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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Diffeomorphism Group Representations in Relativistic Quantum Field Theory

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Lake Bacterial Assemblage Composition Is Sensitive to Biological Disturbance Caused by an Invasive Filter Feeder

One approach to improve forecasts of how global change will affect ecosystem processes is to better understand how anthropogenic disturbances alter bacterial assemblages that drive biogeochemical cycles. Species invasions are important contributors to global change, but their impacts on bacterial community ecology are rarely investigated. Here, we studied direct impacts of invasive dreissenid mussels (IDMs), one of many invasive filter feeders, on freshwater lake bacterioplankton. We demonstrated that direct effects of IDMs reduced bacterial abundance and altered assemblage composition by preferentially removing larger and particle-associated bacteria. While this increased the relative abundances of many free-living bacterial taxa, some were susceptible to filter feeding, in line with efficient removal of phytoplankton cells of <2 μm. This selective removal of particle-associated and larger bacteria by IDMs altered inferred bacterial functional group representation, defined by carbon and energy source utilization. Specifically, we inferred an increased relative abundance of chemoorganoheterotrophs predicted to be capable of rhodopsin-dependent energy generation. In contrast to the few previous studies that have focused on the longer-term combined direct and indirect effects of IDMs on bacterioplankton, our study showed that IDMs act directly as a biological disturbance to which freshwater bacterial assemblages are sensitive. The negative impacts on particle-associated bacteria, which have been shown to be more active than free-living bacteria, and the inferred shifts in functional group representation raise the possibility that IDMs may directly alter bacterially mediated ecosystem functions.Freshwater bacteria play fundamental roles in global elemental cycling and are an intrinsic part of local food webs. Human activities are altering freshwater environments, and much has been learned regarding the sensitivity of bacterial assemblages to a variety of these disturbances. Yet, relatively few studies have focused on how species invasion, which is one of the most important aspects of anthropogenic global change, affects freshwater bacterial assemblages. This study focuses on the impact of invasive dreissenid mussels (IDMs), a globally distributed group of invasive species with large impacts on freshwater phyto- and zooplankton assemblages. Here, we show that IDMs have direct effects on lake bacterioplankton abundance, taxonomic composition, and inferred bacterial functional group representation.

16S rRNA gene↗
DOE OSTI2022

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

We report numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

42 ENGINEERING↗
DOE OSTI2018

Nonunitary Representations of the Groups of U(p, q)-currents for q ≥ p > 1

The purpose of this paper is to give a construction of representations of the group of currents for semisimple groups of rank greater than one. Such groups have no unitary representations in the Fock space, since the semisimple groups of this form have no nontrivial cohomology in faithful irreducible representations. Thus we first construct cohomology of the semisimple groups in nonunitary representations. The principal method is to reduce all constructions to Iwasawa subgroups (solvable subgroups of the semisimple groups), with subsequent extension to the original group. The resulting representation is realized in the so-called quasi-Poisson Hilbert space associated with natural measures on infinite-dimensional spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Double crystallographic groups and their representations on the Bilbao Crystallographic Server

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations ( DGENPOS ) and of irreducible representations of the double (point and space) groups ( REPRESENTATIONS DPG and REPRESENTATIONS DSG ). The tool DCOMPREL provides compatibility relations between the irreducible representations of double space groups at different k vectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The program DSITESYM implements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description of and the search for topological insulators.

Chemistry↗
DOE OSTI2025

Attention-based functional-group coarse-graining: a deep learning framework for molecular prediction and design

Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML training. In this study, we report a data-efficient, deep-learning framework for molecular discovery that integrates a coarse-grained functional-group representation with a self-attention mechanism to capture intricate chemical interactions. Our approach exploits group-contribution concepts to create a graph-based intermediate representation of molecules, serving as a low-dimensional embedding that substantially reduces the data demands typically required for training. Using a self-attention mechanism to learn the subtle but highly relevant chemical context of functional groups, the method proposed here consistently outperforms existing approaches for predictions of multiple thermophysical properties. In a case study focused on adhesive polymer monomers, we train on a limited dataset comprising only 6,000 unlabeled and 600 labeled monomers. The resulting chemistry prediction model achieves over 92% accuracy in forecasting properties directly from SMILES strings, exceeding the performance of current state-of-the-art techniques. Furthermore, the latent molecular embedding is invertible, enabling the design pipeline to automatically generate new monomers from the learned chemical subspace. We illustrate this functionality by targeting several properties, including high and low glass transition temperatures (Tg), and demonstrate that our model can identify new candidates with values that surpass those in the training set. The ease with which the proposed framework navigates both chemical diversity and data scarcity offers a promising route to accelerate and broaden the search for functional materials.

