On November 12th, 2025 the LIGO--Virgo--KAGRA (LVK) collaboration reported gravitational waves (GWs) from a compact object merger candidate (S251112cm) with at least one sub-solar mass component. Using the Dark Energy Camera (DECam), the Fraunhofer Telescope at Wendelstein Observatory (FTW), and the Zwicky Transient Facility (ZTF), we surveyed $56\%$ of the GW localization region beginning $2.4$~hours after the GW alert. We find no kilonova (KN) counterpart, and use radiative-transfer models to rule out $42\%$ (ZTF), $68\%$ (DECam), and $92\%$ (FTW) of the KN models as possible emission from this GW candidate. Within the recently proposed disk-fragmentation (``superkilonova'') model for generating sub-solar mass neutron star mergers from stellar core-collapse, the delay between the supernova explosion time and the GW merger time is estimated to be less than a few days. Searching this time window prior to the GW event, we identify and spectroscopically classify a IIb supernova (SN~2025adtq), with a spatial association odds ratio of $\log_{10}\mathcal{I} \approx 4.8$, a chance coincidence probability of ${\sim}2$--$9\%$, and an estimated explosion time ${\sim}2$ days prior to S251112cm. SN~2025adtq is the second Type~IIb supernova found in spatial and temporal coincidence with a sub-solar mass GW candidate, following the previously reported S250818k/SN~2025ulz association; jointly, we measure an odds ratio that favors the association hypothesis over the null, however, when conditioned on finding a coincident supernova by chance, the odds ratio disfavors association. Together, these results provide suggestive but inconclusive evidence for the superkilonova formation channel.

The Spherical Fourier-Bessel (SFB) basis, in separating the angular and radial modes of the power spectrum, permits a targeted identification and mitigation of systematics in clustering surveys while retaining more cosmological signal than traditional bases. We demonstrate this principle on the eBOSS DR16 LRG and QSO samples, identifying modes which may be contaminated by systematics. Our initial inference on the LRG sample yields an fNL value consistent with zero, while the QSO value is in slight tension with zero. Using the SFB basis, we vary the selection of angular and radial modes to search for inconsistencies in the inferred value of fNL, an indicator of underlying systematics. In the QSO sample, we find evidence (p < 0.005 compared to the same cuts on EZMocks) of a systematic afflicting large physical scales, which is consistent with residual stellar contamination; we also find evidence (p < 0.05) for an unknown systematic in the QSO and LRG samples at the approximate angular plate and imaging scale of eBOSS.

Solid-state processors require control layers whose errors are legible to quantum-error-correction decoders. We show that crystallographic symmetry can provide such a layer in strain-active Lambda manifolds. When the projected strain tensor and Lambda-transition operators share a multiplicity-one two-dimensional irreducible representation, symmetry fixes the linear strain interaction to a scalar dot product. Two phase-locked mechanical modes synthesize a circular strain field, enabling complex phononic Lambda-leg control without local microwave near fields. On this manifold we construct a superadiabatic echo-lune holonomic gate using Lambda-leg control and a resonant double-quantum counterdiabatic tone. Rotating-frame simulations of a nitrogen-vacancy center give 99.88% conditional average fidelity in 1.833 microseconds, or 99.40% when leakage is counted as error. A resonant gigahertz high-overtone bulk acoustic resonator analysis translates the Hamiltonian into Rabi-rate, linewidth, and envelope-tracking requirements. The bright-state structure organizes noise: A2-sector perturbations are parity-filtered into an optically distinguishable auxiliary state, whereas transverse E-sector faults are echo suppressed and retained as a decoder stress axis. The extracted channel has 0.47% erasure probability and 0.168% residual Z error. In XZZX code-capacity simulations, this biased-erasure model yields a nominal 64% fit-extrapolated data-qubit reduction relative to an unstructured Rabi baseline. Repeated-round detector-model diagnostics preserve the nominal distance-9 proxy and identify missed erasures, transverse floors, leakage/flag timing, and strong crosstalk as validation limits. Extensions to orbital Lambda systems and bright-projector phonon-bus diagnostics identify crystallographic symmetry as a principle for co-designing phononic actuation, leakage, noise bias, and quantum decoding.

