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All sources NASA NTRS DOE OSTI

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 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↗

NASA NTRS1991

Coherent laser radar performance for general atmospheric refractive turbulence

A general theory for the signal-to-noise ratio (SNR) of a coherent detection laser radar is developed using the path-integral formulation (Fresnel approximation), which is valid for any typical path-integrated atmospheric refractive turbulence. The principal effects of refractive turbulence are discussed, and analytical expressions are presented for the case of untruncated Gaussians for the transmitted field, local oscillator field, and transmitter/receiver optics. The physical mechanisms that reduce heterodyne efficiency are identified.

Frehlich, Rod G.↗

DOE OSTI2026

Spacetime quantum mechanics for bosonic and fermionic systems

We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic structure, thereby unifying the axioms that traditionally distinguish the treatment of spacelike and timelike separations. Standard quantum evolution can be recovered from timelike correlators, defined by means of a quantum action operator, a quantum version of the action of classical mechanics. The corresponding map also provides an alternative perspective on the path integral formulation that, in the case of fermions, does not require the use of Grassmann variables. In addition, the formalism can be interpreted in terms of generalized quantum states, codifying both the conventional information of a quantum system at a given time and its evolution. We show that these states are solutions to a quantum principle of stationary action grounded in timelike correlations and pseudo-entropies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

Description of quantum noise by a Langevin equation

General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.

Metiu, H.↗

DOE OSTI2024

The Einstein–Hilbert action for entropically dominant causal sets

Abstract In the path integral formulation of causal set quantum gravity, the quantum partition function is a phase-weighted sum over locally finite partially ordered sets, which are viewed as discrete quantum spacetimes. It is known, however, that the number of ‘layered’ sets—a class of causal sets that look nothing like spacetime manifolds—grows superexponentially with the cardinalityn, giving an entropic contribution that can potentially dominate that of the action. We show here that in any dimension, the discrete Einstein–Hilbert action for a typicalK-layered causal set reduces to the simple link action to leading order inn. Combined with earlier work, this completes the proof that the layered sets, although entropically dominant, are very strongly suppressed in the path sum of causal set quantum gravity whenever the discreteness scale is greater than or equal to a (mildly dimension-dependent) order one multiple of the Planck scale.

Astronomy & Astrophysics↗

DOE OSTI2026

Extended JT supergravity and random matrix models: The power of the string equation

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as e$^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of $\mathcal{N} = 2$ and (small) $\mathcal{N} = 4$ JT supergravity, and then explore the new cases of spectra from $\mathcal{N} = 3$ and $\mathcal{N} = 4$ large JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.

Extended Supersymmetry↗

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 OSTI2025

Criticality analysis of nuclear binding energy neural networks

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics. However, these ANNs are typically treated as ‘black boxes’, with their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters chosen empirically by optimizing learning based on limited exploration. We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width. This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory. We use a prototypical example to test the applicability of this approach: a simple ANN for nuclear binding energies. We find that with training using a stochastic gradient descent optimizer, the predicted criticality behavior is realized, and optimal performance is found with critical tuning. However, the use of an adaptive learning algorithm leads to somewhat superior results without concern for tuning and thus obscures the analysis. Nevertheless, the criticality analysis offers a way to look within the black box of ANNs, which is a first step towards potential improvements in network performance beyond using adaptive optimizers.

artificial neural network↗

NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗

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

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 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)↗

NASA NTRSDate not supplied

Path Planning: Differential Dynamic Programming and Model Predictive Path Integral Control on VTOL Aircraft

This paper explores two optimal control approaches, widely used in robotics, to establish their viability as real-time trajectory planners for vehicle configurations envisioned for the emerging aviation sector of Urban Air Mobility (UAM). Differential Dynamic Programming (DDP) enables planning over highly nonlinear dynamics using second-order approximations along a nominal trajectory, and displays quadratic convergence to a local solution. Model Predictive Path Integral (MPPI) is a stochastic sampling-based algorithm that can optimize for general cost criteria, including potentially highly nonlinear formulations, and supports parallel computation through the use of modern GPU hardware. In this work, DDP and MPPI were implemented using model predictive control (MPC), and the results indicate they are able to successfully transition the aircraft over different flight envelopes and generate trajectories unique to UAM vehicles.

Differential Dynamic Programming↗

NASA NTRS2000

New Millennium EO3

The New Millennium Program (NMP) is a NASA technology program that focuses on the validation of advanced spacecraft and instrumentation technologies in space. This program specifically seeks technologies that could significantly benefit future space and Earth science missions by enabling new science capabilities and reducing life cycle costs. These technologies must also require a validation in space to mitigate risks to the first science users, and provide cross-cutting benefits to both NASA's Earth and Space Science enterprises. The NASA Office of Earth Science (OES) directed the NMP to focus the third Earth Observing mission, E03, on innovative measurement concepts that would facilitate remote sensing observations from orbits beyond conventional low-Earth orbit (LEO). These orbits include geosynchronous orbits, highly elliptical orbits, mid-Earth and high-Earth orbits, and other unique vantage points such as L1 and L2. To maximize the input from the Earth science community, a NASA Research Announcement (NRA) was released to solicit innovative measurement concepts for this NMP flight. Because the NMP is a technology validation program, rather than a conventional science program, the NRA required that these measurement concepts employ revolutionary technologies and/or measurement strategies that will enable future science missions from orbits beyond LEO. Another requirement was that a validation in space was needed to reduce real or perceived risks of this concept to future science users. The proposals submitted in response to this NRA were peer reviewed by the NASA OES. The measurement concepts selected through this process will be summarized in this presentation. The E03 measurement concept NRA did not solicit complete mission concepts or flight hardware. Instead, the selected investigators will join integrated project formulation teams to define the mission for the demonstration of the measurement technique and participate in mission design trades and implementation planning. The teams will define and document the measurement approach, the required technologies, the validation plan, the scalability of the design to future science missions, and the infusion path for the completely validated instrument. During this project formulation phase, the specific technologies required to implement each measurement concept will be solicited through an open technology solicitation, and the technology providers will be added to the integrated teams. Once a complete candidate mission concept has been formulated for each measurement concept, these concepts will be subjected to a comprehensive review. The Associate Administrator of the OES will use the results of this review to select a single concept for the E03 flight opportunity. That mission concept will enter its implementation phase, which is expected to last for less than 36 months before launch. During this phase, and after launch, the implementation team will work with the NMP to document and disseminate the information gathered during the flight qualification testing and operations of the measurement concept and its component technologies. This information will be archived and published, where appropriate, to encourage the rapid infusion of these validated technologies into future space and Earth science missions. I

Li, Fuk K.↗

DOE OSTI2026

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

2D Gravity↗

DOE OSTI2025

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

FOS: Physical sciences↗

NASA NTRS1994

Elevated Temperature Crack Propagation

This paper is a summary of two NASA contracts on high temperature fatigue crack propagation in metals. The first evaluated the ability of fairly simple nonlinear fracture parameters to correlate crack propagation. Hastelloy-X specimens were tested under isothermal and thermomechanical cycling at temperatures up to 980 degrees C (1800 degrees F). The most successful correlating parameter was the crack tip opening displacement derived from the J-integral. The second evaluated the ability of several path-independent integrals to correlate crack propagation behavior. Inconel 718 specimens were tested under isothermal, thermomechanical, temperature gradient, and creep conditions at temperatures up to 650 degrees C (1200 degrees F). The integrals formulated by Blackburn and by Kishimoto correlated the data reasonably well under all test conditions.

Orange, Thomas W.↗