Papers

Classical resistive tearing theory assumes a prescribed current-sheet equilibrium, but a finite normal magnetic field can evolve the background on the tearing timescale. For a transversely pressure-balanced Harris profile of initial half-thickness $a$ and asymptotic reconnecting-field magnitude $B_0$, threaded by uniform $B_n$ ($\xi=B_n/B_0$), we derive an exact evolution in ideal magnetohydrodynamics: counter-propagating Alfvenic fronts broaden the neutral layer and generate a central sheet-parallel flow with shear at its flanks. Inner-layer estimates recover $\xi_{\mathrm{crit}}\sim S^{-3/4}$ for breakdown of the classical resistive balance, where $S$ is the Lundquist number based on $a$. Numerical frozen-profile calculations show loss of central resistive dominance and decreasing tearing growth as the neutral layer expands. Eigenfunction comparisons at fixed wavenumber and predominantly Doppler-shifted propagation support a normal-field-modified continuation of classical tearing. The normal field supplies no net perturbation energy. Energy extraction from the reconnecting-field gradient weakens as the sheet broadens. The velocity-gradient contribution becomes comparable when the neutral-layer width approaches the initial sheet thickness, without reversing the decline in growth. For $S=10^6$, $\mathrm{Pr}_m=0$, and $\xi=10^{-4}$, the maximum growth rate falls by a factor of about ten from its initial value at neutral-layer half-width $w\simeq1.59a$, where the growth and broadening times become equal. Only about 0.18 additional upper-envelope e-folds are estimated between this crossing and $w/a=2$, where the growth rate is about 25 times smaller than its initial value. These results support dynamical suppression of further linear amplification over the sampled evolution, even though the instantaneous spectrum remains unstable.

We investigate the optical and thermodynamic properties of quantum Oppenheimer-Snyder (qOS) spacetimes in both the black hole and naked singularity regimes. By analyzing test-particle motion and employing numerical ray tracing of thin accretion disk models, we identify their characteristic optical signatures. We find that increasing the quantum correction parameter reduces the apparent shadow size. While qOS black holes exhibit dark inner shadows, naked singularities produce central bright rings, driven by an infinite repulsive core barrier, yet still retain key optical features such as photon rings. Furthermore, using a semi-analytical approach, we obtain higher-order photon-ring impact and gap parameters that closely align with our numerical findings. Notably, the gap parameter intervals for qOS naked singularities deviate from the Schwarzschild case, providing a concrete criterion for observational tests. Finally, in the black-hole sector, the application of Geometrothermodynamics (GTD) identifies the specific-heat divergence at the Davies point. By linking photon-ring observables to GTD curvature scalars, we reveal a direct connection between qOS black hole shadows, thermodynamic stability, and microscopic interaction structures.

Evaluating AI agents on scientific research tasks is constrained by the time and resources required for the underlying experiments or calculations. In computational materials research, repeating the same expensive simulations across agents and trials can make evaluation impractical. We introduce CompMat-Bench, a benchmark of 94 tasks derived from recently published computational materials studies, each asking agents to complete a step toward achieving the study's scientific goal. We reproduce the research steps in advance and assess agents on preparing inputs and analyzing outputs for expensive simulations, so expensive simulations can be avoided during evaluation. The reproduced inputs and results serve as ground truth for grading agents with fixed rules, without an LLM judge. The benchmark supports four evaluation conditions: single tasks and workflows composed of related tasks, each with full or reduced methodological guidance. With full guidance on single tasks, agents based on three LLMs demonstrate the ability to complete individual materials research steps, with pass rates of 66.0-90.4% across 94 tasks. Both longer workflows and reduced guidance can limit agent performance, but in different ways for different agents: they lower the pass rates of the weaker agents, whereas the strongest agent falls only when a long workflow is combined with reduced guidance. Failure analysis attributes most failures to scientific errors rather than to errors in software usage. CompMat-Bench provides a basis for comparing agents on the steps of real materials research and for analyzing agent failure modes.