The redshifted 21\,cm line is an emerging tool in observational cosmology that can serve as a direct probe of the intergalactic medium throughout the cosmic timeline. However, the observation of the cosmological 21\,cm signal from early epochs is extremely challenging in practice, regardless of the scale of interest and redshift. The presence of bright astrophysical foregrounds and residual systematic errors along the line of sight poses challenges for its detection. Machine-learning-based Gaussian process regression\,(ML-GPR) has proven to be the most effective strategy for signal separation in LOFAR and NenuFAR observations to measure the 21\,cm signal power spectrum from the Cosmic Dawn\,(CD) and Epoch of Reionization\,(EoR). In this work, we extend this framework to synthetic CD/EoR SKA1-Low observations to assess its robustness in mitigating residual foregrounds against instrumental and environmental systematic effects. We use our developed end-to-end realistic simulation pipeline (\textsc{21cmE2E}) for SKA-Low observations. Our 4-hour tracking simulation includes extragalactic point sources, the AA* telescope configuration, primary beam response, and error models. The modelled errors incorporate residual antenna-based gain calibration errors, residual ionospheric phase errors, partial de-mixing of the out-of-field sources, and instrumental noise for 1000\,hours of deep integration time. We compare different Bayesian GPR frameworks to assess their ability to suppress residual foreground contamination while minimizing signal loss and providing reliable uncertainty estimates. Our analysis demonstrates that the 21\,cm signal can robustly recover within the $2σ$ credible interval for almost all k-modes over the range of $0.06 \leq k \leq 1.0$~h Mpc$^{-1}$.

Ozone (O3) is a triatomic molecule of central importance in the chemistry and physics of the Earth's and other planetary atmospheres. Beyond its environmental significance, a detailed understanding of the electronic structure and ionization dynamics of ozone is essential for modeling atmospheric, ionospheric, and astrochemical processes. In the present work, we substantially extend the experimental and theoretical characterization of ozone into the regime of valence double photoionization. Using HeII-alpha, HeII-beta, and higher-energy vacuum ultraviolet radiation in combination with a versatile multiple charged-particle correlation detection technique, we report the first single-photon valence double ionization electron spectrum of O3. To interpret the experimental observations, we mapped the lowest potential energy surfaces of dicationic ozone employing post-Hartree-Fock multi-configurational-interaction methods, and computed with high accuracy the energetics of the relevant dissociation channels. Our results demonstrate that dissociative double ionization of ozone produces electronically excited cationic atomic oxygen fragments in addition to the ground-state dissociation pathway, revealing a richer fragmentation dynamics than hitherto recognized.

We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary Clifford gates that reduces a given symplectic matrix representation of a Clifford circuit to the identity. This formulation permits a simple learning curriculum based on random walks from the identity. We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation, and which is size-agnostic, allowing a single learned policy to be applied across different qubit counts without circuit splicing or network reparameterization. On six-qubit Clifford circuits, the largest regime for which optimal references are available, our agent finds circuits within one two-qubit gate of optimality in milliseconds per instance, and finds optimal circuits in 99.2% of instances within seconds per instance. After continued training on ten-qubit instances, the agent scales to unseen Clifford tableaus with up to thirty qubits, including targets generated from circuits with over a thousand Clifford gates, where it achieves lower average two-qubit gate counts than Qiskit's Aaronson-Gottesman and greedy Clifford synthesizers.

We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$, where $\mathcal{P}(p)$ is the theory of $\mathbb{Z}_p$-parafermions and $\mathcal{P}(p)^\vee$ is an appropriate dual theory, with global symmetry characterized by the centralizer of $\mathbb{Z}_{pA}$. By tracking the symmetries of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$ through the non-invertible gauging, we argue that the diagonal Monster CFT has $\mathrm{Rep}(\mathfrak{so}(3)_p) \boxtimes \mathrm{Rep}(\mathfrak{so}(3)_p)^\mathrm{op}$ symmetry, and hence that the holomorphic Monster theory has symmetry $\mathrm{Rep}(\mathfrak{so}(3)_p)$. We then compute the defect McKay-Thompson series associated to these symmetries, and prove that their invariance subgroups are $Γ_1(p+2)$.

