Papers

Electron density is a fundamental quantity of electronic structure, yet most machine learning density models treat it solely as a reconstruction target and are developed separately from machine learning interatomic potentials. Here, we introduce a virtual-atom formulation within the DPA3 framework, in which density query points are represented as virtual nodes and processed by the same parameterized encoder used for real atoms. An asymmetric neighbor construction allows virtual atoms to receive information from nearby real atoms without altering the real-atom interaction graph. The resulting framework supports density, energy, and force prediction through task-specific readout heads. The proposed model achieves state-of-the-art density reconstruction accuracy on the Materials Project benchmark, matches the best reported performance on nickel-manganese-cobalt battery cathode materials, and is competitive with dedicated density models on QM9. When density labels are used jointly with energy and force supervision, the model improves in-domain accuracy, makes local environment information more accessible under linear probing, and reduces zero-shot force errors on larger QM40 molecules. Density-only checkpoints also provide useful initializations for downstream energy-force learning under the fixed fine-tuning protocol. Together, these results support electron density as a source of electronic-structure supervision for interatomic-potential representations.

Charged-particle telescopes play an essential role in studies of nuclear clustering, which require high-resolution detection of charged breakup fragments. GAGG(Ce) is a promising scintillator for charged-particle detection at high counting rates because of its high light yield, fast response, and non-hygroscopic nature. However, systematic data on its light-output response to different charged particles remain scarce. In this work, we present a systematic study of the scintillation light-output response of GAGG(Ce) crystals to various charged particles and quantify the associated quenching behavior. The relationship between the scintillation light output and the deposited energy is established over a broad range of particle species and energies, providing essential experimental input for response modeling and energy calibration of GAGG(Ce)-based charged-particle detector systems.

We derive the secular Hamiltonian of a hierarchical triple from the 1PN ADM three-body Hamiltonian by a two-stage Lie-Hori-Deprit transformation carried out entirely in canonical variables, and use it to settle the relativistic cross terms left open in Paper I. A bookkeeping rule enumerates all contributions to each order in the 1PN parameter $\delta$ and the hierarchy parameter $\varepsilon$. The 1PN monopole interaction reduces to a renormalization of the inner mass by its binding energy, and the order $\delta\varepsilon^{3/2}$, at which Lim and Rodriguez (LR) found a libration term, is empty. The electric and magnetic 1PN $\times$ quadrupole cross terms agree exactly with the effective-field-theory result of Kuntz, Serra, and Trincherini; for the magnetic term this is the first independent derivation. We give the next-to-leading order 1PN $\times$ quadrupole term in closed form; it depends on the outer argument of pericenter $\omega_2$. At quadrupole-squared order we obtain the complete secular Hamiltonian, which generates the secular equations of Will and of Conway and Will; its $2\omega_2$ harmonic is a gauge term, removable even on the commensurability between the ZLK period and the nodal precession, by a generator given in closed form via Tremaine's fictitious time. The EIH and ADM descriptions coincide at 1PN order; the formulations differ only in the definition of the elements, for which we give the osculating-contact map. In secular integrations of LR's triples, the eccentricity enhancement with the octupole is controlled by the $\omega_2$-dependent part of the next-to-leading order term and is two to three times that of Paper I, while LR's accelerated mergers remain absent.

GS 1843+00 (Ginga 1843+009) is a poorly studied Be/X-ray binary system that underwent a major X-ray outburst in 2026 February-May after nearly sixteen years of quiescence. We present an X-ray, optical, and radio study of GS 1843+00 during this outburst, focusing on the evolution of the neutron star emission geometry, Be-disk connection, and possible outflow activity. We analyse three NuSTAR observations obtained at different stages of the outburst, complemented by archival RXTE and Chandra data, optical spectroscopy and imaging with the Nordic Optical Telescope, and a MeerKAT radio observation. NuSTAR observations reveal coherent X-ray pulsations around 29.7 s with a spin-up rate of $(-5.1\pm0.1)\times10^{-8}$ s s$^{-1}$ during the outburst. The pulse profiles show strong evolution with energy and outburst phase, with distinct morphologies even at comparable luminosities. The pulsed fraction varies between 1 and 16% and exhibits a complex reversal in energy dependence above 7 keV, increasing with energy during the first two observations and decreasing during the third. The 3-79 keV broadband spectra are described by thermal Comptonization with a blackbody and an Fe K$\alpha$ emission line, with no evidence for a cyclotron absorption feature. Phase-resolved spectroscopy reveals variations in the Comptonization and blackbody parameters, indicating changes in the accretion-column structure. Optical spectroscopy confirms the presence of a Be-circumstellar disk through H$\alpha$ and Paschen-series emission lines. No radio counterpart is detected, with a $3\sigma$ upper limit of 36 $\mu$Jy beam$^{-1}$ at 1.28 GHz. Weaker H$\alpha$ emission compared with previous epochs indicates that the Be-circumstellar disk was in a different state during the current episode, while the radio non-detection suggests that any associated outflow activity was faint or below the detection limit.