Non-ergodic quantum many-body dynamics offers a route to persistent quantum coherence far from equilibrium, beyond the conventional expectations of thermalizing statistical mechanics. Most known examples have been identified through intuition, analogy, or numerical search, rather than by systematic Hamiltonian design. This leaves few general methods for engineering robust non-ergodic dynamics in disorder-free interacting quantum many-body systems, especially in higher dimensions where enhanced connectivity generally disfavors ergodicity breaking. Here, we use an eigenstate-to-Hamiltonian construction approach to systematically engineer two-dimensional quantum spin Hamiltonians with tunable non-ergodic properties. Starting from a common parent model and input eigenstate, we construct two target Hamiltonians on the square lattice that differ in their interaction geometry: axial versus diagonal. We show that the resulting interaction geometry and coupling pattern control the Hilbert-space structure and dynamics. The axial model forms a connected Hilbert-space network and exhibits an anisotropy-driven crossover from ergodic to non-ergodic behavior through the suppression of resonances. In contrast, the diagonal model exhibits Hilbert-space fragmentation and, within its largest irreducible sector, signatures of quantum many-body scar dynamics including towers of highly localized, low-entanglement eigenstates, and long-lived coherent revivals. These results establish a direct link between Hamiltonian design, Hilbert-space network structure, and emergent non-ergodic dynamics.

Activity can enhance the long-wavelength density fluctuations of a solid beyond the equilibrium fluctuations predicted by the Mermin-Wagner-Hohenberg theorem, but the microscopic origin of this enhancement remains unclear. We study a two-dimensional active Brownian crystal whose longitudinal and transverse displacement covariances scale as $C^u_\lambda(q)\sim q^{-3}$ as compared to the passive counterpart with $q^{-2}$ law. This spectrum predicts an MSD-plateau divergence proportional to $L$ in two dimensions, logarithmic in three dimensions, and finite in four dimensions, in close correspondence with recent results reported in Dey et al. [Nat. Commun. 16, 5498 (2025)]. Inverse of the Covariance gives $H^{\mathrm{cov}}_\lambda\sim |q|^3$ with the corresponding dispersion $\omega_{\mathrm{cov},\lambda}\sim q^{3/2}$, whereas direct mechanical response gives $K_{\mathrm{resp},\lambda}\sim q^2$ and acoustic modes with $\omega_{0,\lambda}\sim q$. The nonlinear dispersion is therefore covariance-defined rather than mechanical. The mobility and integrated active-force correlations remain non-singular, although a finite-persistence crossover cannot be ruled out completely with the existing data. Microscopically, the longitudinal and transverse Irving-Kirkwood interaction-stress spectra scale as $q^{-1}$. The transverse stress-stress correlation connects well with the anomalous displacement field, indicating that activity anomalously populates ordinary acoustic modes, while the conservative interaction network transmits the resulting fluctuations as long-ranged stress. A three-dimensional active FCC crystal exhibits the same paired low-$q$ trends.

Initially discovered optically, Tidal Disruption Event (TDE) AT2018hyz was first detected in radio 972 days later. The continued monitoring of the event revealed a late-time (1370-2160 days) radio brightening. The source for this radio brightening has been associated with an afterglow originating from an off-axis jet or a delayed mildly relativistic outflow. In this work, we explored the conditions required for a delayed off-axis jet to explain the observed radio brightening. We find that the combined effect of different delay times (t_delay) and observer angles (theta_obs) can produce radio afterglow, as observed for AT2018hyz. The further off-axis from the jet core an observer is, the shorter is the delay inferred between the optical disruption and launching of the jet. This presents a degeneracy between different theta_obs and tdelay. We estimate the sky projection of the jet for these different combinations to break this degeneracy. The spread in sky images ranges from 0.6 mas for a 30 deg off-axis observer to 0.3 mas for an observer perpendicular to the jet core. Future VLBI observations should be able resolve these structures. Thus a combined observation of the light curve and sky images for AT2018hyz (and other jetted TDEs) can be used to narrow down the observer angle and any delay in launching of the underlying jet.

