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DOE OSTI2023

Role of three-body dynamics in nucleon-deuteron correlation functions

Correlation functions of hadrons can be accessed in high-energy collisions of atomic nuclei, revealing information about the underlying interaction. This work complements experimental efforts to study nucleon-deuteron Nd—with N=p (proton) or N=n (neutron)—correlations with theory evaluations using different techniques. The correlation functions C nd and C pd are calculated based on a scattering wave function, extending previous benchmarks for the Nd scattering matrix to this new observable. We use hyperspherical harmonics and Faddeev techniques with one of the widely used nucleon-nucleon (NN) interactions, the Argonne v18 potential. Moreover, in the low-energy region we perform additional calculations in the framework of pionless effective field theory. The pd correlation function is computed in the large-energy region to make contact with a recent measurement by the ALICE Collaboration. We show that the scattering wave function has the proper dynamical input to describe an initial rise and subsequent oscillations of C pd as a function of the energy. Effects on the observables using different NN and three-nucleon potentials are evaluated with the conclusion that variations of around 2% are observed. Although these effects are small, future measurements can go beyond this accuracy, allowing for new detailed studies of strong interaction in light nuclear systems. Furthermore, the present study supports the current efforts devoted to the measurement of correlation functions in systems dominated by the strong interactions, such as pd, ppp, Λd, and ppΛ.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

SILVERRUSH. XIV. Ly α Luminosity Functions and Angular Correlation Functions from 20,000 Ly α Emitters at z ∼ 2.2–7.3 from up to 24 deg 2 HSC-SSP and CHORUS Surveys: Linking the Postreionization Epoch to the Heart of Reionization

Abstract We present luminosity functions (LFs) and angular correlation functions (ACFs) derived from 18,960 Ly α emitters (LAEs) at z = 2.2−7.3 over a wide survey area of ≲24 deg 2 that are identified in the narrowband data of the HSC-SSP and CHORUS surveys. Confirming the large sample with 241 spectroscopically identified LAEs, we determine Ly α LFs and ACFs in the brighter luminosity range down to 0.5 L ⋆ , and confirm that our measurements are consistent with previous studies but offer significantly reduced statistical uncertainties. The improved precision of our ACFs allows us to clearly detect one-halo terms at some redshifts, and provides large-scale bias measurements that indicate host halo masses of ∼10 11 M ⊙ over z ≃ 2−7. By comparing our Ly α LF (ACF) measurements with reionization models, we estimate the neutral hydrogen fractions in the intergalactic medium to be x H i < 0.05 (= 0.06 − 0.03 + 0.12 ) at z = 5.7 and x H i = 0.1 5 − 0.08 + 0.10 ( 0.21 − 0.14 + 0.19 ), 0.1 8 − 0.12 + 0.14 , and 0.7 5 − 0.13 + 0.09 at z = 6.6, 7.0, and 7.3, respectively. Our findings suggest that the neutral hydrogen fraction remains relatively low, x H i ≲ 0.2, at z = 5−7, but increases sharply at z > 7, reaching x H i ∼ 0.9 by z ≃ 8−9, as indicated by recent JWST studies. The combination of our results from LAE observations with recent JWST observations suggests that the major epoch of reionization occurred at z ∼ 7−8, likely driven by the emergence of massive sources emitting significant ionizing photons.

Umeda, Hiroya (ORCID:0009000801675129)↗

DOE OSTI2025

Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

Source functions are obtained from p – p and d – α correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the p – p and d – α correlation functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2022

Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Second-order photon correlation measurements [g (2) (τ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of g (2) (τ = 0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g (2) (τ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g (2) (τ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g (2) (τ = 0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g (2) (τ) functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g (2) (τ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. Furthermore, this work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

What do the two times in two-time correlation functions mean for interpreting tr-ARPES?

Not provided.

