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DOE OSTI2020

Scattering using real-time path integrals

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While imaginary time treatments of scattering are possible, imaginary time is not a natural framework for treating scattering problems. More importantly, quantum algorithms for calculating path integrals require real-time evolution. Purpose: Here, we test a recently introduced method for performing direct calculations of scattering observables using real-time path integrals in order to understand the challenges facing real-time path integral calculations of scattering observables. Method: The computations are based on a new interpretation of the path integral as the expectation value of a potential functional on cylinder sets of continuous paths with respect to a complex probability distribution. The method can in principle be applied to arbitrary short-range potentials. Results: The method is applied to compute matrix elements of Møller wave operators applied to narrow wave packets. These are used to calculate half-shell sharp-momentum transition matrix elements for one-dimensional potential scattering. The calculations for half-shell transition operator matrix elements converge to the numerical solution of the Lippmann-Schwinger equation. Conclusions: This work presents a proof in principle that scattering observables can be computed using real-time Feynman path integrals. While the computational method is not efficient, it can be improved. It provides a laboratory for studying quantum computational algorithms that are applicable to scattering problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Estimating β eff from static, late-time Feynman neutron noise measurements

The effective delayed neutron fraction, β eff , is a kinematic parameter describing the contribution of delayed neutrons to the effective multiplication factor, $\kappa$ eff , and is of great interest to the nuclear criticality safety community and beyond. In fact, $\kappa$ eff presently must be inferred (as opposed to directly measured) since variables like β eff must be obtained from simulation, reference tables, or a dynamic or pulsed measurement where the assembly of fissile material is perturbed and not in steady state. Several recent works have proposed neutron noise techniques to estimate β eff from static measurements (such as benchmark experiments). This work experimentally investigates an approach based on looking at late-time (up to thousands of seconds) correlated neutrons in Feynman histograms. This work utilizes measurements of weapons grade plutonium and highly enriched uranium to construct late-time Feynman histograms and investigate a proposed methodology of estimating β eff from a fit of the distribution. Data is shown from both He-3 detectors and an organic scintillator array. This work is preliminary in nature, demonstrating some experimental feasibility and proposing improvements for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

DL_POLY Quantum 2.0: A modular general-purpose software for advanced path integral simulations

DL_POLY Quantum 2.0, a vastly expanded software based on DL_POLY Classic 1.10, is a highly parallelized computational suite written in FORTRAN77 with a modular structure for incorporating nuclear quantum effects into large-scale/long-time molecular dynamics simulations. This is achieved by presenting users with a wide selection of state-of-the-art dynamics methods that utilize the isomorphism between a classical ring polymer and Feynman’s path integral formalism of quantum mechanics. Here, the flexible and user-friendly input/output handling system allows the control of methodology, integration schemes, and thermostatting. DL_POLY Quantum is equipped with a module specifically assigned for calculating correlation functions and printing out the values for sought-after quantities, such as dipole moments and center-of-mass velocities, with packaged tools for calculating infrared absorption spectra and diffusion coefficients.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A multisite decomposition of the tensor network path integrals

Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the non-equilibrium dynamics of extended quantum systems coupled with local dissipative environments. In this work, we extend the tensor network path integral (TNPI) framework to efficiently simulate such extended systems. The Feynman–Vernon influence functional is a popular approach used to account for the effect of environments on the dynamics of the system. In order to facilitate the incorporation of the influence functional into a multisite framework (MS-TNPI), we combine a matrix product state (MPS) decomposition of the reduced density tensor of the system along the sites with a corresponding tensor network representation of the time axis to construct an efficient 2D tensor network. The 2D MS-TNPI network, when contracted, yields the time-dependent reduced density tensor of the extended system as an MPS. The algorithm presented is independent of the system Hamiltonian. We outline an iteration scheme to take the simulation beyond the non-Markovian memory introduced by solvents. Applications to spin chains coupled to local harmonic baths are presented; we consider the Ising, XXZ, and Heisenberg models, demonstrating that the presence of local environments can often dissipate the entanglement between the sites. We discuss three factors causing the system to transition from a coherent oscillatory dynamics to a fully incoherent dynamics. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Enhancing the efficiency of time-dependent density functional theory calculations of dynamic response properties

X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density–density correlation function, which naturally emerges in Feynman’s path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.

