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DOE OSTI2025

Impossibility of obtaining time-independent, three-dimensional, spherically symmetric densities of confined systems of relativistically moving constituents

The quantum-mechanical definition of probability, the uncertainty principle, and Poincaré invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of confined systems of relativistically moving constituents. Despite this, many papers ignore one or more of these restrictions. Here I show how to obtain time-independent , two-dimensional densities that are consistent with the stated restrictions. This is done using the light-front, infinite momentum frame formalism. Two-dimensional density interpretations of the axial-vector form factor and all three gravitational form factors is obtained. The resulting mass radius is smaller than the charge radius. Additionally, an expression of a two-dimensional mass density related to the trace of the energy momentum tensor is obtained. I also show that all known methods for finding three-dimensional densities—using the Breit frame, Abel transformations, Wigner distributions, and spherically symmetric wave packets with vanishing spatial extent—violate the basic restrictions in different ways. Furthermore, the use of the latter leads to densities that vanish almost everywhere in space as time increases from an initial value.

form factors↗

DOE OSTI2020

Dimensional crossover in spin Hall oscillators

Auto-oscillations of magnetization driven by direct spin current have been previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic systems such as nanomagnets and nanocontacts. Recently, it was shown that pure spin Hall current can excite coherent auto-oscillatory dynamics in quasi-one-dimensional (1D) ferromagnetic nanowires but not in quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D dimensional crossover of current-driven magnetization dynamics in wire-based Pt/Ni 80 Fe 20 bilayer spin Hall oscillators via varying the wire width. We find that increasing the wire width results in an increase of the number of excited auto-oscillatory modes accompanied by a decrease of the amplitude and coherence of each mode. We also observe a crossover from a hard to a soft onset of the auto-oscillations with increasing wire width. The amplitude of auto-oscillations rapidly decreases with increasing temperature suggesting that interactions of the phase-coherent auto-oscillatory modes with incoherent thermal magnons play an important role in suppression of the auto-oscillatory dynamics. Our measurements in this work set the upper limit on the dimensions of an individual spin Hall oscillator and elucidate the mechanisms leading to suppression of coherent auto-oscillations with increasing oscillator size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators

We report the recent observations of nonlinear Hall effect in time-reversal symmetry protected systems and on the surface of three-dimensional topological insulators due to an in-plane magnetic field have attracted immense experimental and theoretical investigations in two-dimensional transition metal dichalcogenides and Weyl semimetals. The origin of this type of second order effect has been attributed to the emergence of a Berry curvature dipole, which requires a low-symmetry environment. Here, we propose a mechanism for generating such a second order nonlinear Hall effect in Kane-Mele two-dimensional topological insulators due to spatial and time reversal symmetry breaking in the presence of Zeeman and Rashba couplings. By actively tuning the energy gaps with external electromagnetic fields we also demonstrate that the nonlinear Hall effect shows remarkable signatures of topological phase transitions existing in the considered two-dimensional systems.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Dark Energy Survey Year 3 results: Measurement of the baryon acoustic oscillations with three-dimensional clustering

The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, ξ p to measure the baryonic acoustic oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range 0.6< z p < 1.1 over a footprint of 4108 deg 2 . Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-z approximation. ξ p is obtained by projecting the three-dimensional correlation to the transverse direction. To increase the signal-to-noise of the measurements, we have considered a Gaussian stacking window function in place of the commonly used top-hat. ξ p is sensitive to D M (z eff )/r s , the ratio between the comoving angular diameter distance and the sound horizon. Using the full sample, D M (z eff )/r s is constrained to be19.00 ± 0.67 (top-hat) and 19.15 ± 0.58 (Gaussian) at z eff = 0.835. The constraint is weaker than the angular correlation w constraint 18.84 ± 0.50), and we trace this to the fact that the BAO signals are heterogeneous across redshift. While ξ p responds to the heterogeneous signals by enlarging the error bar, w can still give a tight bound on D M s in this case. When a homogeneous BAO-signal subsample in the range 0.7 < z p <1.0 (z eff = 0.845) is considered, ξp yields 19.80 ± 0.67 (top-hat) and 19.84 ± 0.53 (Gaussian). The latter is mildly stronger than the w constraint (19.86 ± 0.55). We find that the ξ p results are more sensitive to photo-z because ξ p keeps the three-dimensional clustering information causing it to be more prone to photo-z noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. ξ p and the angular statistics such as w have their own pros and cons, and they serve an important crosscheck with each other.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

(2 + δ)-dimensional theory of the electromechanics of lipid membranes: Electrostatics

The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, called the (2 + δ)-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a generic dimension reduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain the (2 + δ)-dimensional theory that captures potential differences across and electric fields within lipid membranes. Finally, this model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Quasi-one-dimensional Ising-like antiferromagnetism in the rare-earth perovskite oxide TbScO 3

