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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Path-Integrated X-Ray Images for Multi-Surface Digital Image Correlation (PI-DIC)

X-ray imaging offers unique possibilities for Digital Image Correlation (DIC), opening the door for full-field deformation measurements of a test article in complex environments where optical DIC suffers severe biases or is impossible. While X-ray DIC has been performed in the past with standard DIC codes designed for optical images, the path-integrated nature of X-ray images places constraints on the experimental setup, predominantly that only a single surface of interest moves/deforms. These requirements are difficult to realize for many practical situations and limit the amount of information that can be garnered in a single test. Other X-ray based diagnostics such as Digital Volume Correlation (DVC) and Projection DVC (P-DVC) overcome these obstacles, but DVC is limited to quasi-static tests, and both DVC and P-DVC necessitate high-resolution computed tomography (CT) scan(s) and often require a potentially invasive pattern throughout the volume of the specimen. Here this work presents a novel approach to measure time-resolved displacements and strains on multiple surfaces from a single series of 2D, path-integrated (PI) X-ray images, called PI-DIC. The principle of optical flow or conservation of intensity—the foundation of DIC—was reframed for path-integrated images, for an exemplar setup comprised of two plates moving and deforming independently. Synthetic images were generated for rigid translations, rigid rotations, and uniform stretches, where each plate underwent a unique motion/deformation. Experimental specimens were fabricated (either an aluminum plate with tantalum features or a plastic plate with steel features) and the two specimens were independently translated. PI-DIC was successfully demonstrated with the synthetic images and validated with the experimental images. Prescribed displacements were recovered for each plate from the single set of path-integrated, deformed images. Errors were approximately 0.02 px for the synthetic images with 1.5% image noise, and 0.05 px for the experimental images. These results provide the foundation for PI-DIC to measure motion and deformation of multiple, independent surfaces with subpixel accuracy from a single series of path-integrated X-ray images.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

On the lapse contour in the gravitational path integral

The gravitational path integral is usually implemented with a covariant action by analogy with other gauge field theories, but the gravitational case is different in important ways. A key difference is that the integrand has an essential singularity, which occurs at zero lapse where the spacetime metric degenerates. The lapse integration contour required to impose the local time reparametrization constraints must run from − ∞ to + ∞ , yet must not pass through zero. This raises the question: for an application—such as a partition function—where the constraints should be imposed, what is the correct integration contour, and why? We study that question by starting with the reduced phase space path integral, which involves no essential singularity. We observe that if the momenta are to be integrated before the lapse, to obtain a configuration space path integral, the lapse contour should pass below the origin in the complex lapse plane. This contour is also consistent with the requirement that quantum field fluctuation amplitudes have the usual short distance vacuum form, and with obtaining the Bekenstein-Hawking horizon entropy from a Lorentzian path integral. Published by the American Physical Society 2025

Banihashemi, Batoul (ORCID:0000000228679209)↗
DOE OSTI2022

Quantum Simulations of Vibrational Strong Coupling via Path Integrals

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. Furthermore, this result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations

The recently introduced multisite tensor network path integral (MS-TNPI) allows simulation of extended quantum systems coupled to dissipative media. We use MS-TNPI to simulate the exciton transport and the absorption spectrum of a B850 bacteriochlorophyll (BChl) ring. The MS-TNPI network is extended to account for the ring topology of the B850 system. Accurate molecular-dynamics-based description of the molecular vibrations and the protein scaffold is incorporated through the framework of Feynman–Vernon influence functional. To relate the present work with the excitonic picture, an exploration of the absorption spectrum is done by simulating it using approximate and topologically consistent transition dipole moment vectors. Comparison of these numerically exact MS-TNPI absorption spectra are shown with second-order cumulant approximations. Finally, the effect of temperature on both the exact and the approximate spectra is also explored.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The phase of the gravitational path integral

The gravitational path integral on S 2 × S 2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S 1 × S 2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S 2 × S D−2 , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

AdS-CFT correspondence↗
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 OSTI2024

Collective coordinate fix in the path integral

Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parametrize a manifold of zero modes and more broadly provide judicious coordinates on the space of fields. However, changing from local coordinates around a saddle point to more global collective coordinates is remarkably subtle. The main complication is that the mapping from local coordinates to collective coordinates is generically multivalued. Consequently one is forced to either restrict the domain of path integral in a delicate way, or otherwise correct for the multivaluedness by dividing the path integral by certain intersection numbers. We provide a careful treatment of how to fix collective coordinates while accounting for these intersection numbers, and then demonstrate the importance of the fix for free theories. We also provide a detailed study of the fix for interacting theories and show that the contributions of higher intersections to the path integral can be nonperturbatively suppressed. Using a variety of examples ranging from single-particle quantum mechanics to quantum field theory, we explain and resolve various pitfalls in the implementation of collective coordinates. Published by the American Physical Society 2024