We demonstrate a compact, fully stabilized, all-polarization-maintaining (all-PM) Er:fiber optical frequency comb (OFC) implemented on a silica optical-cube platform. The optical comb module, including the oscillator, amplifier, spectral-broadening stage, 780-nm frequency-doubling branch, and f-to-2f interferometer, occupies a volume of 0.88 L. Without active temperature control, the free-running repetition frequency exhibits a peak-to-peak excursion of 75 Hz over 10 h, corresponding to 0.375 ppm. Under the same laboratory conditions, this excursion is 6.2 times smaller than that of a mechanically mounted non-PM reference comb. The amplified pulses are compressed to 94 fs and spectrally broadened in a PM highly nonlinear fiber. A coherent-population-trapping-based chip-scale atomic clock is employed for the first time as the radio-frequency reference for comb locking, thereby reducing the footprint of the microwave-reference subsystem. The resulting in-loop, optical-frequency-normalized tracking instability reaches 6.03E-17 at 1 s and 2.57E-18 at 10,000 s. These results demonstrate a compact comb architecture with reduced sensitivity to environmental perturbations, providing a practical route toward portable optical atomic clocks.

Most of the mass of the visible universe originates from the strong interaction. Quantitatively reproducing the origin of the nucleon mass is one of the important challenges in fundamental science. Since the next-generation Electron-Ion Collider has identified resolving this problem as one of its major goals, further theoretical studies are needed to develop approaches to investigating the origin experimentally. In this paper, we explore the possibility of evaluating the “gluon condensate term” which is particularly difficult to determine among the contributions to the nucleon mass, using high-energy scattering experiments. We first express the gluon condensate term in terms of experimentally accessible twist-4 lightcone matrix elements. We then derive, for the first time, analytic formulas for the cross section including all twist-4 contributions from pure quark, quark-gluon, and pure gluon matrix elements in $ep$ collisions, and show how these contributions can be related to the gluon condensate term.

We derive Bondi four-momentum balance between past and future null infinity in the radiative phase space of the null-surface formulation (NSF). Weyl matching at spatial infinity, together with vanishing endpoint News, gives antipodal continuity of the Bondi mass aspect. Its translation projection is independent of the infrared shear term and transforms as a Lorentz four-vector. Bondi evolution relates the incoming and outgoing News fluxes to the timelike endpoint momenta; in the Dominguez–Kozameh–Ludvigsen radiative sector these momenta vanish and the fluxes are equal. On a common radiative Fock domain, unitary conjugation transports the flux observables. Adopting their classical balance as an additional quantum condition yields exclusive four-momentum conservation. We also calculate the outgoing energy expectation without imposing that condition. For an incoming energy eigenstate, the second-generator commutator vanishes diagonally, leaving a second-order coefficient determined by the cubic generator. Direct canonical contractions isolate the contribution connected to all four external legs. For the equal-energy center-of-mass preparation, axial rotational covariance forces the angularly integrated exchange coefficient to vanish under the finite helicity-projection prescription of Part~I. The connected energy defect therefore vanishes through second order. The full expectation (including spectators) and higher-order balance remain open.

