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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Temperature-dependent mechanical properties and crystal plasticity parameters for additively manufactured Haynes-214 alloy: Experiments and numerical modeling

Our experimental mechanical testing data demonstrated that the additively manufactured (AM) laser powder bed fusion (L-PBF) Haynes-214 alloy exhibits non-linear mechanical properties as the temperature rises from ambient to 870 °C. Crystal plasticity (CP) simulations provide an effective approach to gaining deeper insights into microstructure-property linkages under thermomechanical loading. This method can reduce the need for costly high-temperature mechanical testing while accounting for the effects of crystallographic texture and grain morphology on the mechanical behavior of AM materials. However, calibrating a CP model is time-consuming because individual simulations are computationally expensive and hundreds (or more) of iterations over parameter sets may be required. To address this issue, we have designed a machine learning-differential evolution (ML-DE) CP framework that can accurately interpolate the tensile properties of AM L-PBF Haynes-214 alloy across a wide temperature range from ambient to 870 °C, with minimal reliance on experimental data. The framework uses electron backscatter diffraction (EBSD) measurements to generate statistically equivalent microstructural volume elements to serve as inputs to the CP modeling framework. Stress–strain curves were generated from 1000 CP simulations, which serve as the training data set for the three ML regression algorithms explored: linear, extra-trees, and multi-layer perceptron. These three regression models were independently evaluated to compare their efficiency and identify the most suitable algorithm for the given problem. Results revealed that the extra-trees ML regressor outperforms the other models in both qualitative and quantitative aspects with an R 2 of 0.98. Subsequently, the differential evolution optimization approach is employed to calibrate the ML-based CP material parameters with experimental results obtained at various temperatures. Finally, temperature-dependent CP material parameters are formulated. The effectiveness and efficiency of the designed framework are validated through comparison with experimental results, demonstrating a high degree of agreement. These calibrated parametric constitutive equations enable further use of the CP model to study the deformation behavior of this alloy under a wide range of thermo-mechanical loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Computational Review of Privacy-Preserving Mechanisms for the Smart Grid

Smart grid technologies have rapidly become one of the largest and most comprehensive sources of data for the modern utility. For the most part, data streams are seen as an essential tool that enable utilities to carry their day-to-day business operations, but they also create the need for efficient and secure data management strategies. In the context of the smart grid, ensuring data privacy is becoming an increasing concern due to a combination of factors that range from shifts in operational paradigms and rapid technology evolution to changes in legislation. Furthermore, researchers have highlighted the risks associated with improperly protected energy records. For example, energy consumption data from homes could be used to infer the behaviors and habits of home occupants through activity recognition or user profiling (Fan, 2017), which may lead to unfair service pricing, targeted advertising, or other personal security violations. Similarly, Electric Vehicles’ (EVs) charging metadata could be used to reveal private information about the owner such as their payment methods, preferred charging stations, and other locational and timing information that could be used to reconstruct the vehicle owner’s behaviors. The privacy of user data, even when used for statistical analysis or machine learning training processes, also needs to be carefully considered, as an individual’s private traits may still be vulnerable if their inclusion/exclusion greatly impacts the result or could be linked to a public dataset through cross-reference. The breach of user privacy also has severe impacts for organizations that store, transmit, or work on the data in the form of diminishing the public’s trust in them while potentially incurring legal consequences (e.g., fines and suspensions under the European Union General Data Protection Regulation, Health Insurance Portability and Accountability Act, etc.). Because of these risks, several privacy-preserving mechanisms are available to help organizations comply with privacy legislations and prevent the unauthorized and malicious use of user data. In light of these concerns, this report focuses on performing a computational review of privacy-preserving mechanisms that have received a significant amount of interest in literature. It specifically focuses on 1) homomorphic encryption, 2) zero-knowledge proofs, 3) differential privacy, and 4) federated learning. It is worth noting that although many of the methods presented in this document rely on cryptographic primitives, their intent is not to provide perfect secrecy, but rather to enable users to maintain privacy, and thus they shall not be compared or equated to other constructs that are aimed to address cybersecurity constructs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Adaptively controlled fast production of defect-free beryllium ion crystals using pulsed laser ablation