We formulate the corner transfer matrix equations, and the corner transfer matrix renormalization group built on them, as a set of local equations on general planar graphs. These equations depend only on the local subgraphs of the planar graph and are glued together consistently to describe the whole graph. Solving them yields message tensors and corner matrices, which can be used to construct an MPS environment for any connected subgraph. We test the proposed equations on the ferromagnetic Ising model, on a variety of infinite lattices (including hyperbolic ones) and on finite graphs, and find systematic improvement over belief propagation.

The microscopic mechanism governing the zero-field incommensurate magnetic order in the honeycomb cobaltate $\mathrm{BaCo}_2(\mathrm{AsO}_4)_2$ remains a significant unresolved problem, particularly concerning the relative contributions of bond-directional Kitaev-type interactions and exchange frustration. This study investigates an extended $J_1\text{--}K\text{--}\Gamma\text{--}\Gamma'\text{--}J_2\text{--}J_3$ model, which incorporates XXZ-type exchange anisotropies on the honeycomb lattice. Nearest-neighbor parameters are constrained by ab initio electronic structure calculations. By integrating the analytical Luttinger-Tisza approach with exact diagonalization calculations under twisted boundary conditions, we delineate the classical and quantum phase diagrams across the $(J_2, J_3)$ parameter space. We demonstrate that the stabilization of the experimentally observed incommensurate spiral phase, propagating along the $\Gamma\to M$ direction, does not necessitate an anomalously dominant Kitaev coupling. Instead, this phase arises naturally from the synergistic interplay between exchange frustration, driven by further-neighbor couplings ($J_2, J_3$), and intermediate off-diagonal bond anisotropies ($\Gamma, \Gamma'$). In the quantum regime, we elucidate the competition between this incommensurate manifold and an out-of-plane ferromagnetic ($\mathrm{FM}_z$) phase, which is selectively stabilized via a quantum order-by-disorder mechanism. Our findings reconcile conflicting interpretations of the magnetic interactions in $\mathrm{BaCo}_2(\mathrm{AsO}_4)_2$ and establish the microscopic origin and stability range of its incommensurate ground state.

We investigate the distributions of off-diagonal scattering matrix elements and cross-sections in the Ericson regime for time-reversal invariant systems with odd spin. Within the universal Heidelberg approach we prove that Gaussian and exponential behavior is found as the leading-order term of an asymptotic expansion of the aforementioned distributions. Furthermore, the subleading-order term is derived and compared with numerical simulations.

We present the first detailed X-ray and optical study of the intermediate polar Swift J0614.0+1709 based on a pointed XMM-Newton observation complemented by long-term optical photometry from TESS. A strong coherent modulation at the white dwarf spin period was detected in X-rays, with a period of $\sim$1411 s, confirming the magnetic nature of the system. The X-ray spin pulse exhibits a pronounced energy dependence, with the modulation amplitude decreasing towards higher energies, consistent with phase-dependent absorption in the accretion flow. Phase-resolved spectroscopy further shows that the spin variability is primarily driven by changes in the covering fraction of the partial-covering absorber. The broadband X-ray spectrum is well described by a partially absorbed thermal plasma model with a temperature of $\sim$12 keV and a soft blackbody component at $\sim$63 eV. The inferred bolometric luminosity of $\sim$5$\times$10$^{34}$ erg s$^{-1}$ places the source among the more luminous intermediate polars. The TESS observations reveal substantial sector-to-sector variability in the relative strengths of the orbital and spin modulations. While the spin signal remains persistently dominant, the beat modulation varies significantly and disappears entirely in one Sector, suggesting temporal changes in the contribution of the reprocessing region(s). The orbital and, to a lesser extent, spin modulation amplitudes show some tendency to be stronger during brighter optical states, suggesting that changes in the mass transfer rate may influence the optical emission and modulation amplitudes. Overall, Swift J0614.0+1709 is a comparatively X-ray luminous intermediate polar exhibiting complex optical variability characterised by changes in pulse morphology and recurrent brightening events, making it a valuable target for future simultaneous optical and X-ray studies.

