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Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi-Yau targets at large volume. Focusing on the examples of K3 and the quintic, we show that the spectrum, averaged over a region in complex structure moduli space, possesses the same statistical properties as the Gaussian orthogonal ensemble of random matrix theory.
Abstract We initiate a study of gravity focusing on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic Poisson brackets, employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint. It is well-known that the null Raychaudhuri equation describes how the geometric data of a null hypersurface evolve in null time in response to gravitational radiation and external matter. Our analysis leads to three complementary viewpoints on this equation. First, it can be understood as a Carrollian stress tensor conservation equation. Second, we construct spin-0, spin-2 and matter stress tensors that act as generators of null time reparametrizations for each sector. This leads to the perspective that the null Raychaudhuri equation can be understood as imposing that the sum of CFT-like stress tensors vanishes. Third, we solve the Raychaudhuri constraint non-perturbatively. The solution relates the dressing time to the spin-2 and matter boost charge operators. Finally we establish that the corner charge corresponding to the boost operator in the dressing time frame is monotonic. These results show that the notion of an observer can be thought of as emerging from the gravitational degrees of freedom themselves. We briefly mention that the construction offers new insights into focusing conjectures.
The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z 2 topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.
X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly suitable for time- or dose-critical in vivo/in situ/operando (tomography) experiments because it requires only a single intensity measurement. However, the phase information of the wave field is lost during the measurement and must be recovered. Conventional algebraic and iterative methods often rely on specific approximations or boundary conditions that may not be met by many samples or experimental setups. In addition, they require manual tuning of reconstruction parameters by experts, making them less adaptable for complex or variable conditions. Here we present a self-learning approach for solving the inverse problem of phase retrieval in the near-field regime of Fresnel theory using a single intensity measurement (hologram). A physics-informed generative adversarial network is employed to reconstruct both the phase and absorbance of the unpropagated wave field in the sample plane from a single hologram. Unlike most state-of-the-art deep learning approaches for phase retrieval, our approach does not require paired, unpaired, or simulated training data. This significantly broadens the applicability of our approach, as acquiring or generating suitable training data remains a major challenge due to the wide variability in sample types and experimental configurations. The algorithm demonstrates robust and consistent performance across diverse imaging conditions and sample types, delivering quantitative, high-quality reconstructions for both simulated data and experimental datasets acquired at beamline P05 at PETRA III (DESY, Hamburg), operated by Helmholtz-Zentrum Hereon. Furthermore, it enables the simultaneous retrieval of both phase and absorption information.
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.
In systems near phase transitions, macroscopic properties often follow algebraic scaling laws, determined by the dimensionality and the underlying symmetries of the system. The emergence of such universal scaling implies that microscopic details are irrelevant. Here, we locally investigate the scaling properties of the metal-insulator transition at the LaAlO 3 /SrTiO 3 interface. We show that, by changing the dimensionality and the symmetries of the electronic system, coupling between structural and electronic properties prevents the universal behavior near the transition. By imaging the current flow in the system, we reveal that structural domain boundaries modify the filamentary flow close to the transition point, preventing a fractal with the expected universal dimension from forming.
Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in (d+2)-dimensional Minkowski spacetime for any d ≥ 2, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in (d+2)-dimensional spacetime.
Nonlinear modeling and optimization is a valuable tool for aiding decisions by engineering practitioners, but programming an optimization problem based on a complex electrical, mechanical, or chemical process is a time-consuming and error-prone activity. Therefore, there is a need for model analysis and debugging tools that can detect and diagnose modeling errors. One such tool is the Dulmage–Mendelsohn decomposition, which identifies structurally under- and over-determined subsets in systems of equations and variables by partitioning the bipartite graph of the system. This work provides the necessary background to understand the Dulmage–Mendelsohn decomposition and its application to the analysis of nonlinear optimization problems, demonstrates its use in diagnosing a variety of modeling errors, and introduces software implementations for analyzing nonlinear optimization problems in the Pyomo and JuMP algebraic modeling languages.