Han, Ming [Univ. of Chicago, IL (United States)]↗
DOE OSTI2021

Lorentz invariance of basis tensor gauge theory

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.

Physics↗
DOE OSTI2024

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Qudit Designs and Where to Find Them

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing exponential separations between classical and quantum query complexity. While unitary designs originating from a group structure, such as the Clifford group, have proven to be incredibly useful for qubit systems, unfortunately, this is no longer true for qudits. In fact, the classification of finite-group representations rules out the existence of unitary 2-designs for arbitrary qudit dimensions. This severely limits the applicability of standard quantum information primitives when it comes to qudit systems. We overcome these limitations with a three-fold contribution. First, we introduce a general technique to construct families of weighted state t-designs in arbitrary qudit dimensions. These weighted state-designs generalize classical shadow tomography protocol from qubits to qudits. Second, we introduce a Clifford character RB that allows us to benchmark the qudit Clifford group in any dimension, including non-prime-power dimensions. And third, we establish bounds on the quantum circuit complexity of generating approximate unitary-designs from native gates in existing quantum hardware such as high-spin and cavity-QED qudits. Our work further highlights the analogy between spin and optical coherent states by proving that spin-GKP codewords form a state 2-design while spin coherent states do not; in direct analogy with the optical case. This work is structured as a pedagogical and self-contained introduction to unitary designs and their applications to qudit systems.

Anand, Namit [NASA, Ames; Unlisted, US] (ORCID:000↗
DOE OSTI2018

Dedekind η-Function in Modern Research

In this paper, we describe properties of the Dedekind η-function, constructions arising from it, and their applications in various topics of the number theory and algebra. We discuss connections with the group representation theory and the study of the structure of spaces of modular forms. Special attention is paid to the special class of modular forms, namely, η-functions with multiplicative coefficients.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

On domain symmetry and its use in homogenization

The present study focuses on solving partial differential equations in domains exhibiting symmetries and periodic boundary conditions for the purpose of homogenization. We show in a systematic manner how the symmetry can be exploited to significantly reduce the complexity of the problem and the computational burden. This is especially relevant in inverse problems, when one needs to solve the partial differential equation (the primal problem) many times in an optimization algorithm. The main motivation of our study is inverse homogenization used to design architected composite materials with novel properties which are being fabricated at ever increasing rates thanks to recent advances in additive manufacturing. For example, one may optimize the morphology of a two-phase composite unit cell to achieve isotropic homogenized properties with maximal bulk modulus and minimal Poisson ratio. Typically, the isotropy is enforced by applying constraints to the optimization problem. However, in two dimensions, one can alternatively optimize the morphology of an equilateral triangle and then rotate and reflect the triangle to form a space filling D 3 symmetric hexagonal unit cell that necessarily exhibits isotropic homogenized properties. One can further use this D 3 symmetry to reduce the computational expense by performing the “unit strain” periodic boundary condition simulations on the single triangle symmetry sector rather than the six fold larger hexagon. In this paper we use group representation theory to derive the necessary periodic boundary conditions on the symmetry sectors of unit cells. The developments are done in a general setting, and specialized to the two-dimensional dihedral symmetries of the abelian D 2 , i.e. orthotropic, square unit cell and nonabelian D 3 , i.e. trigonal, hexagon unit cell. We then demonstrate how this theory can be applied by evaluating the homogenized properties of a two-phase planar composite over the triangle symmetry sector of a D 3 symmetric hexagonal unit cell.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Entanglement entropy of a color flux tube in (1+1)D Yang–Mills theory

