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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2024

Path-Integrated Stereo X-Ray Digital Image Correlation: Resolving the Violation of Conservation of Intensity

In this study, x-ray imaging addresses many challenges with visible light imaging in extreme environments, where optical diagnostics such as digital image correlation (DIC) and particle image velocimetry (PIV) suffer biases from index of refraction changes and/or cannot penetrate visibly occluded objects. However, conservation of intensity—the fundamental principle of optical image correlation algorithms—may be violated if ancillary components in the X-ray path besides the surface or fluid of interest move during the test. The test series treated in this work sought to characterize the safe use of fiber-epoxy composites in aerospace and aviation industries during fire accident scenarios. Stereo X-ray DIC was employed to measure test unit deformation in an extreme thermal environment involving a visibly occluded test unit, incident surface heating to temperatures above 600°C, and flames and soot from combusting epoxy decomposition gasses. The objective of the current work is to evaluate two solutions to resolve the violation of conservation of intensity that resulted from both the test unit and the thermal chamber deforming during the test. The first solution recovered conservation of intensity by pre-processing the path-integrated X-ray images to isolate the DIC pattern of the test unit from the thermal chamber components. These images were then correlated with standard, optical DIC software. The second solution, called Path-Integrated Digital Image Correlation (PI-DIC), modified the fundamental matching criterion of DIC to account for multiple, independently-moving components contributing to the final image intensity. The PI-DIC algorithm was extended from a 2D framework to a stereo framework and implemented in a custom DIC software. Both solutions accurately measured the cylindrical shape of the undeformed test unit, recovering radii values of R = 76.20±0.12 mm compared to the theoretical radius of R theor = 76.20 mm. During the test, the test unit bulged asymmetrically as decomposition gasses pressurized the interior and eventually burned in a localized jet. Both solutions measured the heterogeneous radius of this bulge, which reached a maximum of approximately R = 91 mm, with a discrepancy of 2–3% between the two solutions. Two solutions that resolve the violation of conservation of intensity for path-integrated X-ray images were developed. Both were successfully employed in a stereo X-ray DIC configuration to measure deformation of an aluminum-skinned, fiber-epoxy composite test unit in a fire accident scenario.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Using Machine Learning to Greatly Accelerate Path Integral Ab Initio Molecular Dynamics

Ab initio molecular dynamics (AIMD) has become one of the most popular and robust approaches for modeling complicated chemical, liquid, and material systems. However, the formidable computational cost often limits its widespread application in simulations of the largest-scale systems. Furthermore, the situation becomes even more severe in cases where the hydrogen nuclei may be better described as quantized particles using a path integral representation. Here, we present a computational approach that combines machine learning with recent advances in path integral contraction schemes, and we achieve a 2 orders of magnitude acceleration over direct path integral AIMD simulation while at the same time maintaining its accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Path integral factorization and the gravitational effective action

Abstract We discuss the factorization and continuity properties of fields in the Euclidean gravitational path integral with higher dimension operators constructed from powers of the Riemann tensor. We construct the boundary terms corresponding to the microcanonical ensemble and show that the saddle point approximation to the path integral with a quasilocal energy constraint generally yields a saddle point with discontinuous temperature. This extends a previous result for the Euclidean Schwarzschild–de Sitter geometry in Einstein gravity and shows that it is robust against at least some types of quantum corrections from heavy fields. As an application, we compute the entropy of SdS in D = 4 using the BTZ method. Our result matches the entropy calculated using Wald’s formula.

Astronomy & Astrophysics↗
DOE OSTI2024

Fermions at finite density in the path integral approach

Abstract We study relativistic fermionic systems in 3 + 1 spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for theiεterm that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the U(1) symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler-Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas-van Alphen effect. Finally, we consider a (generalized) Gross-Neveu model forNinteracting fermions at finite density. We compute its non-perturbative effective potential in the large-Nlimit, and discuss the fate of the U(1) vector and$$ {\mathbb{Z}}_2^A $$ ℤ 2 A axial symmetries.

Physics↗
DOE OSTI2023

A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons

A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to L=256 L = 256 sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2025

Hollow-grams: generalized entanglement wedges from the gravitational path integral

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the “hollowed” RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy Sn depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n → 1 limit.