Bhattacharya, Arindam (ORCID:0000000244578926)↗
DOE OSTI2025

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗
DOE OSTI2022

Complex saddles and Euclidean wormholes in the Lorentzian path integral

We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms of a 3-form flux, which include the Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using the Lorentzian path integral and with the help of Picard-Lefschetz theory. The number and nature of saddles is shown to qualitatively change in the presence of a bilocal operator that could arise, for example, as a result of considering higher-topology transitions. We also analyze the stability of the Giddings-Strominger wormhole in the 3-form picture, where we find that it represents a perturbatively stable Euclidean saddle of the gravitational path integral. This calls into question the ultimate fate of such solutions in an ultraviolet-complete theory of quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

MixPI: Mixed-time slicing path integral software for quantized molecular dynamics simulations

We introduce the MixPI software to implement path integral molecular dynamics (PIMD) simulations for the study of condensed phase systems where nuclear quantum effects (NQEs) are important. In contrast to existing PIMD simulation software, MixPI enables the implementation of mixed quantum–classical path integral simulations where only a subset of system degrees of freedom (dofs) are treated quantum mechanically in an extended phase space while the remaining dofs are described classically. We expect this software to be particularly useful for simulations of electron and proton transfer in condensed phase systems, as well as for the study of biological and material systems where only a handful of dofs contribute significantly to the observed NQEs. We demonstrate the use of MixPI in two different systems. The first is a simple water model where we implement a set of mixed quantum–classical simulations to compute average energy and radial distribution functions. We use these simulations to benchmark the effectiveness of MixPI and to demonstrate how it enables systematic investigation into the origin of observed NQEs. We then compute radial distribution functions for a system where MixPI is essential: a solvated metal (M 2+ ) cation described using an explicit quantized electron localized on an M 3+ ion in water.

chemical physics↗
DOE OSTI2025

Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs

We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result.

Feynman diagrams↗
DOE OSTI2021

A compendium of sphere path integrals

We study the manifestly covariant and local 1-loop path integrals on S d+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Path-Integrated X-Ray Digital Image Correlation using Synthetic Reference Images

X-rays can provide images when an object is visibly obstructed, allowing for motion measurements via x-ray digital image correlation (DIC). However, x-ray images are path-integrated and contain data for all objects between the source and detector. If multiple objects are present in the x-ray path, conventional DIC algorithms may fail to correlate the x-ray images. A new DIC algorithm called path-integrated (PI)-DIC addresses this issue by reformulating the matching criterion for DIC to account for multiple, independently-moving objects. PI-DIC requires a set of reference x-ray images of each independent object. However, due to experimental constraints, such reference images might not be obtainable from the experiment. Here, this work focuses on the reliability of synthetically-generated reference images, in such cases. A simplified exemplar is used for demonstration purposes, consisting of two aluminum plates with tantalum x-ray DIC patterns undergoing independent rigid translations. Synthetic reference images based on the “as-designed” DIC patterns were generated. However, PI-DIC with the synthetic images suffered some biases due to manufacturing defects of the patterns. A systematic study of seven identified defect types found that an incorrect feature diameter was the most influential defect. Synthetic images were re-generated with the corrected feature diameter, and PI-DIC errors were improved by a factor of 3-4. Final biases ranged from 0.00-0.04 px, and standard uncertainties ranged from 0.06-0.11 px. In conclusion, PI-DIC accurately measured the independent displacement of two plates from a single series of path-integrated x-ray images using synthetically-generated reference images, and the methods and conclusions derived here can be extended to more generalized cases involving stereo PI-DIC for arbitrary specimen geometry and motion. This work thus extends the application space of x-ray imaging for full-field DIC measurements of multiple surfaces or objects in extreme environments where optical DIC is not possible.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Path Integral Monte Carlo Simulations of Iron Plasmas (Final Technical Report)