The observation of superconductivity emerging from a spin- and valley-polarized normal state in rhombohedral graphene raises a basic puzzle: intravalley Cooper pairs involve states that are not generically degenerate because of trigonal warping, and therefore lack the particle–particle nesting underlying the conventional Cooper instability. While recent model studies suggest that nontrivial band geometry can strongly promote chiral pairing, how this geometric enhancement competes with realistic band-structure-induced pair breaking remains unclear. Here we study Kohn–Luttinger superconductivity in electron-doped rhombohedral tetralayer graphene using a DFT-fitted multiorbital tight-binding model, retaining the full Bloch-wave-function form factors in both RPA screening and the projected Cooper interaction. We separate the superconducting instability into three contributions: the symmetry-resolved form-factor-dressed interaction, the Cooper-pair phase space determined by the symmetrized pair dispersion, and the energy mismatch generated by trigonal warping. We find that the Bloch form factors strongly favor intravalley pairing, with a leading predominantly $p_x-ip_y$ instability and a substantially larger maximum $T_c$ than the intervalley reference state. At the same time, trigonal-warping-induced mismatch cuts off the Cooper logarithm and confines intravalley superconductivity to a much narrower region of the phase diagram. The dominant instability occurs near pair-Lifshitz transitions and primarily in reconstructed annular or three-lobed Fermi-surface regimes. Our results show that superconductivity in rhombohedral graphene is controlled by the combined effects of quantum-geometry-dressed interactions, pair fermiology, and trigonal-warping-induced pair breaking.

Trapped ion quantum computing based on the quantum charge coupled device (QCCD) architecture uses functional zoning and ion transport to enable high fidelity computation and all to all qubit connectivity. As trapped ion quantum processing units (QPU) scale, 90{\deg} X-junction turns account for an increasing fraction of total transport time. Frequent junction crossings, therefore, make transport speed and final phonon excitation direct determinants of quantum algorithm execution efficiency. However, complex electric fields in X-junctions complicate waveform design, making it difficult to achieve high speed and low final phonon excitation simultaneously. Here, we develop a waveform design method for low-phonon-excitation high-speed X-junction(LHX-T) transport. It integrates low barrier pseudopotential channel design using multiple radio frequency (Multi-RF), multidimensional shortcut to adiabaticity dynamics, and constrained DC voltage optimization over the entire transport sequence. This framework connects waveform design, control, and computational validation, with smooth multichannel waveforms computed rapidly through a Karush-Kuhn-Tucker(KKT) linear system. The resulting waveform transports a single $^{171}Yb^+$ ion through a 90{\deg} turn in $5\mu s$ at an average speed of 14.6 m/s. Over 50 consecutive round trips, the final equivalent coherent phonon number consistently stays below 0.001, with no noticeable accumulation over time. System level evaluations at the QCCD scale show that the median duration of a single execution cycle is reduced by about $30\%$ across various circuit types. The fraction of execution time spent on transport decreases from approximately $70\%$ to $55\%$. This approach offers a means of designing fast ion transport waveforms with low phonon excitation for scalable QCCD based QPUs and provides a technical basis for efficient execution of quantum algorithms.

We establish an exact correspondence between the quasi-Wronskian and quasi-Grammian constructions for the anti-self-dual Yang–Mills (ASDYM) equations with complex \(2\times2\) matrix-valued fields. Starting from vacuum wave functions associated with \(2M\) pairwise distinct nonzero constant spectral parameters, we restrict attention to a nonempty local domain on which the corresponding interpolation matrix is invertible. We show that both constructions are governed by the same uniquely solvable matrix-polynomial interpolation problem. In particular, the quasi-Wronskian Darboux polynomial \(T(\lambda)\) and the quasi-Grammian rational dressing matrix \(W(\lambda)\) satisfy \[ T(\lambda)=q_\xi(\lambda)W(\lambda), \] where \(q_\xi(\lambda)\) is the monic scalar polynomial whose zeros are the prescribed poles of \(W(\lambda)\). This identity yields explicit relations between the corresponding Yang and potential matrices and shows that the two constructions generate identical ASDYM gauge potentials in the same gauge.

We consider spin-coupled Grover walks on hypercubes within the framework of quantum Bernoulli noises (QBN). We identify parity-dependent harmonic subspaces generated by the central Hamming layers: in even dimension they give a fixed-point subspace, whereas in odd dimension the walk reduces on the harmonic subspace to an explicit eight-dimensional reduced dynamics. Using symmetric-group representation theory, we characterize the corresponding isotypic structure and determine the reduced spectrum. The harmonic reduction also yields explicit long-time probability behavior and shows that the resulting states may occupy an asymptotically vanishing fraction of the hypercube while still spanning its full Hamming diameter.

