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DOE OSTI2021

Numerically exact generalized Green's function cluster expansions for electron-phonon problems

We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Green's function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Green's function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein + Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. Furthermore, the GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Neutrinoless double-β decay: Combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism

Neutrinoless double beta decay searches can determine the Majorana nature of neutrinos, the absolute neutrino mass, and provide invaluable insights on the matter dominance of the universe. However, the uncertainty in the nuclear matrix elements that govern the decay limits the physics reach of these experiments. Here, we devise a novel framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of nuclei used in the most advanced experiments, including 76 Ge, 130 Te, and 136 Xe. Our results cover all relevant terms, including the leading-order short-range operator recognized recently. We validate our method in light nuclei by comparing against accurate variational Monte Carlo results. On heavy systems we obtain reduced nuclear matrix elements compared with previous calculations due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, suggesting longer decay half-lives than previously considered. On the other hand, we find an enhancement of the nuclear matrix elements due to the new short-range operator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Evaluating Lyman- α constraints for general dark-matter velocity distributions: Multiple scales and cautionary tales

One of the most important observational constraints on possible models of dark-matter physics exploits the Lyman-α absorption spectrum associated with photons traversing the intergalactic medium. Because these data allow us to probe the linear matter power spectrum with great accuracy down to relatively small distance scales, finding ways of accurately evaluating such Lyman-α constraints across large classes of candidate models of dark-matter physics is of paramount importance. While such Lyman-α constraints have been evaluated for dark-matter models that give rise to relatively simple dark-matter velocity distributions, more complex models—particularly those whose dark-matter velocity distributions stretch across multiple scales—have recently been receiving increasing attention. In this paper, we undertake a study of the Lyman-α constraints associated with general dark-matter velocity distributions. Although such Lyman-α constraints are difficult to evaluate in principle, in practice there currently exist two classes of methods in the literature through which such constraints can be recast into forms which are easier to evaluate and which therefore allow a more rapid determination of whether a given dark-matter model is ruled in or out. Accordingly, we utilize both of these recasts in order to determine the Lyman-α bounds on different classes of dark-matter velocity distributions. Here we also develop a general method by which the results of these different recasts can be compared. For relatively simple dark-matter velocity distributions, we demonstrate that these two classes of recasts tend to align and give similar results. However, we find that the situation is far more complex for distributions involving multiple velocity scales: while these two classes of recasts continue to yield similar results within certain regions of parameter space, they nevertheless yield dramatically different results within precisely those regions of parameter space which are likely to be phenomenologically relevant. This, then, serves as a cautionary tale regarding the use of such recasts for complex dark-matter velocity distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Shedding light on shadow generalized parton distributions

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄$^{2}_{0}$) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that 𝑄 2 evolution, given empirical data over a wide range of skewness (𝜉 ) and 𝑄 2 scales, constrains the SGPDs studied at low 𝑥 and low 𝜉. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of 𝑥 and 𝜉.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Generalized gluon distribution for quarkonium dynamics in strongly coupled N = 4 Yang-Mills theory

We study the generalized gluon distribution that governs the dynamics of quarkonium inside a non-Abelian thermal plasma characterizing its dissociation and recombination rates. This gluon distribution can be written in terms of a correlation function of two chromoelectric fields connected by an adjoint Wilson line. We formulate and calculate this object in N = 4 supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence, allowing for a nonzero center-of-mass velocity v of the heavy quark pair relative to the medium. The effect of a moving medium on the dynamics of the heavy quark pair is described by the simple substitution T → γ T in agreement with previous calculations of other observables at strong coupling, where T is the temperature of the plasma in its rest frame, and γ = ( 1 − v 2 ) − 1 / 2 is the Lorentz boost factor. Such a velocity dependence can be important when the quarkonium momentum is larger than its mass. Contrary to general expectations for open quantum systems weakly coupled with large thermal environments, the contributions to the transition rates that are usually thought of as the leading ones in Markovian descriptions vanish in this strongly coupled plasma. This calls for new theoretical developments to assess the effects of strongly coupled non-Abelian plasmas on in-medium quarkonium dynamics. Finally, we compare our results with those from weakly coupled QCD, and find that the QCD result moves toward the N = 4 strongly coupled result as the coupling constant is increased within the regime of applicability of perturbation theory. This behavior makes it even more pressing to develop a non-Markovian description of quarkonium in-medium dynamics. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Systematic improvement of x -dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of 2 + 1 + 1 flavors of highly improved staggered quarks with a physical pion mass at lattice spacing a ≈ 0.09 fm and a box width L ≈ 5.76 fm . We present results for the nucleon H and E generalized parton distributions (GPDs) with average boost momentum P z ≈ 2 GeV at momentum transfers Q 2 = [ 0 , 0.97 ] GeV 2 at skewness ξ = 0 as well as Q 2 ∈ 0.23 GeV 2 at ξ = 0.1 , renormalized in the modified minimal subtraction ( MS ¯ ) scheme at scale μ = 2.0 GeV , with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Nonlocal chiral anomaly and generalized parton distributions