This work details some of the recent radiological studies performed at National Synchrotron Light Source II (NSLS-II) using the Monte Carlo (MC) particle transport code FLUKA. In particular, it assesses the radiation protection challenges posed by the anticipated NSLS-II facility upgrade, taking into consideration various upgrade options. Also, it evaluates the impact related to the use of different shielding materials and the employment of ambient dose H* as the external radiation exposure estimator of effective dose. Lastly, a demonstration of synchrotron radiation transport is provided for an in-silico beamline, all the way from the radiation source to end-station, utilizing FLUKA's recent X-ray reflectivity capabilities.

In quantum mechanics, the properties of an unstable system are closely related to its corresponding energy distribution. One of the predictions of the theory is the emergence of a late-time power law in the survival probability $P(t)$ of the unstable state. However, in complex systems, similar effects may emerge due to other phenomena. This is the case for nonextensive statistical models, for some continuous lifetime distribution models, and also for certain energy-migration models applied to fluorescence. In this work, these alternative interpretations are confronted with data from time-resolved fluorescence spectroscopy experiments with erythrosine B and eosine Y as fluorophores. It turns out that some of the features expected within the quantum-mechanical description, such as the sharp transition from the exponential to the power-law regime, cannot be reproduced by the specific statistical and energy-migration parametrizations fitted in the analysis.

In this paper, we give exact combinatorial expressions for all CUE joint moments on the unit circle, in the case that all exponents are even positive integers, yielding the corresponding asymptotics. We offer two equivalent expressions for these quantities: the first is a sum involving Kostka numbers; the second is related to counting integer matrices (magic squares). As an application of our results, we unify many results in the literature, which were previously disconnected. Moreover, we prove a conjecture of Basor et al. (2018) regarding an irregular conformal block structure.

RR Lyraes (RRLs) are important tracers of old stellar populations and crucial distance indicators. To complement large variability surveys such as Gaia and Rubin-LSST, the topology of the RRL instability strip (IS) and their period-luminosity-metallicity (PLZ) and period-Wesenheit-metallicity (PWZ) relations need to be updated using state-of-the-art stellar evolution and pulsation models. We employ the updated set of BaSTI horizontal-branch (HB) evolutionary models, with finer sampling in effective temperature and metallicity, and compute the corresponding pulsation models using the mesa-rsp module building on the approach of Marconi et al. (2015). We compute a grid of linear non-adiabatic radial pulsation models with mesa-rsp, covering -2.2 <= [Fe/H] <= +0.06 dex. Seven convection configurations are explored including the recently empirically calibrated prescription for RRLs by Kovacs et al. (2024). Analytical IS boundaries are derived for RRab and RRc pulsators and transformed into several photometric systems (Gaia, OGLE, 2MASS, and LSST) and the Kiel diagram. The updated evolutionary models do not substantially change the pulsation predictions: RRab IS edges agree well with previous results, while the RRc red edge is slightly redder. The width of the IS decreases systematically with increasing alpha_MLT, and RRc is relatively more sensitive to the convection prescription than RRab. The PLZ and PWZ relations are also in good agreement with previous empirical and theoretical calibrations across the NIR bands; however, the convection prescription giving the closest match is wavelength dependent. The predicted IS boundaries and PLZ/PWZ relations exhibit a coupled dependence on pulsation mode, metallicity, and convective treatment, with no single prescription performing uniformly best across all observational planes.

Bell nonlocality allows secret key to be certified without trusting the internal operation of the devices, and even against eavesdroppers constrained only by the no-signaling principle. We ask whether generalized contextuality, a notion of nonclassicality available in prepare-and-measure experiments on a single system, can play an analogous role. In our approach, Alice and Bob first establish operational equivalences among their local preparation and measurement procedures, which are then treated as theory-independent constraints that any physical intervention on the communication channel, including that of an adversary, must respect. Eve is otherwise unrestricted, that is, her intervention on the transmitted system is not assumed to be described by quantum theory. Within this adversarial model, we show that Eve's optimal guessing probability against individual attacks is the solution of a finite linear program, and hence that a worst-case asymptotic key rate follows from the observed statistics and the operational equivalences alone. We prove that contextuality is necessary for a positive key rate. However, we also show that it is not sufficient. Concretely, the (3,2)-parity-oblivious random access code, known to yield secret key against a quantum eavesdropper, yields none certifiable key rate against a post-quantum one. Conversely, operational equivalences with no analogue among no-signaling constraints can strictly increase the asymptotic key rate. We illustrate this with the prepare-and-measure version of the standard CHSH protocol with an aligned key-generating setting.