Shearing motion and magnetic flux cancellation around the polarity inversion line (PIL) play significant roles in the build-up of free magnetic energy and magnetic flux rope (MFR) in source region of major solar flares. Here we investigate the magnetic evolution of a highly-sheared PIL in active region (AR) 13842, hosting the largest X9.0 flare of Solar Cycle 25. Since 2024 September 29, a positive-polarity pore persistently drifted northward along the western side of the AR's main negative-polarity sunspot. The main sunspot remained stationary until negative-polarity patches successively emerged to its east and approached. Rear-ended by these same-polarity patches, the sunspot then began moving westward toward the opposite-polarity pore around October 1, forming a collisional PIL. Meanwhile, on the PIL's other side, the pore was also rear-ended by same-polarity patches sequentially emerging behind it, accelerating the shearing motion around the PIL, where frequent flux cancellations were also observed. Synchronous rapid accumulation of free magnetic energy and formation of MFR were then observed in the PIL, where multiple major flares successively occurred within two days. Before these large flares, the area and total free energy of the high-free-energy-density PIL region gradually decreased in the photosphere, which could be caused by the initial ascent of MFR before eruption and serve as a precursor of solar eruptions. These results suggest that persistent flux emergences with cross separation directions facilitates rapid formation of collisional shearing PIL and frequent flux cancellations, leading to repeated MFR formations and multiple large flares in a relatively short time.

Solar filament/prominence eruptions can significantly perturb geospace when originating from favorable source locations and directions. While stellar analogs have been recently reported, the disk locations and magnetic environments of their source regions remain spatially unresolved on other stars. To bridge this gap, we investigate the typical Sun-as-a-star H$α$ temporal spectral characteristics of solar filament/prominence eruptions with different source region locations (on-disk vs. limb, active region vs. quiet-Sun region). It is revealed that limb eruptions are characterized by blueshifted/redshifted emission caused by the bright off-limb erupting structures, whereas on-disk eruptions may show blueshifted absorptions due to the dark erupting filaments. Among the limb eruptions, front-side limb eruptions usually display line center emission before the blueshifted/redshifted emission, while far-side limb eruptions show the opposite sequence. Moreover, the magnetic environment at source also shapes the spectral characteristics. On-disk filament eruptions from active region exhibit much more intense flare-ribbon-dominated line center emission features compared with those from quiet-Sun region. Limb active region eruptions often show single-wing emissions, whereas large-scale quiet-Sun region (quiescent) prominence eruptions frequently display expansion-induced emission in both wings followed by line center absorption due to the disappearance of bright prominence. These distinct Sun-as-a-star H$α$ spectral characteristics, dependent on eruption location, provide a diagnostic basis for inferring source regions of stellar filament/prominence eruptions from spatially unresolved H$α$ spectra.

We consider nonlinear functionals of discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of $\mathbb{Z}^{2}$, including i.i.d. supercritical percolation clusters, where the conductances are possibly unbounded but satisfy an integrability condition. As our main result, we show that, for almost every realisation of the environment, the nonlinear functionals of the rescaled field converge to their continuum counterparts in the Sobolev space $H^{-s}(D)$ for suitable $s > 0$. To obtain the latter, we establish pointwise bounds for the Green's function of the associated random walk among random conductances with Dirichlet boundary conditions, which are valid for all $d \geq 2$.

