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DOE OSTI2024

Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions

Conformal field theory in a Minkowski setting is discussed in an embedding space approach, paying special attention to causality constraints for four-point amplitudes. The physics of dilatation and Lorentz boost is emphasized in specifying the noncompact maximal Abelian subgroup of S O ( d , 2 ) . Reduction of a conformal field theory four-point amplitudes as functions of cross ratios is shown to be equivalent to enforcing H bi-invariance, i.e., F ( h g h ′ ) = F ( g ) , with g ∈ S O ( d , 2 ) and H an appropriate subgroup. Causality is imposed by introducing appropriate semigroups. Causal zonal spherical functions are constructed, making contact with Minkowski conformal blocks introduced previously. Published by the American Physical Society 2024

Agarwal, Pulkit (ORCID:0000000346581691)↗

DOE OSTI2025

Lorentzian OPE inversion formula: A geometric perspective

We give a new perspective on the Lorentzian operator product expansion inversion formula [S. Caron-Huot, Analyticity in spin in conformal theories, .; D. Simmons-Duffin, D. Stanford, and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, .], building on [P. Agarwal , companion paper, Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions, .]. We introduce an “auxiliary” fourpoint function that can be related to the traditionally defined ones via a Radon transform. The Mellin amplitudes associated with this auxiliary function can be shown to be equivalent to the conventional partial wave amplitudes. This has the intuitive geometrical meaning of a generalization of the projection-slice theorem. Published by the American Physical Society 2025

Agarwal, Pulkit (ORCID:0000000346581691)↗

DOE OSTI2021

Gauge invariance and Ward identities in nonlinear response theory

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Denoising and Extension of Response Functions in the Time Domain

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Angular correlations of causally-coherent primordial quantum perturbations

In this work, we consider the hypothesis that nonlocal, omnidirectional, causally-coherent quantum entanglement of inflationary horizons may account for some well-known measured anomalies of cosmic microwave background (CMB) anisotropy on large angular scales. It is shown that causal coherence can lead to less cosmic variance in the large-angle power spectrum C &ell; of primordial curvature perturbations on spherical horizons than predicted by the standard model of locality in effective field theory, and to new symmetries of the angular correlation function C (Θ). Causal considerations are used to construct an approximate analytic model for C (Θ) on angular scales larger than a few degrees. Allowing for uncertainties from the unmeasured intrinsic dipole and from Galactic foreground subtraction, causally-coherent constraints are shown to be consistent with measured CMB correlations on large angular scales. Reduced cosmic variance will enable powerful tests of the hypothesis with better foreground subtraction and higher fidelity measurements on large angular scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Causal interaction in high frequency turbulence at the biosphere–atmosphere interface: Structure–function coupling

At the biosphere–atmosphere interface, nonlinear interdependencies among components of an ecohydrological complex system can be inferred using multivariate high frequency time series observations. Information flow among these interacting variables allows us to represent the causal dependencies in the form of a directed acyclic graph (DAG). Here, we use high frequency multivariate data at 10 Hz from an eddy covariance instrument located at 25 m above agricultural land in the Midwestern US to quantify the evolutionary dynamics of this complex system using a sequence of DAGs by examining the structural dependency of information flow and the associated functional response. We investigate whether functional differences correspond to structural differences or if there are no functional variations despite the structural differences. We base our analysis on the hypothesis that causal dependencies are instigated through information flow, and the resulting interactions sustain the dynamics and its functionality. To test our hypothesis, we build upon causal structure analysis in the companion paper to characterize the information flow in similarly clustered DAGs from 3-min non-overlapping contiguous windows in the observational data. We characterize functionality as the nature of interactions as discerned through redundant, unique, and synergistic components of information flow. Through this analysis, we find that in turbulence at the biosphere–atmosphere interface, the variables that control the dynamic character of the atmosphere as well as the thermodynamics are driven by non-local conditions, while the scalar transport associated with CO and H 2 O is mainly driven by short-term local conditions.