Searches for dense packings of congruent shapes move rigid pieces. Hardening starts each piece as its inscribed disk and deforms it into the target shape while the container is compressed. We ask whether it is a search worth running alongside existing ones, and test it at matched budget and comparable tuning against rigid starts, growth, simulated annealing and perturbation–compression on seven families of squares, triangles, hexagons and disks in squares, triangles and circles (188 instances), scoring each method by the lowest container size it reaches. Hardening is not a better default: tuned rigid starts reach the lowest size most often. It is a different search. On squares in a square it reaches packings the other four methods miss, including Trump's n = 11 and Wainwright's n = 19 in 32 runs per method, and in a targeted follow-up campaign at ten times the budget (16 runs per method) it is the only one to reach the best known packings for n = 17 and n = 26, while annealing alone reaches n = 27. In exploratory ablations, compressing disks and then switching to polygons at once, or growing rigid polygons along hardening's area schedule, shows no detectable difference from rigid starts, and hardening's unique packings contain more tilted pieces. The bias costs elsewhere: hardening is worse on triangles and on four families held out from all development, where the short-pilot policy we tested showed no detected advantage over always starting rigid. Shape continuation is an alternative search that reaches different packings, worth keeping beside rigid ones; we did not show that splitting a fixed budget between them pays, and we have no test that predicts where it helps. Search campaigns were planned before they ran, with amendments, exploratory analyses and post-hoc checks identified separately; every run is replayable and every number is generated from an event log.

Can a holographic theory be reconstructed from its equation of state? We investigate this question using physics-informed neural networks in the bosonic-mass sector of the Pilch–Warner model. We first validate the PINN approach against an analytic solution encoding the leading high-temperature corrections to the conformal equation of state. We then reconstruct nonlinear black-brane geometries and the scalar potential using thermodynamics, ultraviolet asymptotics, Ward identities, and horizon regularity. Independent solutions of the bulk Einstein-scalar equations demonstrate that accurately reproducing thermodynamics with a trained PINN does not guarantee an accurate reconstruction of the scalar potential. High-precision knowledge of the high-temperature equation of state constrains nonlinear interactions in the bulk scalar potential. Fixing the cubic coupling to its exact PW value, motivated by this high-temperature extraction, reduces the maximum sampled error in the reconstructed scalar self-interactions by a factor of $\sim 15$ compared with constraining only the bulk scalar mass. Adding knowledge of the bulk viscosity of the gauge theory plasma further reduces this error by an additional factor of $\sim 13$, with independent forward solutions reproducing the bulk viscosity within $0.09\%$.

We show that a quantum reservoir computer optimized with its quantum Fisher information (QFI) has a quantum advantage over a classical reservoir of equal readout cost, provided by a quantum-information advantage: optimizing the quantum parameters with the QFI metric. On Mackey-Glass forecasting, a driven Jaynes-Cummings reservoir with one to three atoms beats a tuned echo-state network at every size from 4 to 30 trained weights, by 25-69% in held-out error, and is ahead of 99.5% of 10,000 random networks. After grid and Bayesian searches saturate, the QFI-aware stage lowers the error by 29-51% at 12-30 weights, beyond equal-budget black-box search or classical-parameter gradients alone, and at 30 weights turns a loss into a win. We then derive a fundamental QFI bound on the first-order rate of change of the retrained loss and factorize the gap to this bound into five link efficiencies that identify the physical mechanism limiting optimization.

We present the concept of quadrature-detected zero-to-ultralow-field nuclear magnetic resonance (QD ZULF NMR). Two orthogonal sensors, atomic optically pumped magnetometers, are used to separately detect components of oscillating sample magnetization, which are then combined into a quadrature signal. This approach enables the distinction of positive and negative resonance frequencies with respect to the laboratory frame—such that absolute signs of gyromagnetic ratios can be determined. In addition, QD ZULF NMR reduces peak density and overlap compared to ZULF NMR with single-axis detection, while providing richer information about nuclear-spin dynamics. As an illustration, we present experimental $J$-spectra for thermally polarized [$^{13}$C]-formic acid and [$^{13}$C]-methanol, compounds commonly used in ZULF NMR which represent XA and XA$_3$ spin systems, respectively. A theoretical framework describing QD ZULF NMR signals is provided.