Trapped atomic ions find wide applications ranging from precision measurement to quantum information science and quantum computing. Beryllium ions are widely used due to the light mass and convenient atomic structure of beryllium; however, conventional ion loading from thermal ovens exerts undesirable gas loads for a prolonged duration. Here, we demonstrate a method to rapidly produce pure linear chains of beryllium ions with pulsed laser ablation, serving as a starting point for large-scale quantum information processing. Our method is fast compared to thermal ovens, reduces the gas load to only 10 -12 Torr (10 -10 Pa) level, yields a short recovery time of a few seconds, and also eliminates the need for a deep ultraviolet laser for photoionization. We also study the loading dynamics, which show non-Poissonian statistics in the presence of sympathetic cooling. In addition, we apply feedback control to obtain defect-free ion chains with desirable lengths.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Potentials of mean force fail to describe chemical bond-breaking in solution

Many liquid phase studies assume that the potential energy surfaces of reacting molecules are the same as in the gas phase, neglecting complex solvent dynamics that can completely alter the nature of chemical reactivity. Even studies that include solvent effects typically only consider them in an average, equilibrium way as part of a potential of mean force (PMF). In this work, we use mixed quantum/classical simulations to compare how equilibrium and non-equilibrium solvent motions affect the photodissociation of a simple diatomic molecule, NaK + , in liquid tetrahydrofuran. A PMF analysis shows that as the excited-state molecule dissociates with the solvent at equilibrium, the bonding electron remains associated with K + at short bond distances but eventually localizes on Na + at the end of dissociation. When we examine non-equilibrium dynamical photodissociation trajectories, however, we find that they fall into three distinct categories: about a quarter of them have the bonding electron mainly associated with Na + , another quarter stay mainly associated with K + , and about half have the bonding electron shared roughly equally between the two ions. The results show that equilibrium PMFs cannot accurately describe the dynamics of bond-breaking chemical reactions in solution because there is insufficient time for the solvent to reach equilibrium on the time scale over which bond dissociation occurs. Furthermore, our analysis shows that the solvent coupling between the electronic energy surfaces is similar at and away from equilibrium, suggesting that other factors, such as solute velocity-driven solvent memory effects, play a more important role in explaining the failure of the equilibrium PMF to predict the non-equilibrium dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Young but fading radio sources: searching for remnants among compact steep-spectrum radio sources

The incidence of young but fading radio sources provides important information on the life cycle of radio emission in radio-loud active galactic nuclei. Despite its importance for constraining the models of radio source evolution, there are no systematic studies of remnants in complete samples of young radio sources. We report results of the study of 18 compact steep-spectrum (CSS) radio sources, selected from the statistically complete B3-VLA (Very Large Array) CSS sample, characterized by a steep optically thin spectrum (α ≥ 1.0) and no core detection in earlier studies. Our deep multifrequency VLA, pc-scale Very Long Baseline Array, and enhanced Multi Element Remotely Linked Interferometer Network (e-MERLIN) observations allowed us to locate the core component in 10 objects. In three CSS sources, there is no clear evidence of present-time active regions, suggesting that they are likely in a remnant phase. Among sources with core detection, we find three objects that have no clear active regions (hotspots) at the edges of the radio structure, suggesting that the radio emission may have just restarted. Our results support a power-law distribution of the source ages, although the poor statistics prevents us from setting solid constraints on the percentage of remnants and restarted sources in subpopulations of radio sources.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Thermodynamics of quantum measurement and Maxwell's demon's arrow of time

Here, we discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Testing the impact of electromagnetic fields on the directed flow of constituent quarks in heavy-ion collisions