Moldabekov, Zhandos A. [Helmholtz-Zentrum Dresden-↗

DOE OSTI2020

Isotope effects in molecular structures and electronic properties of liquid water via deep potential molecular dynamics based on the SCAN functional

Here, Feynman path-integral deep potential molecular dynamics (PI-DPMD) calculations have been employed to study both light (H 2 O) and heavy water (D 2 O) within the isothermalisobaric ensemble. In particular, the deep neural network is trained based on ab initio data obtained from the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Because of the lighter mass of hydrogen than deuteron, the properties of light water are more influenced by nuclear quantum effect than those of heavy water. Clear isotope effects are observed and analyzed in terms of hydrogen-bond structure and electronic properties of water that are closely associated with experimental observables. The molecular structures of both liquid H 2 O and D 2 O agree well with the data extracted from scattering experiments. The delicate isotope effects on radial distribution functions and angular distribution functions are well reproduced as well. Our approach demonstrates that deep neural network combined with SCAN functional based ab initio molecular dynamics provides an accurate theoretical tool for modeling water and its isotope effects.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Calculation of the C 12 + C 12 sub-barrier fusion cross section in an imaginary-time-dependent mean field theory

The 12 C + 12 C sub-barrier fusion cross section is calculated within the framework of a time-dependent Hartree-Fock-based classical model using the Feynman path-integral method. The modified astrophysical S* factor is compared to direct and indirect experimental results. A good agreement with the direct data is found. In the lower-energy region where recent analyses of experimental data obtained with the Trojan horse method (THM) lead to contrasting results, the model predicts a nonresonant S* factor half-way between those results. Low-energy resonances revealed in the THM data are added to the calculation, and the relative reaction rate in the Gamow region is calculated. In particular, including 0 + resonances result in some agreement with the THM data. Here, the role of different resonances is discussed in detail, and their influence on the reaction rate at temperatures relevant to stellar evolution is investigated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green’s function theory of band structure renormalization that incorporates localization and self-trapping. Here, we show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Zero-cost corrections to influence functional coefficients from bath response functions

Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly generate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the accuracy of this procedure depends on the validity of the high temperature approximation. In this work, an alternative derivation based on the Kubo formalism is provided. This enables the calculation of additional correction terms that increases the range of applicability of the procedure to lower temperatures. Because it is based on the Kubo-transformed correlation function, this approach allows the direct use of correlation functions obtained from methods such as ring-polymer molecular dynamics and centroid molecular dynamics in determining the influence functional coefficients for subsequent system-solvent simulations. The accuracy of the original procedure and the corrected procedure is investigated across a range of parameters. It is interesting that the correction term comes at zero additional cost. Furthermore, it is possible to improve upon the correction using zero-cost physical intuition and heuristics making the method even more accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Comparison of Measured and Simulated Neutron Counting with 3He Detectors and the Subcritical Water-Moderated UO2 7uPCX Assembly

An experiment designed to compare neutron noise analysis techniques on subcritical assemblies using differing neutron detector designs was developed as a collaborative effort between the Institut de radioprotection et de surete nucleaire (IRSN), Los Alamos (LANL), Lawrence Livermore (LLNL), and Sandia National Laboratories. This experiment has the final goal of characterizing neutron noise analysis accuracy in determining multiplication in light water systems for various neutron detection systems. This experiment utilized the Seven Percent Critical Experiment (7uPCX) facility at Sandia National Laboratories. The 7uPCX is an assembly designed to investigate light water systems with fuel enrichment above 5% and is able to use square or hex grid plates with varying pitches.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