We construct a chiral algebra $U$ of central charge eight inside the lattice vertex operator algebra $V_{E_6\oplus A_2}$. It is generated by two commuting affine $\mathfrak{sl}_2$ current algebras at levels $1$ and $39$, the stress tensor of the lattice theory, and a single weight-two field built from three lattice exponentials. We announce that $U$ is strongly rational and completely unitary, and that $Rep(U)$ is equivalent, as a unitary ribbon category, to the Drinfeld center $Z(\mathcal{H}_3)$ of the Haagerup fusion category $\mathcal{H}_3$. Its characters are the $\gamma=0$ Evans–Gannon vector. From $U$ we obtain a diagonal full CFT, and also a holomorphic $E_8$ extension on which $\mathcal{H}_3$ acts by topological defects.

We develop a fluctuation based Monte Carlo method for evaluating thermal conductivity within the phonon Boltzmann transport equation (BTE) framework. Starting from the energy based variance reduced formulation of the BTE, we derive a relation between the spatial spreading of deviational phonon energy and the macroscopic heat conduction equation. The resulting formulation expresses thermal conductivity in terms of the mean square displacement of deviational phonon particles, without imposing thermal reservoirs. Consequently, thermal conductivity along multiple directions can be evaluated from a single simulation. The method is demonstrated for crystalline silicon at room temperature in bulk, square nanowires, and anisotropic polycrystalline nanostructures. The calculated thermal conductivities agree with theoretical predictions, including the size dependence induced by phonon boundary scattering and the mode-resolved contributions. For anisotropic polycrystalline structures, the method simultaneously resolves the directional thermal conductivities and captures their dependence on grain morphology. These results demonstrate the validity of the proposed fluctuation-based approach for evaluating thermal conductivity across different transport regimes and structural configurations.

Characteristic modes provide important information about the intrinsic properties and dynamical response of gravitational systems. In this work, we investigate characteristic modes of thick branes with a non-minimally coupled bulk scalar field. Two representative thick brane solutions are considered, corresponding to a single-kink scalar configuration and a deformed kink configuration with internal structure, respectively. By analyzing the tensor perturbation equations, we first examine the localization of the graviton zero mode in the two brane models. For both brane models, the graviton zero mode is localized on the brane. No pronounced resonant Kaluza–Klein (KK) modes are found for the single-kink brane at $\xi=1/7$. For the deformed brane, we investigate the resonant KK modes at $\xi=0.99$, finding that increasing the deformation parameter $k$ leads to more resonant modes and a longer-lived first resonance. We then calculate the quasinormal modes (QNMs) of both brane models independently in the frequency and time domains. The quasinormal frequencies (QNFs) obtained by the independent methods agree well for the low overtones. The masses and decay rates of the resonant KK modes agree closely with the real parts and the magnitudes of the imaginary parts of the corresponding QNFs, respectively.

Two-dimensional (2D) polar oxides with built-in electric fields offer promising opportunities for nanoscale electronics, optoelectronics, and surface charge engineering. However, their discovery remains challenging due to the enormous structural complexity of nonlayered oxide networks. Here, we combine inverse structural design with a machine-learning interatomic potential and first-principles calculations to explore 2D oxide configurations. Using Bi2O3 as a representative system, we identify two previously unreported polar monolayers with tetragonal and orthorhombic symmetries. Both structures exhibit vertically separated Bi and O sublayers, giving rise to pronounced intrinsic polarity with Berry-phase 2D polarizations of 34.12 and 37.15 pC/m, respectively. Notably, the o-Bi2O3 monolayer exhibits one of the largest reported out-of-plane polarizations among 2D oxides. Both monolayers exhibit dynamical stability, finite-temperature structural integrity, and wide band gaps (~3.8 eV). The large polarization originates from dimensionality-induced reconstruction of the nonlayered Bi-O network, which breaks local coordination symmetry and produces out-of-plane charge redistribution, while the stereochemically active Bi 6s2 lone pair further favors asymmetric Bi-O bonding. These findings suggest dimensionality-induced local-coordination symmetry breaking as a promising design motif for high-polarization 2D oxides, and demonstrate the utility of combining inverse design with machine-learning-assisted screening to explore unconventional polar phases in nonlayered oxide networks.

