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DOE OSTI2024

Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ 2 , where κ = (m/M)1/4 is the usual Born–Oppenheimer parameter. The lowest order term is the usual Born–Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born–Oppenheimer theory. Here, we show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born–Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Measurement of t -channel production of single top quarks and antiquarks in pp collisions at 13 TeV using the full ATLAS Run 2 data sample

The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using 140 fb -1 of ATLAS data. The total cross-sections are determined to be σ(tq) = 137$^{+8}_{-8}$ pb and σ($\bar{t}q$) = 84$^{+6}_{-5}$ pb for top-quark and top-antiquark production, respectively. The combined cross-section is found to be σ(tq + $\bar{t}q$) = 221$^{+13}_{-13}$ pb and the cross-section ratio is R t = σ(tq) / σ($\bar{t}q$) = 1.636$^{+0.036}_{-0.034}$. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of R t using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: -0.37 < C$^{3,1}_{Qq}$ /Λ 2 < 0.06 and -0.87 < C$^{3}_{ΦQ}$ / Λ 2 < 1.42. The constraint |V tb | > 0.95 at the 95% confdence level is derived from the measured value of σ(tq + $\bar{t}q$), assuming that the Wtb interaction is a left-handed weak coupling and that |V tb | $\gg$ |V td |, |V ts |. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confdence contours in the corresponding two-dimensional parameter spaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Global analysis of $μ → e$ interactions in the SMEFT

We study current experimental bounds on charged lepton flavor violating (CLFV) μ – e interactions in the model-independent framework of the Standard Model Effective Field Theory (SMEFT). Assuming a generic flavor structure in the quark sector, we consider the contributions of CLFV operators to low-energy observables, including μ → eγ and μ → e conversion for quark-flavor conserving operators and CLFV meson decays for quark-flavor violating operators. At high energy, we consider limits on CLFV decays of the Higgs and Z bosons and of the top quark, and obtain bounds on operators with light quarks by recasting searches for production of eμ pairs in pp collisions at the Large Hadron Collider (LHC). We connect observables at low- and high-energy by taking into account renormalization group running and matching between CLFV operators. We also discuss the sensitivity of the future Electron-Ion Collider, where the prospective bounds are derived by imposing simple cuts on final state particles. We find that, in a single operator scenario, bounds on purely leptonic operators are dominated by μ → eγ and μ → e conversion. Semileptonic operators with down-type quarks are also dominantly constrained by low-energy observables, while LHC searches lead the bounds on up-type quark-flavor violating operators. Taking simplified multiple-coupling scenarios, we show that it is easy to evade the strongest low-energy bounds from spin-independent μ → e conversion, and that collider searches are competitive and complementary to constraints from spin-dependent μ → e conversion and other low-energy probes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Graph neural networks for CO 2 solubility predictions in Deep Eutectic Solvents

Deep Eutectic Solvents (DESs) are a promising class of solvents for CO 2 capture. DESs are complex mixtures that can be designed to optimize CO solubility and overall capture process efficiency. However, the vast design landscape of DES mixtures makes experimental investigation prohibitive; as such, there is a need for computational models that can quickly and efficiently navigate the design space and inform data collection efforts. In this work, we propose Graph Neural Network (GNN) models for predicting CO 2 solubility for DESs; the GNN leverages a mixture graph representation that captures the molecular structure of the DES components as well as their intermolecular interactions. Here, we compare the GNN framework against alternative architectures (neural networks, graph convolution networks, and random forests) and data representations (molecular fingerprints, sigma profiles, and graphs). We show that the proposed approach offers superior predictive performance; specifically, we show that solubility can be predicted reliably directly from molecular structure (without the need of using sigma profiles as proposed in previous studies). This result is important, as obtaining sigma profiles requires expensive density functional theory computations. We also explored the ability of GNNs to predict solubility for new DES mixtures and operating conditions. We found that the model extrapolates across temperature reliably. However, we also found deficiencies in the ability of the model to predict solubility for DES mixtures, pressures, and molar ratio not included in the training sets; we show that this is due to an inherent lack of chemical diversity in datasets available in the literature. The proposed computational capabilities can thus help navigate the design space of DES and inform data collection efforts. Our models, data, and benchmarks are shared as Python code implemented in Jupyter notebooks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis

In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the eigenstate thermalization hypothesis (ETH). After identifying simple operators with an algebra of low-energy observables and tracing out the complementary high-energy Hilbert space, the ETH leads to an exponential suppression of trace distance between the coarse grained eigenstates. Conversely, we show that an exponential hardness of distinguishing between states implies ETH-like matrix elements. Finally, the BBBV lower bound on the query complexity of Grover search then translates directly into a complexity-theoretic statement lower bounding the hardness of distinguishing these reduced states

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Neoclassical Tearing Mode Seeding by Nonlinear Three-Wave Interactions in Tokamaks

We report the experimental observation of seed magnetic island formation by nonlinear three-wave coupling of magnetic island triplets. In this experiment, disruptive 2,1 islands are seeded by the coupling of 4,3 and 3,2 tearing modes to a central 1,1 sawtooth precursor. Three-wave interactions between these modes are conclusively identified by bispectral analysis, indicating fixed phase relationships in agreement with theory. Furthermore, this new observation of this seeding mechanism has important implications for future reactors that must operate in stable plasma equilibria, free of disruptive 2,1 islands.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Clifford transformations for fermionic quantum systems: From Pauli and Majorana operators to Dirac fermions

Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state distillation, quantum communication and cryptography, and qubit tapering. Moreover, circuits composed entirely of Clifford gates are classically simulatable, highlighting their computational significance. In this article we extend the concept of Clifford transformations to Dirac fermions. We demonstrate that discrete Clifford transformations are generated by half-body and pair operators while continuous Clifford transformations are generated by number operators, providing a systematic framework for their characterization. Additionally, we establish connections with fermionic mean-field theories and applications in qubit tapering, offering insights into their broader implications in quantum computing.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

HydroForecast Long-term: Improving hydropower’s resilience to climate change through accurate climate-scale

With hydrologic patterns and water availability across the globe shifting due to climate change, advancements in hydrologic prediction systems can help significantly reduce the uncertainties that utilities and water supply entities have in their decision making. Understanding and estimating hydrology at the climate scale is critical for managing water resources under changing climate scenarios. This project focuses on integrating state-of-the-art neural network modeling with downscaled climate projections to deliver the reliable water supply projections decades into the future to meet an urgent need from hydropower operators and water utilities. In this Phase 1 DOE SBIR proposal, we developed and validated a theory-guided neural network model, HydroForecast Long-term, for climate-scale hydrology and implemented the model within existing HydroForecast infrastructure. HydroForecast Long-term combines the most accurate streamflow modeling system with a flexible and scalable data architecture to generate water supply projections out to the year 2100. This report illustrates that we have achieved our four objectives: 1) create a prototype of HydroForecast Long-term, building the neural network prediction model, 2) build an automated data input pipeline that processes large amounts of data from the latest global temperature and precipitation climate models; 3) benchmark the accuracy of the hydrologic model over the recent two decades over a large set of diverse basins, and 4) create a set of output visuals and summary metrics informed by customer feedback that connect the data to critical decision points. This work empowers water users to make data-informed decisions supporting a resilient, renewable-powered grid and water system. The results advance the Department of Energy’s mission by addressing critical gaps in water supply planning under climate change.

13 HYDRO ENERGY↗
DOE OSTI2026

Hazard Analysis to Support Fusion Systems Safety Assessments

Reliability, safety, and performance are vital aspects of any nuclear operation. Fusion technology continues to grow in public, private, and research interest, and coupled with rapidly growing energy needs, fusion technology research is poised for fast progress. The development of a Fusion Nuclear Science Facility (FNSF) is seen as stepping stone for demonstrating long-cycle fusion. Naturally, such operation requires systems that are available, reliable, and safe. This work provides a novel demonstration of systems theory coupled with traditional hazard analysis to provide insights into the risk priority of components and systems found within the FNSF. The results of this work are a set of identified hazards that should be considered for the risk-informed design and development of the FNSF.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit’s generators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein’s lemma

Abstract For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback–Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein’s lemma for quantum hypothesis testing beyond independent and identically distributed situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.