Spectroscopy↗

DOE OSTI2022

MICCO: An Enhanced Multi-GPU Scheduling Framework for Many-Body Correlation Functions

Calculation of many-body correlation functions is one of the critical kernels utilized in many scientific computing areas, especially in Lattice Quantum Chromodynamics (Lattice QCD). It is formalized as a sum of a large number of contraction terms each of which can be represented by a graph consisting of vertices describing quarks inside a hadron node and edges designating quark propagations at specific time intervals. Due to its computation- and memory-intensive nature, real-world physics systems (e.g., multi-meson or multi-baryon systems) explored by Lattice QCD prefer to leverage multi-GPUs. Different from general graph processing, many-body correlation function calculations show two specific features: a large number of computation-/data-intensive kernels and frequently repeated appearances of original and intermediate data. The former results in expensive memory operations such as tensor movements and evictions. The latter offers data reuse opportunities to mitigate the data-intensive nature of many-body correlation function calculations. However, existing graph-based multi-GPU schedulers cannot capture these data-centric features, thus resulting in a sub-optimal performance for many-body correlation function calculations. To address this issue, this paper presents a multi-GPU scheduling framework, MICCO, to accelerate contractions for correlation functions particularly by taking the data dimension (e.g., data reuse and data eviction) into account. This work first performs a comprehensive study on the interplay of data reuse and load balance, and designs two new concepts: local reuse pattern and reuse bound to study the opportunity of achieving the optimal trade-off between them. Based on this study, MICCO proposes a heuristic scheduling algorithm and a machine-learning-based regression model to generate the optimal setting of reuse bounds. Specifically, MICCO is integrated into a real-world Lattice QCD system, Redstar, for the first time running on multiple GPUs. The evaluation demonstrates MICCO outperforms other state-of-art works, achieving up to 2.25× speedup in synthesized datasets, and 1.49× speedup in real-world correlation functions.

Wang, Qihan↗

DOE OSTI2023

Graph Contractions for Calculating Correlation Functions in Lattice QCD

Computing correlation functions for many-particle systems in Lattice QCD is vital to extract nuclear physics observables like the energy spectrum of hadrons such as protons. However, this type of calculation has long been considered to be very challenging and computing-resource intensive because of the complex nature of a hadron composed of quarks with many degrees of freedom. In particular, a correlation function can be calculated through a sum of all possible pairs of quark contractions, each of which is a batched tensor contraction, dictated by Wick's theorem. Because the number of terms of this sum can be very large for any hadronic system of interest, fast evaluation of the sum faces several challenges: an extremely large number of contractions, a huge memory footprint at runtime, and the speed of tensor contractions. In this paper, we present a Lattice QCD analysis software suite, Redstar, which addresses these challenges by utilizing novel algorithmic and software engineering methods targeting modern computing platforms such as many-core CPUs and GPUs. In particular, Redstar represents every term in the sum of a correlation function by a graph, applies efficient graph algorithms to reduce the number of contractions to lower the cost of computations, and minimizes the total memory footprint. Moreover, Redstar carries out the contractions on either CPUs or GPUs utilizing an internal and highly efficient Hadron contraction library. Specifically, we illustrate some important algorithmic optimizations of Redstar, show various key design features of Hadron library, and present the speedup values due to the optimizations along with performance figures for calculating six correlations functions on four computing platforms.

Chen, Jie↗

DOE OSTI2023

Graph Contractions for Calculating Correlation Functions in Lattice QCD

Chen, Jie↗

DOE OSTI2024

Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions

Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system’s complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

Chemistry↗

DOE OSTI2026

Empirical investigation of nuclear correlation function distributions in lattice QCD

Two-point correlation functions of systems with baryon number 𝐵 ∈ {1,2,3,4} are investigated using lattice quantum chromodynamics (QCD). In particular, the empirical distributions of importance-sampling Monte-Carlo samples of these correlation functions are examined as a function of the spacetime separation between the two points and the baryon number. While the exact forms of these distributions are not known for QCD, recent work has determined asymptotic expressions for analogous correlation function distributions in simpler theories such as scalar field theory and the disordered phase of the 𝑂⁡(𝑁) model. The theoretical 𝑂⁡(𝑁) model distributions are found to provide an accurate description of the empirical QCD distributions at zero momentum over a wide range of temporal separations for each baryon number when assessed with a range of different statistical tests. In particular, the behavior of the baryon number 𝐵 QCD correlation function at large temporal separation is well reproduced by the 𝑂⁡(𝑁 ∼ 2/𝐵) model distribution.