The strong decay $ψ(4040)\to D\bar D$ is anomalously suppressed despite ample phase space, whereas the $D\bar D^*$ and $D_s\bar D_s$ channels remain sizable. In this work, we study this suppression and the associated open-charm hierarchy in the framework of the instantaneous Bethe--Salpeter equation combined with the relativistic $^3P_0$ model, with the pair-creation strength fixed independently from $ψ(3770)\to D\bar D$. Within this framework, we show that the suppressed $D\bar D$ mode can be understood as a consequence of node-induced cancellations in the relativistic decay amplitude. The $D\bar D$ amplitude is strongly reduced because the corresponding overlap integral receives comparable positive and negative contributions from different momentum regions, whereas the $D\bar D^*$ and $D_s\bar D_s$ channels do not undergo the same strong cancellation. This interpretation is further supported by the pronounced sensitivity of the $D\bar D$ width to the initial mass, the charged-neutral $D$-meson mass splitting, and the dip structure in the mass dependence of the partial width. Our results provide a dynamical explanation of the suppressed $D\bar D$ mode and the core open-charm hierarchy of $ψ(4040)$ within a conventional $3\,{}^3S_1$ charmonium picture, while the precise value of the near-vanishing $D\bar D$ width remains model dependent.

Distance measurements are fundamental to radio pulsars' use as astrophysical probes of General Relativity and the interstellar medium. One of the primary methods for determining pulsar distances is HI kinematics, which leverages the radial velocities of HI absorption and emission features detected along pulsar lines-of-sight. This method necessarily assumes a model for Galactic rotation, our knowledge of which continues to evolve in both accuracy and precision. In this research note, we derive kinematic distances for 66 pulsars with archival HI radial velocity measurements using a state-of-the-art Galactic rotation curve. The results and software are provided in an online repository. Our kinematic distances differ by $<1σ$ from published parallaxes for nearly all pulsars in the sample that have both types of distance measurement available. Comparison to the NE2025 Galactic electron density model shows general consistency between measured and predicted distances.

A microscopic framework that combines the Hartree-Fock-Bogoliubov (HFB) approach with the fusion by diffusion (FBD) model is proposed to investigate the synthesis mechanism of superheavy nuclei (SHN). For the reaction $^{48}\text{Ca}+^{208}\text{Pb}$, the calculated evaporation-residue cross section (ERCS) reproduces the experimental data reasonably well. The method enables self-consistent extraction of the fusion injection point and inner barrier from HFB potential-energy surfaces (PES), thereby incorporating nuclear structure effects while eliminating phenomenological tuning at the fusion stage. For cold-fusion reactions, the PES features a hyperasymmetric valley driven by shell effects. This $^{208}$Pb anchored valley connects the entrance channel to compound nucleus formation and provides an exit channel for cluster decay. We further investigate the cold-fusion reactions $^{54}\text{Cr}+^{208}\text{Pb}$ and $^{58}\text{Fe}+^{208}\text{Pb}$, obtaining a near-exponential decrease of $P_{\text{CN}}$ with compound-nucleus charge $Z$, consistent with established systematics. This approach demonstrates a self-consistent framework that can reduce uncertainties in the fusion stage of SHN production.

The Law of Universal Gravitation is part of middle and high school's general physics and astronomy curricula. This topic is included in the most popular physics textbooks available as a fact whose origin remains in the detailed work of Sir Isaac Newton 300 years ago. Consequently, its mathematical form is presented as an equation without any deductive process. Nevertheless, deduction of the mathematical form of this law is an opportunity to discuss how a deductive process can be performed using the data available on the Internet from reliable sources.

Modified gravity theories such as Modified Newtonian Dynamics (MOND) and Scalar-Tensor-Vector Gravity (STVG) have been proposed as alternatives to dark matter, but decisive tests have been hindered by degeneracies between baryonic structure and gravitational laws. Here we break this degeneracy using independent, high-precision constraints: the Milky Way radial rotation curve, vertical phase-space spirals from Gaia, and a broken-exponential stellar disk. A joint reconstruction of the radial and vertical gravitational fields reveals a structural inconsistency in modified gravity -- no model can simultaneously reproduce both observations. Our results strongly disfavor MOND at $>13σ$ and STVG at $>4σ$. In contrast, dark matter halo models naturally explain the observations, providing a self-consistent test of gravity on galactic scales.