Indirect excitons (IXs) in a periodic moiré potential in a van der Waals heterostructure form an experimental platform for exploring Bose-Hubbard physics, including the superfluid state and the Mott insulator state. The realization of these collective states requires low-disorder materials. In particular, the localization due to the Mott insulator must be distinguished from disorder-induced localization. We studied the transport kinetics of IXs in a MoSe$_2$/WSe$_2$ van der Waals heterostructure with an anomalously high IX mobility, consistent with superfluidity. This high-mobility transport demonstrates that disorder-induced localization is negligible. We found a remarkable suppression of this efficient IX transport, directly indicating the Mott insulator. As the IX density increases during the excitation pulse, the IX cloud initially expands and then contracts upon entering the Mott insulator phase. The emergence of IX cloud contraction is accompanied by a peak in the IX spatial distribution at the origin. Our simulations reproduce the observed non-monotonic IX transport kinetics, including the temporal expansion and contraction of the IX cloud, as well as the peak in its spatial distribution.

Detecting weak magnetic fields at hertz frequencies is central to biomagnetism, geophysical sensing, and searches for new physics, yet it remains challenging because of technical systematics and environmental noise. Here, we realize a continuously operating molecular magnetic amplifier. Signal amplification by reversible exchange (SABRE) parahydrogen-based hyperpolarization maintains non-equilibrium spin order at zero field, turning scalar-coupled nuclear spins in liquid state molecules into an active, frequency-selective gain medium. Measurements of its complex magnetic susceptibility ($\chi$) reveal an intrinsic response of $ | \chi | \approx$ 10. By feeding the collectively generated magnetic field back to the spins below the threshold for self-sustained $J$-oscillation, we extend the effective spin coherence and cooperatively enhance the susceptibility up to $ | \chi | \approx$ 80. Near threshold, this produces approximately fourfold amplification of a weak (20 pT) magnetic field at 3.37 Hz at the sensor location. These results establish hyperpolarized molecules as a tunable active magnetic medium for narrowband quantum sensing and precision measurement.

Sensing time-varying signals is essential for precision measurement and for characterizing fluctuations in physical systems. In this work, we show that quantum entanglement provides an exponential advantage in the acquisition time required to learn the temporal statistics of a stationary classical signal. The task is to estimate the characteristic function of joint displacements on selected bosonic modes within a fixed-duration window, using continuous measurements of one signal realization. We present an entanglement-assisted scheme based on two-mode squeezed probes and local Bell measurements with protected idlers, and bound its acquisition time accounting for readout noise and correlations between signal windows. For a strictly stationary pulse family, it achieves polynomial acquisition time at inverse-polynomial accuracy with logarithmic squeezing and polynomial photon number. On the other hand, we prove that any local idler-free protocols require acquisition time exponential in the number of selected temporal modes per window. This lower bound holds for both sequentially prepared and arbitrarily temporally entangled probes, allowing non-Gaussian inputs and measurements and causal classical feedback, as long as each output is measured destructively within its time bin. These results establish an exponential quantum learning advantage for a single continuously monitored stationary signal, with the sensing cost measured by total acquisition time.

This Master's thesis develops and applies the multisymplectic field-theory framework to (pure) Yang-Mills theory. Building from the geometric foundations of jet bundles and the Poincaré-Cartan forms, the work constructs the Lagrangian multisymplectic formalism for first-order field theories, recovering the usual Euler-Lagrange field equations and extending the Poisson brackets of symplectic mechanics to a full graded Lie algebra. It then establishes the Legendre correspondence with the multisymplectic Hamiltonian formalism (in which Hamilton equations are retrieved) including the case of singular Lagrangians (where a constraint algorithm is reproduced). Breaking Lorentz covariance via a Cauchy surface slicing, the thesis then relates the covariant multisymplectic picture to an instantaneous presymplectic (infinite-dimensional) formulation in which the instantaneous De Donder equations and presymplectic brackets are obtained in a compatible way. A comprehensive treatment of symmetries then leads to multisymplectic and instantaneous momentum maps generalizations and to several versions of Noether's theorems. Specializing the formalism to principal-bundle gauge theory, the thesis identifies the multisymplectic configuration space with the bundle of connections, gauge symmetries with symmetries in the multisymplectic language and builds the Yang-Mills Lagrangian. Lastly, among many computations, the standard tensorial Yang-Mills equations and the Bianchi identity in local trivializations are retrieved, Yang-Mills conserved currents and charges are obtained and the graded algebra is derived for a special class of Hamiltonian forms.