The discrete geometry on an $n$-dimensional simplicial manifold are studied, in order to incorporate torsion into Regge calculus. In each simplex, the edge vectors are assigned to the edges to encode the information of their lengths and directions. In addition, the holonomies along the curves across the interfaces of two adjacent simplices are represented by the internal gauge group elements. The torsion manifests itself as the difference between an edge vector on an interface belonging to one simplex and the parallel transported edge vector, via the holonomy, of the same edge but belonging to the adjacent simplex. The simplicial Einstein–Cartan actions are then constructed as functions of the edge vectors and holonomies in three and four dimensions with Euclidean and Lorentzian signatures, respectively. It is shown that they return to the corresponding Regge actions for the torsion-free cases. The variations of the 4-dimensional discrete action with respect to the edge vectors and holonomies, respectively, give two equations of motion. It is shown that the former is consistent with the corresponding equation in the continuum theory, and the torsion-free holonomies satisfy the latter equation as in the continuous case. Thus, the resulting theory on the simplicial manifold can be regarded as a discrete analogue of Einstein–Cartan theory.

Universal machine-learning interatomic potentials now reach held-out energy and force errors so small that they no longer predict how a model behaves in simulation. Here we show that a potential can be graded without any reference calculation, against properties the exact Born-Oppenheimer surface satisfies by mathematical or physical necessity. We organise these properties into four families, symmetry and invariance, self-consistency and integrability, statistical-mechanical equilibrium and regularity, and turn them into fourteen inexpensive probes, each certifying against a target that is exact and independent of chemistry and reference method. Every probe therefore returns an absolute, architecture-comparable score from the energies, forces and stresses a potential already exposes, and reveals failures a fixed test set cannot. Applied to 64 pretrained potentials, the suite resolves two orders of magnitude of certified quality at comparable reported accuracy, and flags a fine-tuned potential whose reference errors improve while its surface degrades until molecular dynamics fails. An interactive leaderboard of all 64 models is available at https://jhaens.github.io/pescert-bench.

It is well-known that every n-qubit unitary can be decomposed into a product of controlled single-qubit unitaries. We show that the control conditions in such a decomposition naturally define a quasi-process function, an object that originally came up in the study of indefinite causal order. Here quasi-process functions yield a representation of every n-qubit unitary in a canonical form, namely, as a quasi-process function unitary (qPFU). We use this representation to show how quantum nonlocality without entanglement (QNLWE) can be understood in terms of unitaries that encode the trade-off between causal order and locality noted in R. Kunjwal and Ä. Baumeler, arXiv:2202.00440. Specifically, we obtain two sufficient (but not necessary) criteria—mutual exclusivity of control conditions (MECC) and Unambiguity—for a unitary to be a process function unitary (PFU), i.e., it admits a qPFU representation where the quasi-process function is a process function, an object that can model paradox-free classical causal loops. We also show the inequivalence of these criteria, neither implying the other. We then show that the circuit depth of MECC unitaries admits a characterization in terms of clique-partitioning problems on Hamming graphs and use this correspondence to provide bounds on the circuit depth of n-qubit MECC unitaries. Finally, we show how MECC unitaries provide a recipe for constructing a unitary purification of the associated process function, thereby providing a large class of unitary processes of interest in quantum causality. The generality of this causality-inspired representation of unitaries makes it a versatile tool for analyzing the structure of quantum circuits in other domains.