It has been proposed that strong electromagnetic fields produced in the early stages of heavy-ion collisions can lead to splitting of the rapidity-odd directed flow of positive and negative hadrons. For light hadrons, the interpretation of such measurements is complicated by the low magnitude of directed flow as well as by ambiguities arising from transported quarks. To overcome these complications, we propose measurements using only hadrons carrying produced quarks (u¯, d¯, s s¯ ). Here, we discuss how to identify the kinematics where such hadrons are produced via the coalescence mechanism and therefore their flow is the sum of the flow of their constituent quarks. With this sum rule verified for certain combinations of hadrons, the expected systematic violation of this rule with increasing electric charge can be measured, which could be a consequence of the electromagnetic fields produced in the collisions. Our approach can be tested with the high statistics data from Phase II of the Beam Energy Scan program at the Relativistic Heavy Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Worldwide Physics-Based Lifetime Prediction of c-Si Modules Due to Solder-Bond Failure

Lifetime prediction of the fielded c-Si solar modules due to location-specific weather conditions has been an important topic of photovoltaic research and the economic viability of solar energy. Data analytic techniques such as the performance ratio method, Statistical clear sky model, and Suns-Vmp methods quantify the degradation from measured data of a solar farm, however, the nonlinear time-dependence and correlated degradations make it difficult to use the empirical degradation rates for ultimate lifetime projection. In this article, we propose a complementary physics-based model to predict the solder bond failure caused by mechanical stress associated with the variations of the temperature. Integrating the worldwide weather information from NASA/NSRDB databases, the model predicts the location-specific output-power degradation and the lifetime of a module due to solder bond failure. The model parameters are calibrated against qualification tests involving thermal cycling of specific batches of modules from a specific technology/manufacturer. The results may be summarized as: 1) Modules installed at higher latitudes show a longer lifetime due to reduced damage accumulation. 2) The reduction of temperature fluctuation close to large bodies of water, such as seashores, increases solder bond lifetime significantly. 3) Relatively speaking, modules installed close to the Tropic of Cancer/Capricorn (23.5 degrees North/South) suffer from a higher solder bond damage and have a shorter lifetime, suggesting a conservative design. This model should serve as a building block of a comprehensive reliability framework that can predict the lifetime of a module that experiences simultaneous and correlated degradation mechanisms involving yellowing, corrosion, and potential-induced degradation.

14 SOLAR ENERGY↗
DOE OSTI2023

Flexoelectricity and New Phenomena

It is easy to miss the scientific implications of our recent work on Triboelectricity. Everyone knows that rubbing and contact can produce static electricity; less appreciated is that the thermodynamic driver has been an open question since static electricity was first observed by Thales of Miletus around 585 BC. People think they understand it, for instance one common explanation that can still be found in the current literature is that differences in the work function drives charge transfer, often called the Volta-Helmholtz hypothesis. As summarized in 1967 by Harper, this fails to explain many experimental observations, for instance that charging can occur when two pieces of the same material are rubbed against each other. We are the first to place triboelectricity on a solid foundation rooted in quantum mechanics – the flexoelectric effect. We were able to explain a significant number of previously unexplained phenomena: 1) Bipolar tribocurrents associated with stick-slip, due to the change in sign of the strain gradients. 2) A one-third power scaling of tribocurrents with indentation force. 3) Tribocharging when two identical materials are used, these being due to local variations in the asperities so there are usually local potential differences. 4) Inhomogeneous charging of insulators, related to the statistical nature of asperities. 5) An experimentally observed reversal in the sign of charge transfer for negative and positive curvature, which is related to a change in the sign of the strain gradient. Exploiting our DOE prior funded work on flexoelectricity, we obtained semi-quantitative matching to existing experimental measurements of the surface charge in triboelectric experiments. The work has been well received in the literature. The work has been the focus of a number of popular science press articles, and also formed the basis for a Podcast for children 6-10 “The Rise and Fall of Static Man” posted in December 2019 by NPR as part of their “Wow in the World” series. I was also briefly interviewed by the Chicago PBS station in January 2020. This work are significant for a wide range of energy applications; to quote from an independent source: "Triboelectric power has plenty of potential, says Wenzhuo Wu, an assistant professor of engineering at Purdue. If the basics of static electricity are better understood, we could maximize the efficiency of wind or wave power generators, Wu says. The body's own movement could be used to power internal medical devices. Imagine being able to create a roof shaped to harness the power of a raindrop — the friction of the rain passing over the surface — to generate triboelectricity, powering the building below it." This is the start of new science, some of which we already partially understand such as the role of band bending in charge transfer. We need to understand charge transfer combining elasticity, quantum mechanics, band bending and defect states. These directly involve several of the DOE Grand Challenges: "How do we control material processes at the level of electrons? How do remarkable properties of matter emerge from complex correlations of the atomic or electronic constituents and how can we control these properties? How do we characterize and control matter away—especially very far away— from equilibrium?" I will argue that this work truly falls into the class of disruptive science; it is not just a simple extension, linear science. Not everyone will accept the approach. Since we explain far more about triboelectricity than anyone before, the preponderance of evidence supports the model. The feedback I have received is that many agree with the work, to quote: "The model makes sense, says Michael McAlpine, a professor of engineering at the University of Minnesota. "It's such a simple explanation, I was surprised I didn't put my finger on that," McAlpine says." The proposal received strong reviews. It was also publicized on the Department of Energy Web Site.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Adaptive Cognitive Mechanisms to Maintain Calibrated Trust and Reliance in Automation