High Multiplication Neutron Noise Measurements Using the 7uPCX Assembly

The Seven Percent Critical Experiment, or 7uPCX, is a system that mimics the physics of light water nuclear reactor systems by using uranium dioxide fuel pins at an enrichment of approximately 7%. 7uPCX is often used for benchmarking and nuclear data purposes. As part of a collaboration between Lawrence Livermore National Laboratory, Los Alamos National Laboratory, Sandia National Laboratories, and the Institut de Radioprotection et de Sûreté Nucléaire, measurements were performed in support of a high-multiplication, subcritical benchmark candidate for a thermal system. The measurements were completed by making subcritical configurations using the fuel loading pattern of a well-documented configuration of the Seven Percent Critical Experiment at Sandia National Laboratories, which exists as a benchmark in the International Criticality Safety Benchmark Evaluation Project handbook. These measurements, which aimed to capture multiplications ranging from approximately 10 to 1,000, also serve as an intercomparison between both the fielded detector systems and analysis methodologies with the goal of better characterizing the detectors and their ability to capture the state of the criticality these types of systems. Los Alamos National Laboratory’s measurements for this collaboration were made with five linked helium-3 based neutron multiplicity detectors placed on the periphery of the reactor tank beyond the infinite reflector thickness of water, and four organic scintillators placed in dry-wells in-reactor near the edge of the upper fuel grid plate. This work captures the Los Alamos National Laboratory measurements, the Rossi-α and Feynman-Y results, provides an intercomparison between the results of the 3 He neutron detectors and the organic scintillators, compares to simulation where possible, and expands on future work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

On the Feynman-alpha method for reflected fissile assemblies

The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron period may also be used to infer the k eff multiplication factor. The Feynman-alpha method is predicated on time-correlated neutron detections that deviate from a Poisson random variable due to multiplication. Traditionally, such measurements are diagnosed with one-region point kinetics, but two-region models are required when the fissile assembly is reflected. This paper presents a derivation of the two-region point kinetics Feynman-alpha equations based on a double integration of the Rossi-alpha equations, develops novel propagation of measurement uncertainty, and validates the theory. Validation is achieved with organic scintillator measurements of weapons-grade plutonium reflected by various amounts of copper to achieve k eff values of 0.83–0.94 and prompt periods of 5–75 ns. The results demonstrate that Feynman-alpha measurements should use the two-region model instead of the one-region model. The simplified one-region model deviates from the validated two-region models by as much as 10% in the estimate of the prompt neutron period, and the two-region model reduces to the one-region model for small amounts of reflector. The Feynman-alpha estimates of the prompt neutron period are compared to those of the Rossi-alpha approach. The comparative results demonstrate that the Feynman-alpha method is more precise than the Rossi-alpha method and more accurate for k eff < 0.92, whereas the Rossi-alpha method is generally more accurate for higher multiplications. Here, the uncertainty propagation developed in this work should be used for all Feynman-alpha measurements and will therein improve fitting accuracy and appropriate precision estimates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

Post-Minkowskian effective field theory for conservative binary dynamics

We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those, obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Pairwise connected tensor network representation of path integrals

It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. A generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Slow control and data acquisition systems in the Mu2e experiment

The Mu2e experiment at the Fermilab Muon Campus will search for the coherent neutrinolessconversion of a muon into an electron in the field of an aluminum nucleus with a sensitivityimprovement by a factor of 10,000 over existing limits. The Mu2e Trigger and Data AcquisitionSystem (TDAQ) usesotsdaqas the online Data Acquisition System (DAQ) solution. Developed atFermilab,otsdaqintegrates both theartdaqDAQ and theartanalysis frameworks for event transfer,filtering, and processing.otsdaqis an online DAQ software suite with a focus on flexibility andscalability and provides a multi-user, web-based, interface accessible through a web browser. Thedata stream from the detector subsystems is read by a software filter algorithm that selects eventswhich are combined with the data flux coming from a Cosmic Ray Veto System. The DetectorControl System (DCS) has been developed using the Experimental Physics and Industrial ControlSystem (EPICS) open source platform for monitoring, controlling, alarming, and archiving. TheDCS System has been integrated intootsdaq. A prototype of the TDAQ and the DCS systems hasbeen built at Fermilab’s Feynman Computing Center. In this paper, we report on the progress ofthe integration of this prototype in the onlineotsdaqsoftware.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Online DAQ and slow control interface for the Mu2e experiment

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

NESSi : The N on- E quilibrium S ystems S imulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. Here, we present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time points and a high-order implementation of integration routines. The total integrated error scales up to $\mathcal{O}(N^{-7})$, which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