observable properties of substellar and planetary atmospheres, and JWST time-resolved spectroscopy now enables direct tests of their three-dimensional structures. We present an update to the 3D atmospheric framework ADAM, coupling the dynamical core to a miniature kinetic chemistry scheme (mini-chem) and a saturation-relaxation tracer cloud module. Using this framework, we investigate the atmosphere of the brown dwarf orbiting the white dwarf ZTFJ0038+2030 in a 10-hour orbit. The brown dwarf receives stellar irradiation comparable to its internal heat flux, placing the atmosphere in a regime where the circulation is characterized by a standing Matsuno–Gill wave response and equatorial superrotation. Rapid rotation confines these structures closer to the equator, producing more symmetric broadband light curves with smaller hotspot offsets than canonical hot Jupiters, in agreement with recent JWST observations of this system. Although most species are globally homogenized, rapid rotation limits global-scale horizontal mixing and allows circulation-driven vertical transport to maintain strong CO and CO$_2$ inhomogeneities in the photosphere. These chemical inhomogeneities produce asymmetric phase curves in the CO and CO$_2$ absorption bands, which could qualitatively explain the observed CO$_2$ light-curve asymmetry. When clouds are included, Na$_2$S clouds dominate the photosphere and weaken the large-scale circulation, lowering photospheric CO and CO$_2$ abundances, while MgSiO$_3$ and Fe clouds rain out at deeper levels. Because the dominant Na$_2$S clouds reside mostly above the quench region, cloud-driven convection has limited impact on the quenched abundances, which are instead regulated mainly by large-scale circulation.

Practical quantum programs interleave quantum and classical computation: classical data shape the quantum operations that are performed, and measurement outcomes shape the classical computation that follows. Formal verification of such programs in a proof assistant requires mechanizing a program logic that handles this interplay consistently at every level, from the mathematics of quantum mechanics, through program syntax and semantics, to specifications and proof rules. Such mechanizations, along with the program proofs built on them, typically require substantial manual effort. We present QEDIA, a framework for verifying quantum programs with classical variables in Lean 4. At its foundation is an open library that formalizes the quantum Hoare logic QHL+ across all these levels and proves the logic sound for both partial and total correctness. We construct the library and the program proofs, under human supervision, using an LLM-based prover agent, whose general-purpose core we extend for quantum program verification. We illustrate QEDIA with verified programs including the quantum Fourier transform, phase estimation, repeat-until-success circuits, and Hamiltonian simulation.

We prove Yau's number-theoretic conjecture on positive integral points in real right simplices in every dimension $n\ge3$, and apply the resulting sharp polynomial bound to quantum harmonic oscillators. The lattice-point bound holds for every choice of positive real intercepts for which the count is nonzero, with equality precisely when all intercepts equal the same integer. For oscillators in dimensions $n\ge3$, we obtain explicit upper bounds for eigenvalue counts and spectral remainders for arbitrary positive frequencies at every threshold at or above the lowest eigenvalue. For frequencies with rational ratios in dimensions $n\ge2$, an additional lattice coordinate and interpolation give bounds for energy sums, or first Riesz means, at every threshold. When all frequencies are equal (the isotropic case), the oscillator attains these bounds: the counting bound is exact at its energy levels, and interpolation on its natural energy grid recovers the energy sum at every threshold. In three dimensions, the exact formula displays the periodic contribution associated with the resonance discussed by Fefferman and Seco. The proof builds on the slicing method of Yau and Zhang. Arithmetic and geometric consequences include explicit bounds for smooth numbers and lattice-point discrepancies.

Creation and control of Majorana zero modes (MZMs) in solid devices is the key challenge in realizing fault tolerant topological quantum computation. Here we report spectroscopic evidence for number controllable MZMs in stoichiometric one quintuple layer Bi$_{2}$Te$_{3}$/FeTe heterostructures, together with the observation of stacked vortices in superconducting islands. Low temperature scanning tunnelling microscopy and spectroscopy reveal a long period moire superlattice arising from lattice mismatch, which induces nanoscale modulation of superconducting gaps. Magnetic vortices exhibit a stacked core structure with two layer derived bound state branches: a dispersive branch evolving into an X-shaped pattern away from the vortex center, and a quantum-limit branch characterized by a spatially unsplit MZMs together with discrete integer quantized Caroli-de Gennes-Matricon states. Notably, MZMs are observed in all measured vortices, and their number can be tuned by magnetic field and the size of Bi$_{2}$Te$_{3}$ islands. These results establish stoichiometric 1QL-Bi$_{2}$Te$_{3}$/FeTe as a patterned superconducting interface that enables isolated and few-vortex Majorana configurations, providing a controlled platform for fuse MZMs.

We present HiRO-ACEv2 (High Resolution Output Ai2 Climate Emulator), a two-stage framework for AI emulation of the 3~km resolution X-SHiELD global storm-resolving model (GSRM), and highlight its ability to generate large ensembles of data for studying the characteristics of tropical cyclones and extreme events in high-resolution simulations at an inference computational cost over 300 times lower than that of traditional numerical GSRMs. HiRO-ACEv2 expands upon the precipitation-only HiRO-ACEv1 model to generate coherent precipitation, 10~m winds, and sea level pressure outputs, enabling a broader range of events to be simulated at high-resolution. Fine-resolution predictions are generated by running an autoregressive emulator of coarsened X-SHiELD at 100 km, whose multivariate outputs are regionally downscaled to 3~km resolution via a separately trained diffusion model. Particular importance is placed on capturing the statistics of extreme events during the diffusion downscaling step. Our ability to match the tails of distributions and generate realistic-looking extreme events in both the `perfect prediction' case as well as in free-running emulator rollouts is improved via the use of multiple denoisers at inference time and several updates to the data sampling, noise sampling, and loss weighting during training. HiRO-ACEv2 closely matches the high-resolution reference distributions of precipitation and near-surface winds out to their 99.9999th percentile values, and broadly tracks the reference distribution of tropical cyclone intensities.

Density-functional tight binding has yet to yield a transferable description of vanadium oxides; for the standard second-order construction and the tested cells, we demonstrate that two of its approximations deviate by electron volts and offset each other in the band-index centroid separation between the V 3d and O 2p bands: the neutral two-centre reference omits electron-volt environmental terms, whereas the Mulliken charge model assigns the compact V 3d shell less than half of the self-consistent potential shift observed in PBE. Instead, we build a tight-binding model where the reference Hamiltonian derives from superposed neutral atoms, the full PBE exchange-correlation potential and frozen-core orthogonality, without adjustable terms, and where the orbital-resolved charge response employs three screening factors obtained from PBE linear response and an unscreened Coulomb range. Relative to the primary PAW reference, the plane-wave Harris-Foulkes energy differences of VO2 are matched by the reference energy at fixed geometry and the stated numerical settings, with signed deviations of +2.6 meV/atom for M1 relative to rutile (an energy difference of 92 meV/atom) and +6.2 and -5.2 meV/atom under 3% volume compression and expansion; the charge response reproduces 14 of 22 fitted and 5 of 8 held-out matched PBE responses within one tolerance, and 28 of the 30 within twice the tolerance, and in rutile the fitted first-radial V 3d shift is -4.39 eV, 0.47 eV more negative than PBE's -3.92 eV, whereas the tested DFTB2 charge model gives -1.53 eV. The convexity of the spinless model at fixed geometry prevents it from spontaneously differentiating symmetry-equivalent sites under the symmetries respected by its implemented operators and sampling, so within this model such differentiation in the Magnéli phases must arise from electron-lattice coupling or an explicit spin or correlation term.