Cosmological simulations allow us to study galaxy-progenitor stream populations, allowing comparisons with observations to constrain galaxy formation physics. Previous work found that present-day galaxy-progenitor streams in FIRE have larger pericenters than observed in the MW, which might indicate that they tidally disrupt at larger distances, where the Galactic tides are weaker, than in the MW. One possible explanation is that they tidally disrupt too quickly because of limited resolution. At lower resolution, low-mass dwarf galaxies can be puffier and more susceptible to disruption. We build and compare dwarf-galaxy stream catalogs in two FIRE-2 cosmological zoom-in simulations with identical initial conditions (m12i) but different particle mass resolution (7070 $M_\odot$ and 880 $M_\odot$). The higher-resolution run yields a larger dwarf galaxy stream population (22 streams versus 14) using the same cutoff of 100 star particles, primarily because it resolves lower-mass streams (down to $\sim10^{5}$ $M_\odot$). Both simulations form streams at galactocentric radii < 50 kpc, but the higher-resolution Triple Latte simulation produces more streams at these small radii. We find that dwarf galaxies in the higher-resolution simulation begin disrupting at smaller pericenters than in the lower-resolution simulation. By cross-matching stream candidates, we identify counterparts for $\sim$89$\%$ of the systems in the lower-resolution simulation. For matched systems that remain on similar orbits, the higher-resolution counterparts remain intact for longer. The orbital properties of streams in the higher-resolution simulation are broadly consistent with the MW dwarf-galaxy stream population, in contrast to the lower-resolution simulation.

The OrcaQuest CMOS sensor by Hamamatsu Photonics has been found to exhibit a non-linear gain curve at low exposure times. This effect is characterized through the various exposure tests and data reduction pipelines detailed in this report, and a more accurate gain characterization curve is provided. Such data can be used to provide more consistent measures of pixel gain, linearity, and high framerate images.

Full detector simulation and reconstruction of collider events are projected to become major bottlenecks at the High-Luminosity Large Hadron Collider, motivating the development of fast, ML-based surrogates. At the same time, LLMs have driven fast progress in generative discrete modeling: autoregressive transformers trained on tokenized data now represent the state of the art across a range of generative tasks. We extend the discrete modeling paradigm by introducing a particle-level generative model trained on residual-quantized full-event data. We demonstrate the ability of this model family to perform conditional generation from detector-stable particles; we study its scaling behavior across a range of dataset and model sizes, characterize the effects of repeated data exposure and demonstrate that token-level loss systematically predicts downstream physical fidelity. These results provide an empirical framework for scalable collider full-event generation based on residual-quantized representations.

When non-adiabatic coupling mixes electronic states of a molecule, vibronic states of different electronic symmetry become interleaved across the same spectral region. The symmetry of these states cannot be accessed in conventional spectroscopy due to orientation averaging. We show that molecular-frame angular signatures, which are preserved even when states with different symmetry overlap in energy, can be used to resolve them. Using vacuum-ultraviolet transient absorption spectroscopy of aligned carbon dioxide molecules, we separate two electronically distinct classes of vibronic states ($A^{'}$ and $A^{''}$) that arise from Renner-Teller splitting of the $^1\Delta_u$ state. We reconstruct molecular-frame anisotropy continuously across the vibronic manifold showing that the anisotropy crosses over from perpendicular to parallel transition character and maps the interleaved electronic symmetry landscape. By scanning the femtosecond delay between the VUV and a near-infrared pulse through temporal overlap, we measure symmetry-dependent coherence dephasing times of these states and find that the parallel ($A^{'}$) states dephase faster than the perpendicular ($A^{''}$) states. We attribute this to faster departure of the $A^{'}$ wavepacket from the Franck-Condon region due to the distinct topology of the $A^{'}$ excited-state surface. These measurements probe symmetry-resolved ultrafast wavepacket dynamics on the coupled excited-state potential energy surfaces.