In discrete-variable black-box optimization, the number of candidate solutions grows combinatorially, while each evaluation is often expensive. Therefore, it is important to identify promising solutions efficiently within a limited number of trials. Bayesian Optimization of Combinatorial Structures (BOCS), an existing parametric method, works effectively when only a small amount of data is available. However, as the number of observations increases, BOCS tends to repeatedly propose points that have already been evaluated, which leads to search stagnation. A random-point addition strategy has been proposed to address this issue when an evaluated point is proposed, but it cannot sufficiently exploit information from promising data obtained so far. In this study, we propose a hybrid method that uses BOCS as the main search framework and generates alternative unevaluated points using a Gaussian process only when search stagnation is detected. In the Gaussian-process-based component, multiple Lower Confidence Bound (LCB) acquisition functions are adaptively selected to dynamically control the balance between exploitation and exploration. Numerical experiments using fully connected Quadratic Unconstrained Binary Optimization (QUBO) and Higher-order Unconstrained Binary Optimization (HUBO) as black-box functions show that the proposed method finds solutions with better objective values than the conventional random-point addition method in both settings. Additional analyses show that its effectiveness comes from selecting points that promote search progress within Hamming-distance neighborhoods, rather than simply adding low-energy points near promising solutions. Experiments with sparse surrogate models for quantum annealer applications further suggest the importance of retaining near-fully connected representational capacity.

We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every site. Our exact solution is found by generalizing the coherent quantum absorber technique to fermionic systems, and our result establishes the existence of hidden time-reversal symmetry in driven-dissipative fermionic models. The steady state exhibits a first order phase transition in the particle density, with the resulting jump discontinuity in density persisting even for finite dissipation rates. A mean-field description of the model exhibits a bistable regime that encompasses the first-order transition line yet which fails to accurately predict its precise location via a Maxwell construction. We also show that the model's hidden time-reversal symmetry results in an Onsager symmetry of certain two-time correlation functions.

Analog quantum computation offers a route to machine learning using controllable physical dynamics as a computational resource. However, many existing approaches rely on task-specific protocols or observables that are difficult to access experimentally, limiting generality and implementation. Here we introduce Qlustering, an unsupervised clustering framework based on steady-state quantum transport in quantum networks governed by the GKSL master equation, developed through algorithm-hardware co-design. Data are encoded as input states, and cluster assignments are inferred from steady-state output currents, avoiding full state tomography in favor of accessible transport observables. The method realizes a hybrid classical-quantum workflow in which data preparation and training are performed classically, while clustering is carried out by transport dynamics. We benchmark the method on synthetic datasets, localization, and QM9 and Iris, finding competitive performance and stability over a broad range of dephasing strengths. These results show that unlabeled data structure can be extracted directly from steady-state transport observables, identifying terminal-current readout as a native, tomography-free mechanism for unsupervised learning in open quantum networks.

Topologically-ordered quantum states with Abelian excitations can host defects that obey effective non-Abelian statistics, in principle allowing for quantum information processing via defect braiding. These extrinsic defects (or twists) are typically studied as static features of the lattice. However, an alternative proposal considers how an underlying topologically ordered quantum substrate can be locally perturbed to create and manipulate synthetic defects \cite{you_synthetic_2013}. Unfortunately, while largely referenced, elements of this proposal were never systematically studied. Understanding the energy spectrum is particularly important in finite size and finitely perturbed systems, which are crucial for experimental realizations. In this work we announce a significant step in this direction by explicitly constructing, simplifying, and numerically studying the spectral properties of synthetic defects in a model system. First, we introduce two alternative representations of this problem in both spin and Majorana languages. In the former we describe emergent virtual symmetries which constrain and simplify the problem and in the latter we show a direct connection to Kitaev's well-known Majorana chain. We utilize these simplifications to perform numerical calculations to indicate the location of the quantum phase transition driving the emergence of the synthetic defects. We conclude by discussing key steps for future work to more clearly and completely study this phenomena.