58 GEOSCIENCES↗

DOE OSTI2021

Reactome and the Gene Ontology: digital convergence of data resources

Abstract Motivation Gene Ontology Causal Activity Models (GO-CAMs) assemble individual associations of gene products with cellular components, molecular functions and biological processes into causally linked activity flow models. Pathway databases such as the Reactome Knowledgebase create detailed molecular process descriptions of reactions and assemble them, based on sharing of entities between individual reactions into pathway descriptions. Results To convert the rich content of Reactome into GO-CAMs, we have developed a software tool, Pathways2GO, to convert the entire set of normal human Reactome pathways into GO-CAMs. This conversion yields standard GO annotations from Reactome content and supports enhanced quality control for both Reactome and GO, yielding a nearly seamless conversion between these two resources for the bioinformatics community. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Decoding crops one cell at a time: from cell atlases to single-cell genetics

Understanding the mechanisms underlying key agricultural traits remains a central challenge in crop research, but recent advances in technologies are providing powerful tools to address this issue. Among these, single-cell and spatial transcriptomics have revealed tissue heterogeneity and spatial organization, offering unique insights into cellular gene expression dynamics and the coordinated activity of multiple cell types. These approaches help uncover how specific cell types contribute to agricultural traits and refine candidate loci lists through integration with trait-associated loci. Additionally, single-cell and spatial transcriptomics have the potential to serve as cell-level readout platforms integrating cellular perturbations, enabling high-throughput discovery of causal relationships between genotype and gene expression at the cellular level in plants. Successful implementation will accelerate the identification of key genetic variants for crop improvement. Furthermore we review lessons learned from application of single-cell screening in mammalian cells, highlight major technical and biological barriers to its use in plants, and outline potential strategies to overcome these challenges. Together, the widespread application and integration of single-cell and spatial transcriptomics with other technologies enable not only the descriptive cataloging of cell states but also the causal interrogation of sequence functions and regulatory networks at cell type resolution, ultimately advancing gene function studies and accelerating crop improvement.

Cellular heterogeneity↗

DOE OSTI2020

fbWecCntrl

fbWecCntrl is set of MATLAB functions and scripts demonstrating a causal impedance matching approach to wave energy converter (WEC) control design. SAND2020-12219 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Coe, Ryan↗

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 OSTI2021

System risk quantification and decision making support using functional modeling and dynamic Bayesian network

Risk-informed decision-making requires a probabilistic assessment of the likelihood of success of control action, given the system status. This paper presents a systematic state transition modeling approach integrating dynamic probabilistic risk assessment with a decision-making process using a dynamic Bayesian network (DBN) coupled with functional modeling. A functional model designed with multilevel flow modeling (MFM) technique was used to build a system state structure inferred by energy, mass, and information flow so that one can verify the developed model with respect to system functionality. The MFM model represents the causal relationship among the nodes, which captures the structure of process parameters and control units. Each node may have multiple possible states, and the DBN structured by the MFM model represents the time-domain transitions among the defined states. Furthermore, the MFM-DBN integrated state transition modeling is a white-box approach that allows one to draw the system's risk profile by updating the system states and supports the decisions probabilistically with physical inference. An example of a simple heating system has been used to illustrate this process, including decision-making support based on quantitative risk profile. For demonstrating its applicability to a complex system operational decision making, a case study of station blackout accident scenario leading to the seal loss of coolant accident in a nuclear power plant is presented. The proposed approach effectively provided the risk profile along time for each option so that the operators can make the best decision, which minimizes the plant risk.

42 ENGINEERING↗

DOE OSTI2024

Resolving electron and hole transport properties in semiconductor materials by constant light-induced magneto transport

The knowledge of minority and majority charge carrier properties enables controlling the performance of solar cells, transistors, detectors, sensors, and LEDs. Here, we developed the constant light induced magneto transport method which resolves electron and hole mobility, lifetime, diffusion coefficient and length, and quasi-Fermi level splitting. We demonstrate the implication of the constant light induced magneto transport for silicon and metal halide perovskite films. We resolve the transport properties of electrons and holes predicting the material’s effectiveness for solar cell application without making the full device. The accessibility of fourteen material parameters paves the way for in-depth exploration of causal mechanisms limiting the efficiency and functionality of material structures. To demonstrate broad applicability, we further characterized twelve materials with drift mobilities spanning from 10 –3 to 10 3 cm 2 V –1 s –1 and lifetimes varying between 10 –9 and 10 –3 seconds. The universality of our method its potential to advance optoelectronic devices in various technological fields.

