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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Viability of perturbative expansion for quantum field theories on neurons

Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs) [1]. In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number N using scalar ϕ 4 theory in d Euclidean dimensions as an example. We find that the renormalized O(1/N ) corrections to two-and four-point correlators yield perturbative series which are sensitive to the UV cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.

Sen, Srimoyee [Iowa State University, Ames, IA (Un↗
NASA NTRS2004

Renormalization Group Tutorial

Complex physical systems sometimes have statistical behavior characterized by power- law dependence on the parameters of the system and spatial variability with no particular characteristic scale as the parameters approach critical values. The renormalization group (RG) approach was developed in the fields of statistical mechanics and quantum field theory to derive quantitative predictions of such behavior in cases where conventional methods of analysis fail. Techniques based on these ideas have since been extended to treat problems in many different fields, and in particular, the behavior of turbulent fluids. This lecture will describe a relatively simple but nontrivial example of the RG approach applied to the diffusion of photons out of a stellar medium when the photons have wavelengths near that of an emission line of atoms in the medium.

Bell, Thomas L.↗
DOE OSTI2024

Thermal mean-field theories

Several closely related ab initio thermal mean-field theories for fermions, both well-established and new ones, are compared with one another at the formalism level and numerically. The theories considered are Fermi–Dirac theory; thermal Hartree–Fock (HF) theory; two modifications of the thermal single-determinant and the first-order finite-temperature many-body perturbation theory based on a zero-temperature or thermal HF reference. Furthermore, thermal full-configuration-interaction theory is used as the benchmark.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1976

Acoustic radiation and surface pressure characteristics of an airfoil due to incident turbulence

The noise and unsteady surface pressure characteristics of an isolated airfoil in a uniform mean velocity, homogeneous, nearly isotropic turbulence field were investigated. Experiments were performed with a 23 cm chord, two-dimensional airfoil over a Mach number range of 0.1 to 0.5. Far-field noise spectra and directivity as well as surface pressure spectra and cross-spectra were obtained. Incident turbulence statistics were documented. Theory applied to predict far-field noise and surface pressure characteristics from measured inflow turbulence statistics showed good agreement with measurement. The theoretical formulation represents a first-principles solution providing absolute level prediction without recourse to empirical or adjustable constants, and takes into account compressibility as well as source noncompactness effects. All chordwise portions of the airfoil radiated directly to the far-field, the leading edge to the dominant noise producing region. The effect of angle of attack on noise and surface pressures is small. The interaction of incident turbulence of approximately 4 percent intensity with an airfoil was found to be a broadband noise source of high intensity relative to other noise sources.

Paterson, R. W.↗
DOE OSTI2023

Beyond Generalized Eigenvalues in Lattice Quantum Field Theory

Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.

Fleming, George T.↗
NASA NTRS1994

Surface gravity waves at equilibrium with a steady wind

Observations of wave fields' spatial evolution and of gravity wave spectra S(sub omega) are analyzed on the basis of the data reported by several research groups as well as on a 2-year data set of wind and wave measurements by stationary National Oceanic and Atmospheric Administration buoys near the Hawaiian Islands. We seek to clarify the role of the wave energy advection (with the wave group velocity) in the overall energy balance. This advective transfer appears to be no less important than the local (breaking wave induced) dissipation as a factor of wind-wave equilibrium. The advection is found to manifest itself in the shape of wave spectra by reducing the rate at which the spectra density of the wave energy, S(sub omega approximately omega (exp -p), falls off as the frequency increases away from the spectra peak. This and other conclusions are derived by comparing the field observations with theoretical predictions of the weak turbulence theory for a spatially inhomogeneous, statistically stationary, wave field. The observations also indicate that the typical wave age xi = C(sub 0)/U in the open ocean is much greater than the limiting value 1.2 attributed to the 'fully developed sea.' Although the observed spectra can be approximated by a power law with a single 'effective' exponent, this apparent exponent, p, is found to depend on the wave age. At high xi and at frequencies below the generation range, -p tends to -3 rather than the value of -11/3 predicted by the Zakharov-Zaslavskii theory. This deviation is interpreted as pointing to a nonconservative nature of the inverse cascade, the latter including a leakage of energy to low-wavenumber modes. Dependence of the overall effective exponent on xi is shown to be responsible for variation in the coefficients b, B, c, C appearing in empirical fetch laws, such as xi = C bar-x (exp c) and e = B bar-x (exp B), where bar-x and e are the dimensionless fetch and wave energy, respectively.