The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.
We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the “KLT algebra” and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy in addition to locality constraints. We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a ‘heterotic’-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order ∇ 10 R 4 . Finally, we initiate a search for new double-copy kernels.
Lagrangian statistics and particle transport in edge plasma turbulence are investigated using the Hasegawa–Wakatani model and its modified version. The latter shows the emergence of pronounced zonal flows. Different values of the adiabaticity parameter are considered. The main goal is to characterize the role of coherent structures, i.e., vortices and zonal flows, and their impact on the Lagrangian statistics of particles. Computationally intensive long time simulations following ensembles of test particles over hundreds of eddy turnover times are considered in statistically stationary turbulent flows. The flow topology is characterized using the Lagrangian Okubo–Weiss criterion in order to split the flow into topologically different domains. In elliptic and hyperbolic regions, the probability density functions (PDFs) of the residence time have self-similar algebraic decaying tails. However, in the intermediate regions, the PDFs exhibit exponentially decaying tails. Topologically conditioned PDFs of the Lagrangian velocity, and acceleration and density fluctuations are likewise computed. The differences between the classical Hasegawa–Wakatani system and its modified version are assessed, and the role of zonal flows is highlighted. Here, the density flux spectrum, which characterizes the contributions of different length scales, is studied, and its inertial scaling is found to be in agreement with predictions based on dimensional arguments. Analyzing the angular change of particle tracers at different time scales, corresponding to coarse grained curvature, completes the study, and these multiscale geometric statistics quantify the directional properties of the particle motion in different flow regimes.
The structure and dynamics of many-body systems are the result of a delicate interplay between underlying interactions. Fermionic pairing, for example, plays a central role in various physical systems, ranging from condensed matter to nuclear systems, where it can lead to collective phenomena such as superconductivity and superfluidity. In atomic nuclei, the interplay between pairing and particle-hole interactions leads to a high degree of complexity and intricate entanglement structures. Despite this apparent complexity, symmetries emerge and manifest themselves in observable regular patterns. These symmetries and their breakings have long been used to determine relevant degrees of freedom and simplify classical descriptions of many-body systems. Here, this work explores the potential utility of quantum computers with arrays of qudits in simulating interacting fermionic systems, when the qudits can naturally map the relevant degrees of freedom determined by an underlying symmetry group. The Agassi model of fermions interacting via particle-hole and pairing interactions is based on an underlying so(5) algebra. Such systems can intuitively be partitioned into pairs of modes with five basis states, which thus naturally map to arrays of d = 5 qudits (qu5its). Classical noiseless simulations of the time evolution of systems with up to twelve qu5its are performed, by implementing quantum circuits that are developed herein, using PYTHON codes invoking Google's CIRQ software. The resource requirements of the qu5it circuits are analyzed and compared with two different mappings to qubit systems: a physics-aware Jordan-Wigner mapping requiring four qubits per mode pair and a state-to-state mapping requiring three qubits per mode pair. While the dimensionality of Hilbert spaces in mappings to qu5it systems are less than those for the corresponding qubit systems, the number of entangling operations, depending on the available hardware, can either be greater or smaller than for the physics-aware Jordan-Wigner mapping. The state-to-state mapping, while having a smaller Hilbert space than Jordan-Wigner mappings, appears to be the least efficient in gate counts. Further, a previously unknown sign problem has been identified from Trotterization errors in time evolving high-energy excitations. There appear to be advantages in employing quantum computers with arrays of qudits to perform simulations of many-body dynamics that exploit the role of underlying symmetries, specifically in lowering the required quantum resources and in reducing anticipated errors that take the simulation out of the physical space. If the necessary entangling gates are not directly supported by the hardware, physics-aware mappings to qubits may, however, be advantageous for other aspects.
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. Here, we propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.
This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.