Characterizing subsurface fracture networks is challenging because geometry and connectivity are sparsely observed and uncertain away from measurements. We develop a latent diffusion framework for unconditional and observation-conditioned generation of two-dimensional (2D) and three-dimensional (3D) fracture networks. Fractures and the surrounding matrix are represented as binary fields and compressed by a variational autoencoder into compact spatial latent representations, where an Elucidated Diffusion Model learns their distribution. The 3D model operates on native volumetric fields, with a reconstruction objective designed to preserve sparse, thin fracture structures. Sparse borehole observations are incorporated through a conditioning encoder, classifier-free guidance, and diffusion posterior sampling. Generated ensembles reproduce key fracture-network statistics, including fracture area/volume fraction, two-point correlation, and chord-length distributions. Reconstructed fracture counts and gas-production responses are comparable to those of the reference networks under the considered multiphase flow scenarios. Conditional generation satisfies 99.6% of prescribed well observations in 2D. In 3D, where vertical boreholes constrain full voxel columns, conditional realizations satisfy 84.2% of observed well voxels while maintaining fracture volume and geometry comparable to the reference ensemble. These results demonstrate the potential of latent diffusion models as compact probabilistic representations for fracture-network characterization, ensemble generation, and sparse-observation conditioning.

We show that it is possible for three people to win the GHZ game with just the standard real valued misty state formalism, but each party will need to have two balls instead of one. That is, there will be six balls involved, rather than three. In fact, as a general rule, instead of using complex numbers in a quantum computer you can always add a qubit to "tag" complex numbers. But for proofs of non-locality, like the GHZ game, we cannot have a single universal tagging qubit, because all three parties would need access to it and therefore they could potentially transfer information via it. That's where we need to replace the one ball with three that each only need to be accessed locally.

We examine the consistency of the equilibrium magnetic field $\mathbf{B}_0$ used in the analytical calculation of the sideways wall force by A. A. Martynov and S. Yu. Medvedev [Phys. Plasmas 27, 012508 (2020)] and the subsequent reformulation presented in [Phys. Plasmas 27, 054702 (2020)]. In these attempts, the current density $\mathbf{j}_0 = \nabla \times \mathbf{B}_0$ must vanish in the vacuum regions adjacent to the wall, making $\mathbf{B}_0$ curl-free as a complement to the natural $\nabla \cdot \mathbf{B}_0 = 0$. Since the cited works incorporate selected toroidal corrections without explicitly specifying the corresponding differential operators, we test $\mathbf{B}_0$ adopted in these models against Maxwell's equations using both toroidal and quasi-cylindrical formulations. We show that the divergence-free requirement is violated in the toroidal interpretation, while the curl-free condition is not satisfied in the quasi-cylindrical limit. The reformulation likewise fails to define a self-consistent equilibrium field with toroidal effects because the accompanying field corrections required for consistency with Maxwell's equations are not specified. Since the sideways force calculations are built upon these inconsistent field prescriptions, their analytical derivations are consequently compromised. The resulting arguments therefore cannot serve as a valid basis for revising either the earlier results established by D. V. Mironov and V. D. Pustovitov [Phys. Plasmas 24, 092508 (2017)] or those obtained within the single-harmonic analysis [Phys. Plasmas 22, 052502 (2015)].