Null points in synthetically tunable molecular aggregates are predicted to generate flat energy bands analogous to those known in strongly correlated condensed-matter physics. For chemistry, null points provide a powerful design principle for photovoltaic materials with selective charge filtering similar to photosynthesis. However, null points have never been experimentally verified because their defining prediction - state localization with selective electron or hole transfer - has remained unobserved. Here, using a donor-acceptor dyad as a minimal model, we provide the first experimental observation of a null point. Impulsive pump-probe measurements reveal charge separation through a near-instantaneously generated locally excited-charge transfer (LE-CT) intermediate that emerges upon solvent stabilization of CT states. Polarization anisotropy directly reveals state localization and selective charge-filtering, spanning balanced electron-hole transfer to selective hole filtering consistent with synthetic design. A generalized vibronic theory of null points explains these observations and identifies the ideal synthetic parameters for achieving null points which are protected from the vibrational bath.

At the center of our Galaxy lies the bright γ-ray point-like source HESS J1745-290, which is compatible in position with Sgr A star, although an association between the two remains uncertain. Using data obtained between 2004 and 2019 with the High Energy Stereoscopic System (H.E.S.S.) on the Galactic center region, we studied the variability of HESS J1745-290 over 353 hours of observations collected over 16 years, representing the largest dataset gathered yet on this region at TeV energies. We performed a 3D maximum-likelihood analysis of the central source and the diffuse γ-ray emission in the Galactic center region. This analysis allowed us to extract the spectral and morphological intrinsic behavior of the two components. By performing this analysis on an annual basis, we derived the light curve of HESS J1745-290 and the diffuse emission over the past 16 years. The 3D maximum-likelihood analysis method allowed us to separate the central source from the overlapping diffuse emission, enabling a recalibration of the former by the latter and alleviating some of the systematic effects. We find no long-term or yearly variability. We also provide an estimate of the sensitivity of H.E.S.S. to variation of this specific source over 16 years. We rule out any yearly gamma-ray flux variation of this source larger than 30 percent, as well as any linear flux variation exceeding 30% over this time period.

A single-aperture, two-layer Canted-Cosine-Theta (CCT) sextupole magnet using high-temperature superconducting (HTS) ReBCO tape has been developed for the short straight sections (SSS) of FCC through the FCCee-HTS4 project. The magnet was designed, manufactured and tested under cryogenic conditions. Two HTS tapes from two manufacturers have been qualified for this specific application. Design and manufacturing details and cryogenic temperature measurements are presented. This demonstrator represents the first HTS CCT magnet ever constructed.

Complementarity relations constrain the distribution of coherence, predictability, and openness in quantum systems. Here we show that, in open quantum systems, these local constraints acquire a geometric interpretation through quasistatic transport. For a driven dissipative qubit, the complementarity variables define cylindrical coordinates on the Bloch sphere, while openness appears geometrically as a radial deficit associated with reduction from a larger Hilbert space. Quasistatic driving induces a work connection on the resulting steady-state manifold whose curvature determines the cyclic response. Hamiltonian-aligned dissipation produces an exact work connection and vanishing cyclic work, whereas fixed pointer-basis dissipation generates non-integrable transport, finite curvature, and holonomic response. The resulting curvature admits a phase-resolved representation on the triality manifold and develops perturbatively with pointer--Hamiltonian mismatch. In the weak-mismatch limit, the curvature is governed by a competition between coherence-preserving and pure-dephasing channels, producing symmetry-related positive- and negative-curvature sectors. These results establish a direct connection between complementarity, dissipation, and geometric thermodynamic response, and show that cyclic quasistatic work provides an operational probe of nonequilibrium quantum geometry.

Laplacians on metric graphs are used to construct continuous families of Hamiltonians with different topological structure. One such family is used to demonstrate that Hamiltonians with real-valued eigenfunctions may possess non-trivial geometric Berry's phase. Connections between non-trivial Berry's phase and topology change are discussed.

Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a linear associative memory that maps $p$ input embeddings in $\mathbb{R}^d$ to their corresponding~$d$-dimensional targets via a single layer, requiring each mapped input to be well separated from all other targets. Unlike in supervised classification, this strict separation induces~$p$ constraints per association and produces strong correlations between constraints that make a direct characterisation of the storage capacity difficult. Here, we provide a precise characterisation of this capacity in the following way. We first introduce a decoupled model in which each input has its own independent set of competing outputs, and provide numerical and analytical evidence that this decoupled model is equivalent to the original model in terms of storage capacity, spectra of the learnt weights, and storage mechanism. Using tools from statistical physics, we show that the decoupled model can store up to $p_c \log p_c / d^2 = 1 / 2$ associations, and generalise the computation of $p_c$ to linear two-layer architectures. Our analysis also gives mechanistic insight into how the optimal solution improves over a naïve Hebbian learning rule: rather than boosting input-output alignments with broad fluctuations, the optimal solution raises the correct scores just above the extreme-value threshold set by the competing outputs. These findings give a sharp statistical-physics characterisation of factual storage in linear networks and provide a baseline for understanding the memory capacity of more realistic neural architectures.