Physics↗
DOE OSTI2020

A Lagrangian perturbation theory in the presence of massive neutrinos

We develop a Lagrangian Perturbation Theory (LPT) framework to study the clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We follow the trajectories of CDM particles with Lagrangian displacements fields up to third order in perturbation theory. Once the neutrinos become non-relativistic, their density fluctuations are modeled as being proportional to the CDM density fluctuations, with a scale-dependent proportionality factor. This yields a gravitational back-reaction that introduces additional scales to the linear growth function, which is accounted for in the higher order LPT kernels. Through non-linear mappings from Eulerian to Lagrangian frames, we ensure that our theory has a well behaved large scale behavior free of unwanted UV divergences, which are common when neutrino and CDM densities are not treated on an equal footing, and in resummation schemes that manifestly break Galilean invariance. We use our theory to construct correlation functions for both the underlying matter field, as well as for biased tracers using ConvolutionLPT. Redshift-space distortions effects are modeled using the Gaussian Streaming Model. When comparing our analytical results to simulated data from the Quijote 1 simulation suite, we find good accuracy down to r = 20 Mpc h -1 at redshift z = 0.5, for the real space and redshift space monopole particle correlation functions with no free parameters. The same accuracy is reached for the redshift space quadrupole if we additionally consider an effective field theory parameter that shifts the pairwise velocity dispersion. For modeling the correlation functions of tracers we adopt a simple Lagrangian biasing scheme with only density and curvature operators, which we find sufficient to reach down to r = 20 Mpc h -1 when comparing to simulated halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann ( Phys. Fluids , vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$ . The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$ , resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$ . A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

Physics↗
DOE OSTI2021

Discreteness and integrality in Conformal Field Theory

Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the space of CFTs is lacking. We systematically study these constraints in two-dimensional, non-holomorphic CFTs, making use of two main mathematical results. First, we prove a theorem constraining the behavior near the cusp of integral, vector-valued modular functions. Second, we explicitly construct non-factorizable, non-holomorphic cuspidal functions satisfying discreteness and integrality, and prove the non-existence of such functions once positivity is added. Application of these results yields several bootstrap-type bounds on OPE data of both rational and irrational CFTs, including some powerful bounds for theories with conformal manifolds, as well as insights into questions of spectral determinacy. We prove that in rational CFT, the spectrum of operator twists t ≥ c/12 is uniquely determined by its complement. Likewise, we argue that in generic CFTs, the spectrum of operator dimensions Δ > c–1/12 is uniquely determined by its complement, absent fine-tuning in a sense we articulate. Finally, we discuss implications for black hole physics and the (non-)uniqueness of a possible ensemble interpretation of AdS 3 gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Insights into the emergence of mass from studies of pion and kaon structure

There are two mass generating mechanisms in the standard model of particle physics (SM). One is related to the Higgs boson and fairly well understood. The other is embedded in quantum chromodynamics (QCD), the SM’s strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling. As bound states seeded by a valence-quark and -antiquark, pseudoscalar mesons present a simpler problem in quantum field theory than that associated with the nucleon. Consequently, there is a large array of robust predictions for pion and kaon properties whose empirical validation will provide a clear window onto many effects of both mass generating mechanisms and the constructive interference between them. This has now become significant because new-era experimental facilities, in operation, construction, or planning, are capable of conducting such tests and thereby contributing greatly to resolving the puzzles of EHM. These aspects of experiment, phenomenology, and theory, along with contemporary successes and challenges, are reviewed herein. In addition to providing an overview of the experimental status, we focus on recent progress made using continuum Schwinger function methods and lattice-regularised QCD. Further, advances made using other theoretical tools are also sketched. Our primary goal is to highlight the potential gains that can accrue from a coherent effort aimed at finally reaching an understanding of the character and structure of Nature’s Nambu–Goldstone modes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Scaling Field-Theoretic Simulation for Multicomponent Mixtures with Neural Operators

Multicomponent polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, neural operators, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Modeling Ni Coarsening and Migration in the Hydrogen Electrode of Solid oxide Cells under Operating Conditions

Ni coarsening and migration is the most important degradation in the hydrogen electrode of solid oxide cells. This presentation reviews our works on Ni coarsening and migration in NETL over the past years. We used simulation techniques including phase-field modeling and density function theory to investigate possible mechanisms of Ni coarsening and migration, including self-diffusion of Ni, diffusion of gaseous Ni(OH)2, surface diffusion of Ni(OH)x and Ni-YSZ wettability change, and examined the effect of operating conditions on these mechanisms. So far, none of the mechanisms can fully explain the experiments. Remaining questions and possible paths forward are summarized and discussed.

Lei, Yinkai↗