This documents is the final technical report for our grant entitled "Path Integral Monte Carlo Simulations of Iron Plasmas" that focused on developing path integral Monte Carlo (PIMC) computer simulations. This techniques will be developed to study plasmas composed of heavier elements including iron and other third row elements. Equations of state (EOS) and transport properties will be derived in the regime of warm dense matter (WDM) and dense plasmas where existing first-principles methods cannot be applied. While standard density functional theory (DFT) has been used to accurately predict the structure of many solids and liquids up to temperatures on the order of 100,000 K, this method is not applicable at much higher temperature because the number of partially occupied electronic orbitals reaches intractably large numbers or the use of finite-temperature free energy functionals in orbital-free DFT introduces an uncontrolled approximation. Here we focus on PIMC methods that become more and more efficient with increasing temperatures and still include all electronic correlation effects. In this approach, electronic excitations increase the efficiency rather than reduce it. While it had commonly been assumed this method could only be applied to elements without core electrons, we showed that PIMC with free-particle nodes works well for first-row elements (PRL 108 (2012) 115502). Most recently, we extended the applicability range of all-electron PIMC to second-row elements by adopting localized nodal surfaces (PRL 115 (2015) 176403). To simulate third-row elements efficiently under WDM conditions, we propose a new method to remove core electrons by introducing pseudo-nodes. We explain our approach step by step and present preliminary results. We focus our method development on getting PIMC simulations of iron to work because of its fundamental importance for WDM and astrophysics. Then we move on to krypton and copper-doped beryllium, a ICF ablator material. We plan to continue working on key second-row material such as Na, Mg, MgO, Al, silica, and silicon-doped plastic ablators. Our collaborators at LLNL, will use our PIMC EOS data both as comparisons to existing semi-empirical, EOS-generating schemes, and as input for continuum radiation hydrodynamics simulations. We will establish an efficient pipeline from PIMC to macroscopic continuum studies of materials response. An emphasis will be placed on benchmarking such methods for plasmas of heavy elements at the very high temperatures (~100 eV) and low densities that are generated when Hohlraum radiation heats the ablator material in indirect drive laser experiments. Results from changes to the EOS will be of immeasurable importance to the designers at the National Ignition Facility (NIF) and at other facilities. Starting with our EOS of Cu-doped Be, our second collaborator at LLE, will perform real-time simulations of laser fusion experiments at the Omega laser and at the NIF to determine how sensitive the compression path depends on the ablator EOS. Since our collaborator also has experience in performing orbital-free DFT calculations, we propose to compare predictions from this method with PIMC results. In joint publications, we plan to analyze the accuracy of different free-energy functionals in order to understand why existing orbital-free DFT calculations do not predict compression peaks along the shock Hugoniot curve that we see with PIMC. The peaks are caused by the ionization of various electron shells. Their accurate characterization is important to compare with experimental results. We will break new ground by developing PIMC techniques that can simulate iron and all other third row elements in the plasma and WDM regimes. We introduce the concept of pseudo-nodes for the efficient treatment of the core-electrons. The EOS and transport properties will be derived and published online in the form of a new WDM database. Our PIMC EOS calculations will benchmark and possibly replace semi-analytical EOS tables like QEOS or SESAME, which will impact the hydrocode simulation community and will affect the design of NIF targets. Our PIMC results will help to improve the accuracy of orbital-free DFT simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics

This review focuses on a recent class of path-integral-based methods for the simulation of nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. As a result, the remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.

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

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗
DOE OSTI2025

Melting curves of atomic hydrogen and deuterium calculated using path-integral Monte Carlo

We calculate the melting line of atomic hydrogen and deuterium up to 900 GPa with path-integral Monte Carlo using a machine-learned interatomic potential. We improve upon previous simulations of melting by treating the electrons with reptation quantum Monte Carlo, and by performing solid and liquid simulations using isothermal-isobaric path-integral Monte Carlo. Here, the resulting melting line for atomic hydrogen is higher than previous estimates. There is a small but resolvable decrease in the melting temperature as pressure is increased, which can be attributed to quantum effects.

08 HYDROGEN↗
DOE OSTI2025

Stable isotope equilibria in the dihydrogen-water-methane-ethane-propane system. Part 1: Path-integral calculations with CCSD(T) quality potentials

Isotopic compositions of alkanes are typically assumed to be kinetically controlled, but recently is has been proposed that alkanes can isotopically equilibrate for both C and H isotopes during natural gas generation. Evaluation of this requires knowledge of the isotopic equilibrium between alkanes and other common hydrogen and carbon bearing species. Here, in this study, we calculate isotopic equilibria within and between gaseous dihydrogen (H 2 ), water (H 2 O), methane (CH 4 ), ethane (C 2 H 6 ) and propane (C 3 H 8 ), including isotope fractionation among molecules, clumped isotope effects, as well as among sites of propane (i.e., the site-specific isotope effects) from 0°C to 500°C using a path-integral method paired with high-level descriptions of molecular potentials and the diagonal correction to the Born Oppenheimer approximation. While path-integral calculations with high- level CCSD(T) potentials are available for the isotopic equilibria involving methane, the path-integral calculations for ethane and propane have only been performed based on lower-level descriptions of the molecular potentials. We analyze the relative importance of various approximations that are commonly employed when isotopic equilibria are evaluated. We find that clumped isotope effects can be calculated to the same accuracy using computationally inexpensive combination of the Bigeleisen-Mayer-Urey model with the molecular potential from density functional theory. In contrast, fractionation and site preferences of both deuterium and carbon-13 benefit from the use of the higher level CCSD(T) potentials and accounting for anharmonic effects. Additionally, for fractionation and site preference of deuterium corrections to Born-Oppenheimer approximation can also be important.

03 NATURAL GAS↗