We establish a new class of entropy structures for \(3\)-wave kinetic equations with a broad family of interaction weights. Unlike the classical entropies arising from detailed balance, these estimates are generated by a one-sided algebraic balance condition encoded in the interaction weights. To the best of our knowledge, this family of entropy estimates has not previously appeared in the physical literature on wave turbulence. These estimates form the central a priori mechanism of the paper and are the key ingredient in the construction of global weak \(L^1_{\mathrm{loc}}\) solutions. We also prove a long-time rigidity result, showing that the solutions obtained by this entropy compactness method relax locally to the zero equilibrium as \(t\to\infty\).

We explore Krylov complexity in the BMN matrix model following a systematic reduction of it, known as the pulsating fuzzy sphere model. We present an analytical setup that allows us to calculate Lanczos coefficients in both large and small deformation limits of the matrix model.

The KAK decomposition is a fundamental tool in Lie theory and quantum computing. Despite its widespread use, the mathematical foundations remain incomplete, particularly regarding the precise conditions for the decomposition and the characterization of equivalence classes under multiplication by elements of $K$. Here, we present a mathematical theory of the KAK decomposition for connected compact semisimple Lie groups and derive the decomposition for $\mathrm{SU}(4)$. In particular, we clarify the relationship between various definitions of a Cartan decomposition in the literature and give a complete proof of a general KAK decomposition theorem. We then distinguish two distinct notions of KAK equivalence classes, double coset equivalence and projective equivalence, thereby addressing mathematical inconsistencies regarding KAK classification in the literature. Specifically, for $\mathrm{SU}(4)$, we show that local equivalence classes under multiplication by $\mathrm{SU}(2)\otimes \mathrm{SU}(2)$ are geometrically represented not by the usual "Weyl chamber" as claimed in the existing literature. Instead, the "Weyl chamber" is only recovered by the projective-local equivalence which disregards global phases. We develop a systematic theory for determining equivalence and uniqueness for both notions of equivalence. Our work establishes a rigorous Lie-theoretic foundation for the theory of quantum gates and circuits.

Sustained collisionless interpenetrating plasma flows have been generated on the OMEGA laser facility to enable direct investigation of nonlinear evolution of fields generated by electromagnetic kinetic instabilities. FLASH simulations and Thomson scattering measurements are used to determine the plasma conditions achieved. Interpenetrating flows are observed to remain collisionless for at least 11 ns, longer than any prior OMEGA experiment, supporting the growth and nonlinear saturation of the Weibel instability. Resulting magnetic fields are measured using proton radiography. This work establishes a unique platform for late-time filament evolution measurements.

We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a matrix is embedded as a sub-block of a larger unitary operator. Their implementation has so far required deep knowledge of low-level circuit construction, which Unitaria aims to eliminate. The library provides a composable, array-like interface through which users can define block encodings of matrices and vectors, combine them through standard operations such as addition, multiplication, tensor products, and the Quantum Singular Value Transformation, and extract the resulting quantum circuits automatically. A key feature is a matrix-arithmetic evaluation path in which every operation can be computed directly on encoded vectors and matrices without dependence on ancilla qubits or circuit simulation. This enables correctness verification and classical simulation that scale well beyond what state vector simulation permits and also allows resource estimation, including gate counts, qubit counts, and normalization constants, without executing any circuit. Together, these capabilities allow researchers to develop, verify, and analyze quantum linear algebra algorithms today, ahead of the availability of error-corrected hardware. Unitaria is open source and available at https://github.com/tequilahub/unitaria.