Photon loss is a dominant noise process in bosonic quantum hardware, including superconducting cavities. Fixed-total-photon-number qubit encodings in two bosonic modes retain the loss-detection advantage of dual-rail qubits while supporting photon loss correction. Optimizing entanglement fidelity in this setting for $4\leq n\leq25$ over arbitrary encoders and decoders reveals finite-group structure in every best-found code: 11 correspond to two-dimensional irreducible representations and 11 to reducible ones. Motivated by this emergence, we derive the necessary-and-sufficient Knill-Laflamme conditions for arbitrary finite-group-invariant codes, reducing their construction to equations on representation multiplicity spaces. For every finite subgroup of $SU(2)$ and every tensor rank, we explicitly construct the minimum number of operators required to impose all corresponding loss-correction constraints. These results produce analytic counterparts to most numerical codes and predict constructions missed by the initial search. Exact MacWilliams-Farkas certificates show that our codes achieve the maximum possible loss distance in 21 of the 22 sectors, and we prove that the resulting distance bound is monotone in total photon number. Beyond the scan, we identify a binary-polyhedral sequence with photon number $n_d=\lceil(3d^2+1)/4\rceil$ and construct each corresponding code through distance $d=10$. To our knowledge, the constructed $(n,d)=(28,6),(49,8),(76,10)$ codes give the smallest reported $n$ for their respective distances; all members through $d=9$ attain the fixed-$n$ LP distance bound. Together, these constructions, certificates, and a symmetry-reduced constraint count provide evidence for an infinite code family conjectured to attain every distance at the minimum photon number.

In this work we explores the dynamic solutions of a brane system in a five dimensional space-time under the Hamiltonian perspective, using the De Donner Weyl formalism. We obtain the dynamic equations for the scale factors, and obtain the Friedmann-like equations in general way. We present the solutions of the scale factors as a function of the extra coordinate, $y$, we show that the geometry is related to the matter-energy component in the brane. Finally, we develop the ADM formalism in the brane point of view with the foliation of the 3-dimensional space which is embedded in a 5-dimensional manifold.

We introduce a conservative two-exponent dispersive family, with $p>1$ the nonlinear-flux exponent and $r>0$ the gradient-dispersion exponent, that separates the mechanisms governing compactification, free-boundary regularity and linearised spectral structure while retaining an explicit travelling-wave theory. The family reduces to the absolute Rosenau-Hyman equation when $r=1$. The deformation leaves the amplitude-speed law unchanged, but makes the width amplitude dependent except at $r=1$. Two independent transition curves emerge: $pr=1$ separates infinite-tail solitary waves from compactons, whereas $r(p-1)=2$ separates compactons with a regular free boundary from edge-cusped compactons with divergent slope. The latter remain distributional solutions, with no singular measures at either the free boundary or the crest. For $r\ge1$, the linearisation factors through a singular Sturm-Liouville operator whose natural Friedrichs realisation is solvable: after a compacton-adapted change of variable, the eigenvalue equation is of Jacobi-hypergeometric type, with two explicit spectral sequences, exactly one negative eigenvalue and a one-dimensional translation kernel. Numerical experiments connect these exact structures to approximation and dynamics. Measured Fourier tails and projection errors agree with the rates predicted by the free-boundary exponent, while padded Fourier-Galerkin time integration propagates the cusped waves coherently with small phase drift. A structure-adapted Jacobi-Galerkin diagnostic of the full generator finds no detectable real part in the tested truncated point spectra. The family therefore provides an explicit testbed in which geometric singularity, weak admissibility, spectral structure and numerical regularity of compactons can be studied within a single degenerate dispersive model.

Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for general circuits require circuit depths to grow logarithmically with system size, so that noise drives the global output state close to a trivial state. Here we show that local accumulation of noise at a depth independent of system size is already sufficient. Specifically, we prove that any geometrically local circuit composed of unital operations and interspersed with single-qubit depolarizing noise of strength $p$ after $\Theta(p^{-1} \log p^{-1})$ depth can be approximately sampled from a polynomial-time classical computer. This generalizes existing results that impose anticoncentration assumptions or non-universal gate sets in order to obtain a classical sampler at such shallow depths. Our proof maps the output state of the circuit to a polymer model in statistical mechanics, and combines a convergent cluster expansion with hypercontractivity of the depolarizing channel.