Lattice field theory↗

DOE OSTI2026

Euclidean correlation functions in quantum gravity

We calculate Euclidean correlation functions through next-to-leading order in the low-energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop order. We show that quantum fluctuations of the background spacetime must be taken into account in order to obtain gauge invariant expressions, and we point out a subtlety associated with the analytic continuation of the conformal mode. Our final expressions for the correlation functions involve only Newton’s constant and the source-sink separation, and they are a universal prediction of the low-energy effective theory. Thus, they serve as a useful point of comparison for nonperturbative lattice formulations of gravity.

Effective field theory↗

DOE OSTI2024

Correlation functions from tensor network influence functionals: The case of the spin-boson model

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff–Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Chemistry↗

DOE OSTI2024

Multiparticle integral and differential correlation functions

This paper formalizes the use of integral and differential cumulants for measurements of multiparticle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net-charge fluctuations. This enables the introduction of multiparticle balance functions, defined based on differential correlation functions (factorial cumulants), that suppress two- and three-prong resonance decays effects and enable measurements of underlying long-range correlations obeying quantum number conservation constraints. These multiparticle balance functions satisfy simple sum rules determined by quantum number conservation. It is additionally shown that these multiparticle balance functions arise as an intrinsic component of high-order net-charge cumulants. This implies that the magnitude of these cumulants, measured in a specific experimental acceptance, is strictly constrained by charge conservation and primarily determined by the rapidity and momentum width of these balance functions. The paper also presents techniques to reduce the computation time of differential correlation functions up to order n = 10 based on the methods of moments. Published by the American Physical Society 2024

Physics↗

DOE OSTI2021

Theory and application of the vector pair correlation function for real-space crystallographic analysis of order/disorder correlations from STEM images

Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba 5 SmSn 3 Nb 7 O 30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Large-time correlation functions in bosonic lattice field theories

Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, however little is known about the statistical properties of these quantities. In this work, the asymptotic form of the distributions of the correlation functions at vanishing momentum is determined for bosonic interacting lattice field theories with a unique gapped vacuum. It is demonstrated that the deviations from the asymptotic form at large Euclidean times can be utilized to determine the spectrum of the theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

Here, we report a systematic measurement of cumulants, C n , for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, κ n , for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The C n and κ n are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, y, and transverse momentum, p T . The data were taken during the first phase of the Beam Energy Scan (BES) program (2010–2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity (|y| < 0.5) and transverse momentum 0.4 < p T < 2.0 GeV/c, using the STAR detector at RHIC. We observe a nonmonotonic energy dependence ($\sqrt{s_{NN}}$ = 7.7–62.4 GeV) of the net-proton C 4 /C 2 with the significance of 3.1σ for the 0–5% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with $\sqrt{s_{NN}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, κ 2 , of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, κ 4 , of protons plays a role in determining the energy dependence of proton C 4 /C 1 below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Exponential vs Gaussian Correlation Functions in the Characterization of Block Copolymer Grain Structure by Depolarized Light Scattering

Block copolymer (BCP) grain structure affects the mechanical, optical, and electrical properties of BCP materials, making the accurate characterization of this grain structure an important goal. In this study, improved BCP grain parameters were obtained by employing an exponentially decaying correlation function within the ellipsoidal grain model, instead of the Gaussian correlation function that was used in previous work. The exponential correlation function provides a better fit to the experimental depolarized light scattering data, which outweighs the disadvantage that it requires numerical integration to obtain the model scattered intensity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