Volumetric 3D printing motivated by computed axial lithography enables rapid printing of homogeneous parts but requires a high dimensionality gradient-descent optimization to calculate image sets. Here we introduce a new, simpler approach to image-computation that algebraically optimizes a model of the printed object, significantly improving print accuracy of complex parts under imperfect material and optical precision by improving optical dose contrast between the target and surrounding regions. Quality metrics for volumetric printing are defined and shown to be significantly improved by the new algorithm. The approach is extended beyond binary printing to grayscale control of conversion to enable functionally graded materials. The flexibility of the technique is digitally demonstrated with realistic projector point spread functions, printing around occluding structures, printing with restricted angular range, and incorporation of materials chemistry such as inhibition. Finally, simulations show that the method facilitates new printing modalities such as printing into flat, rather than cylindrical packages to extend the applications of volumetric printing.
Multiscale modeling requires the linking of models at different levels of detail, with the goal of gaining accelerations from lower fidelity models while recovering fine details from higher resolution models. Communication across resolutions is particularly important in modeling soft matter, where tight couplings exist between molecular-level details and mesoscale structures. While multiscale modeling of biomolecules has become a critical component in exploring their structure and self-assembly, backmapping from coarse-grained to fine-grained, or atomistic, representations presents a challenge, despite recent advances through machine learning. A major hurdle, especially for strategies utilizing machine learning, is that backmappings can only approximately recover the atomistic ensemble of interest. We demonstrate conditions for which backmapped configurations may be reweighted to exactly recover the desired atomistic ensemble. By training separate decoding models for each sidechain type, we develop an algorithm based on normalizing flows and geometric algebra attention to autoregressively propose backmapped configurations for any protein sequence. Critical for reweighting with modern protein force fields, our trained models include all hydrogen atoms in the backmapping and make probabilities associated with atomistic configurations directly accessible. We also demonstrate, however, that reweighting is extremely challenging despite state-of-the-art performance on recently developed metrics and generation of configurations with low energies in atomistic protein force fields. Through detailed analysis of configurational weights, we show that machine-learned backmappings must not only generate configurations with reasonable energies, but also correctly assign relative probabilities under the generative model. These are broadly important considerations in generative modeling of atomistic molecular configurations.
In holographic duality, a higher dimensional quantum gravity system emerges from a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. We propose a formulation of duality for a general causally complete bulk spacetime region, called subregion-subalgebra duality, which provides a framework to describe how geometric notions in the gravity system, such as spacetime subregions, different notions of times, and causal structure, emerge from the dual CFT. Subregion-subalgebra duality generalizes and brings new insights into subregion-subregion duality (or equivalently entanglement wedge reconstruction). It provides a mathematically precise definition of subregion-subregion duality and gives an independent definition of entanglement wedges without using entropy. Geometric properties of entanglement wedges, including those that play a crucial role in interpreting the bulk as a quantum error correcting code, can be understood from the duality as the geometrization of the superadditivity of certain algebras. Using general boundary subalgebras rather than those associated with geometric subregions makes it possible to find duals for general bulk spacetime regions, including those not touching the boundary. Applying subregion-subalgebra duality to a boundary state describing a single-sided black hole also provides a precise way to define mirror operators. Published by the American Physical Society 2025
Magnetic field fluctuations are observed in current-carrying stellarator plasmas when the rotational transform is close to a rational value at the edge of the plasma. At low plasma pressure, these fluctuations are associated with perturbed currents parallel to the equilibrium magnetic field lines. A model for these magnetohydrodynamic modes in a low-β, three-dimensional stellarator equilibria has been developed. A set of helical current filaments are constrained to mimic the structure of magnetic field lines on rational surfaces derived from three-dimensional (3D) equilibrium reconstructions. Transformation to straight field line coordinates then allows fitting of the poloidal magnetic sensor data to a single harmonic function, which fixes the modeled toroidal mode structure via the field line flow geometry. The developed procedure accurately captures phase and amplitude variation for m/n = 3/2, 3/1, and 4/1 modes in the 3D equilibria of the compact toroidal hybrid experiment.