We establish functional aggregate queries (FAQs) as a unifying language for exact classical simulation of quantum circuits. A circuit becomes a sum-product query: factors encode gates, internal wire variables are aggregated, and free boundary variables index transition amplitudes. The central insight is that distinct sources of simulation tractability can be exploited within the same InsideOut evaluation scheme. The query specifies what is computed; the evaluation plan, semiring, and representation of intermediate factors determine the cost. This view unifies structural and algebraic simulation guarantees. With explicit factor representations, FAQ evaluation recovers the treewidth bound for tensor-network contraction and yields finer sparsity-sensitive bounds via fractional covers. Over a formal phase semiring, compressed intermediate factors recover rank-width-based simulation for compatible quadratic phase representations. For Clifford circuits, affine-quadratic factors are closed under multiplication and marginalization and remain polynomial in size, yielding polynomial-time exact amplitude computation without any bounded-width assumption. Beyond these recoveries, the framework yields a new tractability criterion: tensor layout symmetry width. This parameter combines local cut-rank with separator symmetry through exact tree-tensor representations. We give a constructive evaluation bound and exhibit a circuit family with bounded tensor layout symmetry width but unbounded phase-graph rank-width and circuit line-graph treewidth. These results establish representation-aware FAQ evaluation as a common algorithmic foundation for classical simulation and a systematic route to new tractable regimes.

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

The Hamiltonian of a natural quantum system is usually determined indirectly, by proposing microscopic models and comparing their predicted observables with experiment. A more direct approach is to extract information about the Hamiltonian from measurements on the system itself. In many settings, however, direct access to the full system is unavailable and measurements can be performed only through controllable probes, as in quantum sensing and boundary spectroscopy. Existing Hamiltonian learning protocols under such restricted access typically require a special symmetry, a known parametric form, or controlled operations beyond free evolution. We introduce Quantum Krylov Learning (QKL), a restricted-access framework that avoids these requirements. QKL uses single temperature probe autocorrelators and their operator Krylov structure to extract model-independent spectral information about the unknown system. Rather than fitting a parametrized Hamiltonian, it reconstructs the operator Krylov Jacobi matrix representing the dynamical modes accessible to the probe. The method assumes that the unobserved system is at, or near, infinite temperature. Under this condition, the Jacobi matrix can be reconstructed directly from the autocorrelation of a probe observable, without oracle access to the Hamiltonian. The required operations are free evolution under the unknown $H$, together with probe state preparation and measurement. The learning core therefore requires no symmetry, no parametric model, and no controlled-unitary gates. We show a Lieb–Robinson bound for the operator Krylov chain and derive a data-driven criterion for the required observation window. We also establish an end-to-end sample complexity guarantee: under generic conditions on the spectral gaps and weights, the number of measurement shots required to achieve spectral precision $\varepsilon$ is polynomial in $1/\varepsilon$.

We present a fast, open-source calculation of the vacuum response matrix and surface inductance in non-axisymmetric geometries capable of running with up to 10^5 boundary points in tens of seconds on a laptop. Ideal magneto-hydrodynamic (MHD) stability modeling for free boundary modes requires the perturbed vacuum energy. We extend the VACUUM code to non-axisymmetric geometries in the new Julia implementation of the Generalized Perturbed Equilibrium Code, combining a collocation approach to the boundary integral equations with a high-order singularity correction scheme. The correction is recast into explicit quadrature weights acting on the collocation values, which allows the corrected operator to be assembled explicitly rather than applied to a given surface field, and the structure of that matrix under field-period and stellarator symmetry is then exploited to reduce storage and solve cost. We find that the vacuum response matrix converges at fourth order or greater in the grid spacing, reaching a given accuracy on a coarser grid than previous implementations without the high-order method. The non-axisymmetric calculation converges to the axisymmetric VACUUM result for a tokamak and the CAS3D result for a W7-X stellarator equilibrium. This work enables fast free boundary ideal MHD stability and perturbed equilibrium calculations in stellarators.