Trust calibration for a human–machine team is the process by which a human adjusts their expectations of the automation’s reliability and trustworthiness; adaptive support for trust calibration is needed to engender appropriate reliance on automation. Herein, we leverage an instance-based learning ACT-R cognitive model of decisions to obtain and rely on an automated assistant for visual search in a UAV interface. This cognitive model matches well with the human predictive power statistics measuring reliance decisions; we obtain from the model an internal estimate of automation reliability that mirrors human subjective ratings. The model is able to predict the effect of various potential disruptions, such as environmental changes or particular classes of adversarial intrusions on human trust in automation. Finally, we consider the use of model predictions to improve automation transparency that account for human cognitive biases in order to optimize the bidirectional interaction between human and machine through supporting trust calibration. The implications of our findings for the design of reliable and trustworthy automation are discussed.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Hydrogen effects on the deformation and slip localization in a single crystal austenitic stainless steel

Hydrogen is known to embrittle austenitic stainless steels, which are widely used in high-pressure hydrogen storage and delivery systems, but the mechanisms that lead to such material degradation are still being elucidated. The current work investigates the deformation behavior of single crystal austenitic stainless steel 316L through combined uniaxial tensile testing, characterization and atomistic simulations. Thermally precharged hydrogen is shown to increase the critical resolved shear stress (CRSS) without previously reported deviations from Schmid’s law. Molecular dynamics simulations further expose the statistical nature of the hydrogen and vacancy contributions to the CRSS in the presence of alloying. Slip distribution quantification over large in-plane distances (> 1 mm), achieved via atomic force microscopy (AFM), highlights the role of hydrogen increasing the degree of slip localization in both single and multiple slip configurations. The most active slip bands accumulate significantly more deformation in hydrogen precharged specimens, with potential implications for damage nucleation. For $\langle$110$\rangle$ tensile loading, slip localization further enhances the activity of secondary slip, increases the density of geometrically necessary dislocations and leads to a distinct lattice rotation behavior compared to hydrogen-free specimens, as evidenced by electron backscatter diffraction (EBSD) maps. Finally, the results of this study provide a more comprehensive picture of the deformation aspect of hydrogen embrittlement in austenitic stainless steels.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The effects of carbonaceous inclusions and their distributions on dynamic failure processes in boron carbide ceramics