In recent work Amorosso et al. (2024), we computed a novel flux tube entanglement entropy (FTE) of the color flux tube stretched between a heavy quark-antiquark pair on a Euclidean lattice in (2+1)D Yang–Mills theory. Our numerical results suggested that FTE can be partitioned into an internal color entanglement entropy and a vibrational entropy corresponding to the transverse excitations of a QCD string, with the latter described by a thin string model. Since the color flux tube does not have transverse excitations in (1+1)D Yang–Mills theory, we use this simpler framework to perform an exact analytical computation of the contribution of the internal color degrees of freedom to FTE. For the multipartite partitioning of the color flux tube, we find the remarkable result that FTE depends only on the dimension of the color group representation and the number of times the flux tube crosses the boundary between the traced and untraced spatial regions but not on the string length. Our proof is independent of whether the replica and region boundaries on the lattice are placed on vertices or in plaquette centers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Multiple Dirac nodes and symmetry protected Dirac nodal line in orthorhombic α-RhSi

Exotic multifold topological excitations have been predicted and were recently observed in transition metal silicides like β-RhSi. Herein, we report that interesting topological features of RhSi are also observed in its orthorhombic α phase, which displays multiple types of Dirac nodes very close to the Fermi level ε F . Here, we discuss the symmetry analysis, band connectivity along high-symmetry lines using group representations, band structure, the nature of the Dirac points and of a nodal line occurring near ε F which is protected by the crystalline symmetry. The de Haas–van Alphen effect indicates a Fermi surface in agreement with the calculations. We find an elliptically shaped nodal line very close to ε F around and near the S point on the k y -k z plane that results from the intersection of two upside-down Dirac cones. Both Dirac points of the participating Kramers degenerate bands are only 5 meV apart; hence, an accessible magnetic field might induce a crossing between the spin-up partner of the upper Dirac cone and the spin-down partner of the lower Dirac cone, possibly explaining the anomalies observed in the magnetic torque. α-RhSi is a unique system since all bands crossing ε F emerge from Dirac nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Group-equivariant autoencoder for identifying spontaneously broken symmetries

We introduce the group-equivariant autoencoder (GE autoencoder), a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use group theory to deduce which symmetries of the system remain intact in all phases, and then use this information to constrain the parameters of the GE autoencoder such that the encoder learns an order parameter invariant to these “never-broken” symmetries. This procedure produces a dramatic reduction in the number of free parameters such that the GE-autoencoder size is independent of the system size. We include symmetry regularization terms in the loss function of the GE autoencoder so that the learned order parameter is also equivariant to the remaining symmetries of the system. By examining the group representation by which the learned order parameter transforms, we are then able to extract information about the associated spontaneous symmetry breaking. We test the GE autoencoder on the 2D classical ferromagnetic and antiferromagnetic Ising models, finding that the GE autoencoder (1) accurately determines which symmetries have spontaneously broken at each temperature; (2) estimates the critical temperature in the thermodynamic limit with greater accuracy, robustness, and time efficiency than a symmetry-agnostic baseline autoencoder; and (3) detects the presence of an external symmetry-breaking magnetic field with greater sensitivity than the baseline method. Lastly, we describe various key implementation details, including a quadratic-programming-based method for extracting the critical temperature estimate from trained autoencoders and calculations of the DNN initialization and learning rate settings required for fair model comparisons.

42 ENGINEERING↗
DOE OSTI2018

Improved Delayed-Neutron Spectroscopy Using Trapped Ions

The neutrons emitted following the β decay of fission fragments (known as delayed neutrons because they are emitted after fission on a timescale of the β-decay half-lives) play a crucial role in reactor performance and control. Reviews of delayed-neutron properties highlight the need for high-quality data for a wide variety of delayed-neutron emitters to better understand the time dependence and energy spectrum of the neutrons as these properties are essential for a detailed understanding of reactor kinetics needed for reactor safety and to understand the behavior of these reactors under various accident and component-failure scenarios. For fast breeder reactors, criticality calculations require accurate delayed-neutron energy spectra and approximations that are acceptable for light-water reactors such as assuming the delayed-neutron and fission-neutron energy spectra are identical are not acceptable and improved β-delayed neutron data is needed for safety and accident analyses for these reactors. With improved nuclear data, the delayed neutrons flux and energy spectrum could be calculated from the contributions from individual isotopes and therefore could be accurately modeled for any fuel-cycle concept, actinide mix, or irradiation history. High-quality β-delayed neutron measurements are also critical to constrain modern nuclear-structure calculations and empirical models that predict the decay properties for nuclei for which no data exists and improve the accuracy and flexibility of the existing empirical descriptions of delayed neutrons from fission such as the six-group representation

74 ATOMIC AND MOLECULAR PHYSICS↗