Glazman, Roman E.↗
NASA NTRS1990

Strong Langmuir turbulence generated by electron beams - Electric-field distributions and electron scattering

Strong turbulence and transit-time scattering theory are applied here to calculate the statistical distribution of intense Langmuir fields and the consequent beam scattering in plasma turbulence driven by an electron beam. The experimentally observed electric-field distributions are compared with predictions of strong-turbulence theory, concentrating on the wave levels, the Gaussian tail of the high-field distribution observed in one experiment, the arrest scale of collapse, and the fractional volume occupied by the highest fields. The Guassian form of the tail is confirmed, and the results imply that the collapse is arrested at a scale where the peak electrostatic energy density is of the same order as the thermal energy density. The theory of transit-time interactions is generalized to include relativistic particle dynamics and is applied to predict the scattering of the beam electrons in energy and angle as they pass through strong Langmuir turbulence. The results support the validity of the recently developed scaling theory of strong turbulence.

Robinson, P. A.↗
DOE OSTI2023

Large-time correlation functions in bosonic lattice field theories

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

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Monitored Fluctuating Hydrodynamics

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

classical statistical mechanics↗
DOE OSTI2022

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1994

Representing Learning With Graphical Models

Probabilistic graphical models are being used widely in artificial intelligence, for instance, in diagnosis and expert systems, as a unified qualitative and quantitative framework for representing and reasoning with probabilities and independencies. Their development and use spans several fields including artificial intelligence, decision theory and statistics, and provides an important bridge between these communities. This paper shows by way of example that these models can be extended to machine learning, neural networks and knowledge discovery by representing the notion of a sample on the graphical model. Not only does this allow a flexible variety of learning problems to be represented, it also provides the means for representing the goal of learning and opens the way for the automatic development of learning algorithms from specifications.

Buntine, Wray L.↗
DOE OSTI2025

A Parameter-masked Mock Data Challenge for Beyond-two-point Galaxy Clustering Statistics

The past few years have seen the emergence of a wide array of novel techniques for analyzing high-precision data from upcoming galaxy surveys, which aim to extend the statistical analysis of galaxy clustering data beyond the linear regime and the canonical two-point (2pt) statistics. We test and benchmark some of these new techniques in a community data challenge named “Beyond-2pt,” initiated during the Aspen 2022 Summer Program “Large-Scale Structure Cosmology beyond 2-Point Statistics,” whose first round of results we present here. The challenge data set consists of high-precision mock galaxy catalogs for clustering in real space, in redshift space, and on a light cone. Participants in the challenge have developed end-to-end pipelines to analyze mock catalogs and extract unknown (“masked”) cosmological parameters of the underlying ΛCDM models with their methods. The methods represented are density-split clustering, nearest neighbor statistics, BACCO power spectrum emulator, void statistics, LEFTfield field-level inference using effective field theory (EFT), and joint power spectrum and bispectrum analyses using both EFT and simulation-based inference. In this work, we review the results of the challenge, focusing on problems solved, lessons learned, and future research needed to perfect the emerging beyond-2pt approaches. The unbiased parameter recovery demonstrated in this challenge by multiple statistics and the associated modeling and inference frameworks supports the credibility of cosmology constraints from these methods. The challenge data set is publicly available, and we welcome future submissions from methods that are not yet represented.

Krause, Elisabeth [Univ. of Arizona, Tucson, AZ (U↗
NASA NTRS1977

Quantum statistical theory of semiconductor junctions in thermal equilibrium

Free carrier and electric field distributions of one-dimensional semiconductor junctions are evaluated using a quantum mechanical phase-space distribution and its corresponding Boltzmann equation. Attention is given to quantum and exchange corrections in cases of high doping concentrations when carrier densities become degenerate. Quantitative differences between degenerate and classical junction characteristics, e.g., maximum electric field and built-in voltage and carrier concentration within the transition region, are evaluated numerically.

Von Roos, O.↗