Stiff chemical kinetics is a major computational bottleneck in reacting-flow simulations, while data-driven solvers remain sensitive to training-state coverage and chemical dynamics. This work combines conditional diffusion sampling with a thermochemically constrained multiscale Laplace neural operator (TC-MLNO) for chemistry ODE integration. The diffusion model learns the equivalence-ratio-conditioned joint distribution of temperature and species from low-dimensional flame data, augmenting the state space without independent perturbations. TC-MLNO represents transient, non-periodic responses through pole-residue Laplace layers and assigns fast, medium, and slow species to separate branches. Thermochemical constraints are imposed through losses for mass and elemental conservation and heat release rate. The framework is evaluated in 1D premixed flames, a 2D developing jet, and a 3D turbulent burner flame. With equal-sized datasets, diffusion sampling reduces the 95th-percentile distance to the base flame manifold by up to 37.5% and the a posteriori full-species macro-average error by up to 92.7% versus random sampling, especially for minor species and radicals. TC-LNO yields smaller errors than the DeepONet baseline for 84.9% of retained modes and reduces the 95th-percentile error for the most attenuated modes from 0.372 to 0.081. In multidimensional flames, TC-MLNO better preserves reaction-zone locations, heat-release structures, and chemically sensitive species than DeepONet. Errors of representative radical and nitrogen-containing species in the 3D flame decrease by 88.0%-88.9%. Compared with direct CVODE integration, TC-MLNO reduces mean chemistry and total solution times by 90.1% and 62.6%, respectively. These results show that distribution-aware sampling and Laplace neural operator learning provide an accurate and efficient alternative for stiff chemical ODE integration.

We extend Mark Kac's kinetic framework from single-species Euclidean spaces to a two-species, non-linear interaction space on the open cone $(0, \infty)^2$ governed by the Matsumoto–Yor rational collision involution. We identify a non-linear conserved energy $E(x,y) = x + y + 1/x$ and an invariant conic metric measure $d\mu = \frac{dx \, dy}{x(x+y)}$. By establishing a two-species $H$-theorem, we prove that entropy production vanishes if and only if post-collision velocities are statistically independent ($I(U;V)=0$). In contrast to the transform-domain proof of Letac and Wesołowski~\cite{letac2000}, which relies on joint Laplace transforms of general measures, our approach yields a direct physical derivation in state space via the transformation law for logarithmic gradients and separation of variables. This uncouples the functional-differential system to uniquely characterize the Generalized Inverse Gaussian (GIG) and Gamma distributions as the non-equilibrium thermodynamic equilibria.

We present a suite of 50 unpublished research-level theoretical physics problems with verifiable answers. Without AI assistance, a typical problem in our collection could be solved by a world expert in about a day or less but would take considerably longer for experts in adjacent specialties. We test the ability of off-the-shelf AI agents to tackle these problems autonomously, without human hints. When given access to tools available in a realistic setting, including the ability to search the literature and write scripts for numerical and symbolic work, the best-performing agent, GPT-6-Astra harnessed in Codex, obtains the final answers with a near-perfect accuracy of 98% at an average cost under USD 3 per problem. On average, agents show only small changes in accuracy when denied web search and access to background research papers, suggesting significant memorization of the literature. These results suggest that state-of-the-art agents can accurately perform concrete calculations required across theoretical physics research. We comment on the broader implications of these findings and discuss possible explanations for the current lack of agent-led breakthroughs in theoretical physics despite their outstanding problem-solving abilities.

Based on first principles calculations, we show in hole-doped La2-xSrxCuO4, the Sr dopants prefer to form dimers, rather than be isolated as generally believed. Same trend applies to other superconductors such as Na-doped Ca2CuO2Cl2, and electron type Nd2-xCexCuO4. The dimer structure makes the two doped holes (electrons) bound up and form a singlet which is also polarized. Another type of dopant in cuprates is oxygen which behaves similarly. So, we propose that, for all oxide high TC superconductors, the holes (electrons) are pre-paired (Z-pairs) during the preparation of the superconductor. The spontaneously formed Z-pairs are conceptually different from not only the Cooper pairs, but also the Zhang-Rice singlets. The attraction force in a Z-pair originates basically from the strong antiferromagnetic exchange energy. We also found that the on-site Coulomb repulsion (U) is no longer a constant due to doping. Around a doping site, U can reduce its value discontinuously, which plays a key role in stabilizing the Z-pairs against isolated holes (electrons). A Z-pair is a p-wave like localized state which breaks the symmetry of the CuO2 plain and attracts each other along the direction perpendicular to the polarization. The Z-pairs may be popular in all of the unconventional superconductors and the periodic assembly can result in the emergence of coherence states and superconductivity.