Commercially available boron carbide ceramics typically have heterogeneous microstructures that contain distributions of processing-induced inclusions. The inclusions that are rich in carbon (i.e., carbonaceous) govern the underlying mechanisms of brittle fracture through wing crack formation, and thus dictate the mechanical response of the ceramic. In this study, we investigate the dynamic failure of five boron carbide ceramic materials with different inclusion populations. All of the materials were prepared by hot-pressing; four of these boron carbides contained different sizes and concentrations of carbonaceous inclusions, while one contained no carbonaceous inclusions. The heterogeneity distributions were characterized in some detail for statistical analysis using scanning electron microscopy and quantitative image analysis. A modified compression Kolsky bar setup with in situ ultra-high-speed microscopic imaging (10 million frames per second) was then used to study the influence of the inclusion distributions on the dynamic failure processes in these materials, at nominal high strain rates of 10 2 -10 3 s -1 . The in situ ultra-high-speed microscopy highlighted the link between micro and macroscale failure processes and demonstrated that the carbonaceous inclusions are indeed the preferential sites for nucleation of wing cracks, as previously hypothesized based on post-mortem observations. The relative orientation of an inclusion with respect to the compression axis was shown to affect the likelihood that it would participate in crack nucleation. In conclusion, all of the ceramics were also found to have orientation-dependent peak compressive stress, regardless of the presence of carbonaceous inclusions, suggesting that grain orientation distributions are also important.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Measurement of T-Dependence of the Beam Asymmetry (S) for the Reaction yp --> n'p AT GLUEX

We report on a measurement of the four-momentum transfer (-t) dependence of the Beam Asymmetry (Sigma) for the reaction yp --> n'p with the linearly polarized photon beam at GlueX. The observable is sensitive to the n' production mechanism. The Beam Asymmetry (Sigma) was extracted from azimuthal angular distributions (phi) combined to obtain yield asymmetries. This technique removes most contributions from instrumental asymmetries. These data are based on a data set that is five times more extensive than previous measurements. This allowed us to double the kinematic reach in the four-momentum transfer squared (-t) and reduce the statistical uncertainties. Up to a four-momentum transfer squared (-t) of 1.7 GeV2, the beam asymmetry is positive, close to unity, and shows little dependence on the four-momentum transfer -t. This indicates that the production process continues to be dominated by exchanges of the rho (p) and the omega (w) mesons. Further systematic cross-check was done by analyzing the decay mode nr^0r^0. This analysis also revealed positive asymmetries closer to unity providing an important systematic cross-check for the results obtained using n'-->nr+r-.

Paudel, Churamani↗
DOE OSTI2020

Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data

The physics of ferroelectric domain walls is explored using the Bayesian inference analysis of atomically resolved STEM data. We demonstrate that domain wall profile shapes are ultimately sensitive to the nature of the order parameter in the material, including the functional form of Ginzburg-Landau-Devonshire expansion, and numerical value of the corresponding parameters. The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models. Here, we explore the physics of the ferroelectric domain walls in BiFeO 3 using this method, and derive the posterior estimates of relevant parameters. More generally, this inference approach both allows learning materials physics from experimental data with associated uncertainty quantification, and establishing guidelines for instrumental development answering questions on what resolution and information limits are necessary for reliable observation of specific physical mechanisms of interest.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Markov Chain Monte Carlo Predictions of Neutron-rich Lanthanide Properties as a Probe of r -process Dynamics

Lanthanide element signatures are key to understanding many astrophysical observables, from merger kilonova light curves to stellar and solar abundances. To learn about the lanthanide element synthesis that enriched our solar system, we apply the statistical method of Markov Chain Monte Carlo to examine the nuclear masses capable of forming the r-process rare-earth abundance peak. We describe the physical constraints we implement with this statistical approach and demonstrate the use of the parallel chains method to explore the multidimensional parameter space. We apply our procedure to three moderately neutron-rich astrophysical outflows with distinct types of r-process dynamics. We show that the mass solutions found are dependent on outflow conditions and are related to the r-process path. We describe in detail the mechanism behind peak formation in each case. We then compare our mass predictions for neutron-rich neodymium and samarium isotopes to the latest experimental data from the CPT at CARIBU. Here, we find our mass predictions given outflows that undergo an extended (n,γ)⇌(γ,n) equilibrium to be those most compatible with both observational solar abundances and neutron-rich mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Bayesian-based response expansion and uncertainty quantification using sparse measurement sets

Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.

42 ENGINEERING↗
DOE OSTI2026

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗
DOE OSTI2020

Chaos on the hypercube

We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude φ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at φ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at φ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of φ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

1/N expansion↗