2D Gravity↗
DOE OSTI2026

Path-integral predictions for preasymptotic quantum tunneling

When tunneling occurs out of generic initial states, a significant fraction of probability is lost at early times, during which the dynamics is governed by excited resonance states. However, first-principles analyses based on path-integrals have only captured the leading asymptotic behavior, during which the tunneling rate is dominated by the false vacuum contribution. In this work, we discuss the behavior in the preasymptotic regime from a first-principles path-integral perspective. We demonstrate how the relevant expressions can be evaluated systematically through semiclassical methods in the recently developed steadyon picture. This approach allows one to trace the role of the relevant physical scales, making transparent the underlying assumptions and approximations, and offering a clear path to establishing a systematically improvable framework to evaluate tunneling rates nonperturbatively.

Lin, Joshua↗
DOE OSTI2025

Path integral games with de Sitter α-vacua

The α-vacua are a 1-parameter family of quantum field vacua in de Sitter space which are invariant under the isometry group SO(1, d). In this work give a path integral construction of the de Sitter α-vacua. We explain that these states can be prepared by acting on the Bunch-Davies vacuum with a certain non-local charge operator. While most conserved charges live on a single codimension-1 manifold, we show that this particular charge lives on a pair of two codimension-1 manifolds which are antipodal mirrors of each other. The rules for the manipulation of this charge as an insertion in the path integral are explained. We further explain how this charge can be used to solve for the wavefunctionals of the α-vacua at $\mathcal{I}$ | (in the regime that α is small) by deforming the equator of de Sitter space to $\mathcal{I}$ + /$\mathcal{I}$ – .

Global Symmetries↗
DOE OSTI2026

Thermophysical Properties of Liquid Tritium: A Path Integral Monte Carlo Study

Here, we present worm-algorithm, path integral Monte Carlo simulations of bulk liquid tritium. The simulations are benchmarked against empirically known thermophysical properties of liquid deuterium and liquid tritium. Results for the pair correlation function, chemical potential, isothermal compressibility, isochoric heat capacity, and single-particle momentum distributions are reported. Given the benchmark comparisons, our predictions of liquid tritium properties are expected to be accurate to within a few percent. Our simulations unambiguously demonstrate the significance of nuclear quantum effects to the properties of liquid tritium. In particular, under saturated vapor pressure, the average molecular kinetic energy of the liquid is found to be more than 60% higher than the value expected from the classical equipartition theorem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Integrated path planning and control through proximal policy optimization for a marine current turbine

This paper presents an integrated path planning and tracking control framework for a marine current turbine (MCT), where the MCT is treated as an energy-harvesting autonomous underwater vehicle (AUV). Considering the ocean (space of action) is continuous, the proposed framework employs two modules to address path planning and path tracking enabled by the proximal policy optimization (PPO) algorithm, which is a policy gradient deep reinforcement learning (RL) method. Further, to enable fully autonomous operation in a stochastic oceanic environment, the proposed path planning seeks a primary objective of maximizing the harvested energy; then, the path tracking module is designed to minimize the tracking error and avoid collisions with static and dynamic obstacles. Using field-collected acoustic Doppler current profiler (ADCP) data, the performance of the proposed framework is evaluated. Comparative studies with baseline algorithms in three different scenarios of path planning, path tracking without an obstacle, and path tracking with collision avoidance verify the effectiveness of our proposed approach.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Nucleon clustering at kinetic freezeout of heavy-ion collisions via path-integral Monte Carlo

Clustering of the four-nucleon system at kinetic freezeout conditions is studied using path-integral Monte Carlo techniques. This method seeks to improve upon previous calculations which relied on approximate semiclassical methods or few-body quantum mechanics. Estimates are given for the decay probabilities of the 4N system into various light nuclei decay channels and the strength of spatial correlations is characterized. Additionally, a simple model is presented to describe the impact of this clustering on nucleon multiplicity distributions. Additionally, the effects of a possible modification of the inter-nucleon interaction due to the close critical line (and hypothetical QCD critical point) on the clustering are also studied.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Path integral approach to quantum anomalies in interacting models