We discuss the nonlocal generalization of the QCD chiral anomaly along the light cone and derive relations between twist-two, twist-three, and twist-four generalized parton distributions (GPDs) mediated by the anomaly. We further establish the connection to the “anomaly pole” in the GPD E ˜ recently identified in the perturbative calculation of the Compton scattering amplitudes, and demonstrate its cancellation at the GPD level. Our work helps elucidate the previously unexplored connection between GPDs, the chiral anomaly, and the mass generation of the η ′ meson. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

General signals for charged lepton flavor violating decays

We explore the most general phenomenology of charged lepton flavor violating (CLFV) decays of muon and tau leptons to the three body final states ($\bar{e}ee, \bar{μ}μμ, \bar{e}μμ, \bar{μ}μe, \bar{μ}ee, \bar{e}eμ$). By constructing a complete basis of operators at each dimension, we derive the most general amplitudes for these decay processes. By considering constraints from unitarity and Large Electron-Positron Collider (LEP), we show that operators of mass dimension 6 and 7 are the most likely to be observed in next generation experiments. Focusing on these dimensions, we compute the results of unpolarized (spin-averaged) decays parametrized in terms of the invariant masses of the daughter particles. We also compute the differential decay rates for polarized decays, in anticipation of the experimental search Mu3e, which expects to have a muon beam with ∼ 90% polarization, and the chiral Belle proposal, which aims to have a 70% polarized electron beam. To determine the extent to which the operators may be distinguished experimentally, we plot the differential distributions for each operator, showing that they leave only a few possible degenerate explanations. Through a statistical analysis, we estimate the number of events needed to break the degeneracies using the angular information. These results are adapted to treat ℓ → ℓ′⁢$v\bar{v}$, where the angular distribution of the outgoing charged lepton has enhanced distinguishing power. With many Standard Model extensions predicting these CLFV decays, these results will better enable upcoming searches to identify and/or constrain physics beyond the Standard Model.

phenomenology↗
DOE OSTI2025

Depinning, melting, and sliding of generalized Wigner crystals in Moiré systems

We numerically examine the depinning, sliding, and melting of commensurate and incommensurate Wigner crystals on two-dimensional hexagonal periodic substrates near fillings of 1 / 3 , 1 / 2 , and 2 / 3 to model the dynamics of generalized Wigner crystals in moiré heterostructures. At low temperatures where thermal fluctuations are irrelevant, for commensurate fillings we find a strongly pinned state that depins into a sliding crystal, while at incommensurate fillings the depinning threshold is strongly reduced. For fillings below 1 / 2 , the depinning occurs in a two-step process. Above the first depinning threshold, there is an extended range of drives where the conduction occurs via the sliding of antikinks along the charge stripes, followed by a second threshold where all the charges begin to slide. At finite temperatures, the external driving reduces the effective melting temperature at commensurate fillings and enhances creep at incommensurate fillings. We show that depinning into different sliding states, such as moving fluids or moving crystals, produces nonlinear features in the transport curves. We also show that transport is asymmetric on either side of a commensurate filling due to the different dynamics for interstitials versus holes in the commensurate structure. A variety of sliding states should be accessible for generalized Wigner crystals at finite temperatures even for low drives. If experiments can realize sliding dynamics in moiré systems, it would open another class of commensurate and incommensurate phases for study. Additionally, the sliding dynamics and antikink flow could provide unique functionalities for charge transport in moiré heterostructures. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Neutrino Masses from Generalized Symmetry Breaking

We explore generalized global symmetries in theories of physics beyond the standard model. Theories of Z ′ bosons generically contain “noninvertible” chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well motivated U ( 1 ) L μ − L τ , there is a noninvertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g., U ( 1 ) L μ − L τ ⊂ SU ( 3 ) H , where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas, e.g., y ν ∼ y τ exp ( − S inst ) . These theories require no bevy of new fields nor additional global symmetries but are instead simple, natural, and predictive: The discovery of a lepton family Z ′ at low energies will reveal the scale at which L μ − L τ emerges from a larger gauge symmetry. Published by the American Physical Society 2024

Córdova, Clay (ORCID:0000000205793295)↗
DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗
DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗
DOE OSTI2025

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Unpolarized quarks at nonzero skewness

We extend the formalism of asymmetric frames of reference for generalized parton distributions (GPDs) to the case of nonzero skewness, i.e., including longitudinal momentum transfer. The framework, based on Lorentz-invariant amplitudes and previously developed and numerically implemented for unpolarized, helicity and transversity GPDs at zero skewness, gives efficient access to a broad range of kinematics, making full mapping of GPDs from the lattice realistic. The general-skewness formalism is tested using lattice data with both transverse and longitudinal or only longitudinal momentum transfer, the latter being a special case with a reduced number of independent amplitudes. We extract the amplitudes in coordinate space and express the GPDs 𝐻 and 𝐸 in terms of these amplitudes. This is followed by reconstruction of quasidistributions and their matching to the light cone. We further identify and discuss the principal challenges for nonzero skewness GPDs.