14 SOLAR ENERGY↗

DOE OSTI2020

GW190814: Impact of a 2.6 solar mass neutron star on the nucleonic equations of state

Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system? This is the central question animating this paper. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (i) account for a 2.6 M ⊙ neutron star, (ii) satisfy the original constraint on the tidal deformability of a 1.4 M ⊙ neutron star, and (iii) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support supermassive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Furthermore, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 M ⊙ compact object is likely to be the lightest black hole ever discovered.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Respecting causality for training physics-informed neural networks

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. Here we provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto–Sivashinsky equation in the chaotic regime, and the Navier–Stokes equations. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Test of Causal Nonlinear Quantum Mechanics by Ramsey Interferometry with a Trapped Ion

Quantum mechanics requires the time evolution of the wave function to be linear. While this feature has been associated with the preservation of causality, a consistent causal nonlinear theory was recently developed. Interestingly, this theory is unavoidably sensitive to the full physical spread of the wave function, rendering existing experimental tests for nonlinearities inapplicable. Here, in this work, using well-controlled motional superpositions of a trapped ion, we set a stringent limit of 5.4×10 –12 on the magnitude of the unitless scaling factor $\tilde{ε}_γ$ for the predicted causal nonlinear perturbation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Mapping causal pathways with structural modes fingerprint for perovskite oxides

Abstract Causality is innate to the determination of the fundamental mechanism controlling any physical phenomena. However, combining causality within the standard practices of computational modelling to understand structure-functionality connections is extremely rare. This work proposes a fingerprint based on key structural modes for ABO 3 -type perovskite oxides and its derivatives, combined with causal models, for predicting Kohn–Sham energies. Our study of causal models captures the inherent coupling between structural modes such as rotation, tilt and antiferroelectric displacements, responsible for phase transition, polarization, magnetization and metal–insulator transition, exhibited by these materials. Although developed for modelling specific functionality, this method is universally applicable to derive other functionalities and even different material classes while tracking hidden causal mechanisms via structural distortions.

42 ENGINEERING↗

DOE OSTI2024

On learning what to learn: Heterogeneous observations of dynamics and establishing possibly causal relations among them

Abstract Before we attempt to (approximately) learn a function between two sets of observables of a physical process, we must first decide what the inputs and outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven ways of first deciding “the right quantities” to relate through such a function, and then proceeding to learn it. This is accomplished by first processing simultaneous heterogeneous data streams (ensembles of time series) from observations of a physical system: records of multiple observation processes of the system. We determine (i) what subsets of observables are common between the observation processes (and therefore observable from each other, relatable through a function); and (ii) what information is unrelated to these common observables, therefore particular to each observation process, and not contributing to the desired function. Any data-driven technique can subsequently be used to learn the input–output relation—from k-nearest neighbors and Geometric Harmonics to Gaussian Processes and Neural Networks. Two particular “twists” of the approach are discussed. The first has to do with the identifiability of particular quantities of interest from the measurements. We now construct mappings from a single set of observations from one process to entire level sets of measurements of the second process, consistent with this single set. The second attempts to relate our framework to a form of causality: if one of the observation processes measures “now,” while the second observation process measures “in the future,” the function to be learned among what is common across observation processes constitutes a dynamical model for the system evolution.

Sroczynski, David W.↗

DOE OSTI2024

Advancing a Watershed Hydro-Biogeochemical Theory: Linking Water Travel Time and Reaction Rates Under Changing Climate

The major goal of the project is to answer the question how and to what degree does a warming climate alter hydrological functioning and (biogeochemical and chemical weathering) reaction rates at the watershed scale? In particular, how does hydrological functioning (water storage, flow paths, and travel time) change responding to a warming climate? What are the corresponding alterations in biogeochemical and chemical weathering rates at the watershed scale? What is the general watershed-scale reaction rate law that causally links reaction rates to metrics of hydrological functioning that are determined by external hydroclimatic conditions and internal watershed structure characteristics? To answer these questions, we have used field measurements and reactive transport modeling. We have found that: 1) stream chemistry has altered tremendously in warmer years; 2) In this water-limited environment, hydrology is the dominant driver for soil respiration and carbon lateral export at the watershed scale; 3) deeper carbon respiration plays an essential role in regulating the patterns of stream carbon in low and high flow conditions, and deeper groundwater will become increasingly important as warming intensifies. This indicates in mountain streams, a warming climate will modify not only the timing and magnitude of streamflow as expected, but also the chemistry and quality of stream water.

54 ENVIRONMENTAL SCIENCES↗