The prediction and subsequent discovery of topological semimetal phases of matter in solid state systems has instigated a surge of activity investigating the exotic properties of these unusual materials. Among these are transport signatures which can be attributed to the chiral anomaly; the breaking of classical chiral symmetry in a quantum theory. This remarkable quantum phenomenon, first discovered in the context of particle physics has now found new life in condensed-matter physics, connecting topological quantum matter and band theory with effective field theoretic models. In this paper we investigate the interplay between interactions and the chiral anomaly in field theories inspired by semimetals using Fujikawa's path integral method. Starting from models in one spatial dimension we discuss how the presence of interactions can affect the consequences of the chiral anomaly leading to renormalization of excitations and their transport properties. This is then generalized to the three-dimensional case where we show that the anomalous response of the system, namely, the chiral magnetic and quantum Hall effects, are modified by the presence of interactions. These properties are investigated further through the identification of anomalous modes which exist within interacting Weyl semimetals. These massive excitations are nonperturbative in nature and are a direct consequence of the chiral anomaly. The effects of interactions on mixed axial-gravitational anomalies are then investigated and the conditions required for interaction effects to be observed are discussed.

Anomalies↗
DOE OSTI2025

Machine learning-accelerated path integral molecular dynamics simulations of reactive organic electrolytes

Hydrogen bonded electrolytes that exhibit accelerated proton transport via sequential reactive hops have drawn interest for their promise in clean energy applications. Molecular dynamics simulations of these electrolytes offer the opportunity to uncover microscopic mechanistic details that could be used to design and tune the properties of candidate electrolyte technologies. However, accurately modeling the proton transfer reactions and transport properties that give rise to high charge conductivites in these electrolytes proves computationally challenging because of the need to perform lengthy condensed phase simulations, treating both the electronic and nuclear degrees of freedom quantum mechanically. In this paper, we demonstrate that such a modeling task can be efficiently achieved with the use of density functional theory (DFT)-trained machine learning potentials (MLP) to accelerate path integral molecular dynamics (PIMD) simulations. We highlight the practical utility of this approach by using it to benchmark how closely PIMD simulations employing different DFT exchange–correlation functionals reproduce the composition-dependent densities, diffusion coefficients, and electrical conductivities of mixtures consisting of imidazole and levulinic acid. Even with the speedup afforded by our MLPs, PIMD simulations remain quite expensive. Furthermore, in order to render PIMD more computationally tractable, we introduce and benchmark the accuracy of a ring polymer contraction approach that leverages a computationally efficient short-range MLP to accelerate our PIMD simulations by an additional factor of four.

Chemical bonding↗
DOE OSTI2025

The gravitational path integral from an observer’s point of view

One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this paper, we develop a framework for describing non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially with ${G}_{N}^{-1}$. Similarly, from an observer’s perspective, the dimension of the Hilbert space in a two-sided black hole is increased. We compute various observables probing the experience of a gravitating observer in this Hilbert space. We find that an observer experiences non-trivial physics in the closed universe in contrast to what it would see in a one-dimensional Hilbert space. In the two-sided black hole setting, our proposal implies that non-perturbative corrections to effective field theory for an infalling observer are suppressed until times exponential in the black hole entropy, resolving a recently-raised puzzle in black hole physics. While the framework that we develop is exemplified in the toy-model of JT gravity, most of our analysis can be extended to higher dimensions and, in particular, to generic spacetimes not admitting a conventional holographic description, such as cosmological universes or black hole interiors.

2D gravity↗
DOE OSTI2022

Path integral Monte Carlo approach to the structural properties and collective excitations of liquid $$^3{\text {He}}$$ without fixed nodes

Abstract Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic $$^4{\text {He}}$$ 4 He exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic $$^3{\text {He}}$$ 3 He is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid $$^3{\text {He}}$$ 3 He without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor $$S({\mathbf {q}})$$ S ( q ) , the momentum distribution $$n({\mathbf {q}})$$ n ( q ) , and the static density response function $$\chi ({\mathbf {q}})$$ χ ( q ) . In addition, the dynamic structure factor $$S({\mathbf {q}},\omega )$$ S ( q , ω ) is rigorously reconstructed from imaginary-time PIMC data. From simulations of $$^3{\text {He}}$$ 3 He , we derived the familiar phonon–maxon–roton dispersion function that is well-known for $$^4{\text {He}}$$ 4 He and has been reported previously for two-dimensional $$^3{\text {He}}$$ 3 He films (Nature 483:576–579 (2012)). The comparison of our new results for both $$S({\mathbf {q}})$$ S ( q ) and $$S({\mathbf {q}},\omega )$$ S ( q , ω ) with neutron scattering measurements reveals an excellent agreement between theory and experiment.

97 MATHEMATICS AND COMPUTING↗