Lattice QCD↗
DOE OSTI2026

Generalized definition of the isothermal compressibility in (2+1)-flavor QCD

We introduce a generalized definition of the isothermal compressibility ($𝜅_{𝑇,𝜎{^2_𝑄}}$) calculable by keeping net conserved charge fluctuations rather than total number densities constant. We present lattice QCD results for this isothermal compressibility, expressed in terms of fluctuations of conserved charges that are related to baryon (𝐵), electric charge (𝑄), and strangeness (𝑆) quantum numbers. This generalized isothermal compressibility is compared with hadron resonance gas model calculations as well as with heavy-ion collision data obtained at RHIC and the LHC. We find $𝜅_{𝑇,𝜎{^2_𝑄}}$ = 13.8⁢(1.3) fm 3 /GeV at $𝑇_{\textrm{pc},0}$ =156.5⁢(1.5) MeV and $\hat{𝜇}_𝐵$ = 0. This finding is consistent with the rescaled result of the ALICE Collaboration, where we replaced the number of charged hadrons (𝑁 ch ) by the total number of hadrons (𝑁 tot ) at freeze-out. Normalizing this result with the QCD pressure (𝑃) we find that the isothermal compressibility on the pseudocritical line stays close to that of an ideal gas, i.e., $𝑃⁢𝜅_{𝑇,𝜎{^2_𝑄}} ≃$ 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Tula: Optimizing Time, Cost, and Generalization in Distributed Large-Batch Training

Distributed training increases the number of batches processed per iteration either by scaling-out (adding more nodes) or scaling-up (increasing the batch-size). However, the largest configuration does not necessarily yield the best performance. Horizontal scaling introduces additional communication overhead, while vertical scaling is constrained by computation cost and device memory limits. Thus, simply increasing the batch-size leads to diminishing returns: training time and cost decrease initially but eventually plateaus, creating a knee-point in the time/cost vs. batch-size pareto curve. The optimal batch-size therefore depends on the underlying model, data and available compute resources. Large batches also suffer from worse model quality due to the well-known “generalization gap”. In this paper, we present Tula, an online service that automatically optimizes time, cost, and convergence quality for large-batch training of convolutional models. It combines parallel-systems modeling with statistical performance prediction to identify the optimal batchsize. Tula predicts training time and cost within 7.5−14% error across multiple models, and achieves up to 20× overall speedup and improves test accuracy by ≈9% on average over standard large-batch training on various vision tasks, thus successfully mitigating the generalization gap and accelerating training at the same time.

Tyagi, Sahil [ORNL] (ORCID:0009000783144745)↗
DOE OSTI2023

Ground Vehicle Generalized Forces and Moment Governor Design Via Noncertainty-Equivalent Adaptive Prescribed Performance Control

Torque-vectoring technology demonstrates great potential in improving the safety and performance of ground vehicles. In this paper, a novel generalized forces and moment governor for torque vectoring is suggested. The proposed solution strategically combines prescribed performance control, noncertainty equivalent adaptive control design, and a smooth projection operator. The main advantage of the proposed control strategy lies in its capability to guarantee both the transient performance and prompt recovery of the desired deterministic behavior of the closed-loop adaptive system, even in the presence of parametric uncertainties. ASM simulation results are presented to validate the efficacy of the proposed generalized forces and moment governor and to demonstrate its superiority over a baseline solution.

Zhou, Xingyu↗
DOE OSTI2024

Linear Solvers for Collector Systems of Generalized Large-scale Inverter-Based Resources

Collector systems for inverter-based resources (IBRs) are typically represented by equivalent circuits for electromagnetic transient (EMT) simulations. Recent studies have revealed that modeling a detailed collector system is essential to accurately represent the behavior of IBRs, especially when dealing with partial tripping during external disturbances. However, there are several challenges in simulating a detailed EMT model of a collector system due to the time required to simulate such systems. Thus, this paper investigates the modeling of a detailed collector system, taking into account its configuration and components as defined in IEEE standard 2800. The configurations include the collector systems of generalized large-scale IBR plants. The components include the main IBR transformer, collector bus, and feeders with lines and/or cables. The EMT model of the collector system is represented by differential algebraic equations (DAEs) that are discretized to form linear equations that are solved using linear solvers. In this paper, linear solvers are proposed based on the Schur complement method, which are utilized for simulation of the EMT model of collector systems of generalized large-scale IBRs to accelerate simulation speed while maintaining the accuracy of the results. The proposed solvers are verified by comparing the performance to that of linear solvers provided in MATLAB.

Choi, Jongchan↗