The rare-earth perovskite TbScO 3 has been widely used as a substrate for the growth of epitaxial ferroelectric and multiferroic thin films, while its detailed low-temperature magnetic properties were rarely reported. In this paper, we performed detailed magnetization, specific heat, and single crystal neutron scattering measurements, along with the crystalline electric field calculations to study the low-temperature magnetic properties of TbScO 3. All our results suggest the magnetic Tb 3+ has an Ising-like pseudo-doublet ground state at low temperatures. Due to the constrain of local point symmetry, these Tb 3+ Ising moments are confined in the ab plane with a tilt angle of φ=±48° to the a axis. In zero field, the system undergoes an antiferromagnetic phase transition at T N =2.53 K, and forms a G x A y noncollinear magnetic structure below T N . Here, we find the dipole-dipole interactions play an important role to determine the magnetic ground state, which are also responsible for the quasi-one-dimensional magnetism in TbScO 3 . The significant anisotropic diffuse scatterings further confirm the quasi-one-dimensional magnetism along the c axis. The magnetic phase diagram with the field along the easy b axis is well established. In addition to the G x A y antiferromagnetic state, there is an exotic field-induced phase emerged near the critical field B c ≃0.7 T, where three-dimensional magnetic order is suppressed but strong one-dimensional correlations may still exist.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Quasi-one-dimensional Pb 5 Re 3 O 15 : A 5 d realization of the Heisenberg antiferromagnetic spin-1/2 chain

Quasi-one-dimensional (1D) magnetic compounds connect the exact solutions of low-dimensional magnetic geometries, which promise quantum spin liquid behavior and exotic quasiparticles, with real-world materials, in which competing magnetic interactions affect their implementation in quantum information science. Here, the structural determination and quasi-1D magnetic behavior of a previously unreported compound, Pb 5 ⁢Re 3 ⁡O 15 , is presented. Like the anisotropic triangular A 3 ⁢ReO 5 ⁢Cl 2 (A = Ba, Sr, Ca) materials, Pb 5 ⁢Re 3 ⁡O 15 contains [ReO 5 ] square pyramids inserted into anion-centered quasi-two-dimensional layers and hosts spin-1/2 moments on the Re 6+ ions. Pb 5 ⁢Re 3 ⁡O 15 , however, has a more ideal quasi-1D geometry than the A 3 ⁢ReO 5 ⁢Cl 2 materials, with larger interchain distances and interlayer spacing. Quasi-1D magnetic behavior in Pb 5 ⁢Re 3 ⁡O 15 is confirmed by fitting the temperature-dependent magnetic susceptibility with the Bonner-Fisher model for a spin-1/2 antiferromagnetically coupled chain, yielding an intrachain coupling constant of |J|/k B =54.5K. Pb 5 ⁢Re 3 ⁡O 15 is highly insulating at room temperature, and heat capacity data below 10 K reveal a linear-T contribution that suggests the presence of low-temperature spinon excitations. Finally, with a lack of three-dimensional ordering down to at least 0.6 K, Pb 5 ⁢Re 3 ⁡O 15 is proposed as a model system for studying the quantum magnetism of quasi-1D Heisenberg chains in a real-world 5d 1 antiferromagnetic material.

36 MATERIALS SCIENCE↗

DOE OSTI2024

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Physics-constrained superresolution diffusion for six-dimensional phase space diagnostics

Adaptive physics-constrained superresolution diffusion is developed for noninvasive virtual diagnostics of the six-dimensional (6D) phase space density of charged particle beams. An adaptive variational autoencoder embeds initial beam condition images and scalar measurements to a low-dimensional latent space from which a 32 6 pixel 6D tensor representation of the beam's 6D phase space density is generated. Projecting from a 6D tensor generates physically consistent two-dimensional projections. Physics-guided superresolution diffusion transforms low-resolution images of the 6D density to high resolution 256 × 256 pixel images. Unsupervised adaptive latent space tuning enables tracking of time-varying beams without knowledge of time-varying initial conditions. The method is demonstrated with experimental data and multiparticle simulations at the HiRES UED. The general approach is applicable to a wide range of complex dynamic systems evolving in high-dimensional phase space. The method is shown to be robust to distribution shift without retraining. Published by the American Physical Society 2025

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Composite-dimensional topological codes with boundaries and defects

We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and 0D defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of condensation, our algorithm explicitly describes how to construct the boundary and domain-wall stabilizers starting from the bulk model. This extends the utility of Pauli stabilizer models in describing nontranslationally invariant topological orders with gapped boundaries. To highlight this utility, we provide a series of examples, including a new family of quantum error-correcting codes where the double of ℤ4 is coupled to instances of the double semion (DS) phase. We discuss the codes' utility in the burgeoning area of quantum error correction with an emphasis on the interplay between deconfined anyons, logical operators, error rates, and decoding. We also augment our construction, built using algorithmic tools to describe the properties of explicit stabilizer layouts at the microscopic lattice level, with dimensional counting arguments and macroscopic-level constructions building on pants decompositions. The latter outlines how such codes' representation and design can be automated. Our results are validated by a series of error-correcting threshold calculations comparing our codes' performance with that of standard surface codes. To do so, we introduce a composite-dimensional belief-propagation decoder with ordered statistics that utilizes combination sweeps. Going beyond our worked-out examples, we expect our explicit step-by-step algorithms to pave the path for higher-dimensional codes to be discovered and implemented in near-future architectures that take advantage of various hardware platforms.

Mousa, Mohamad [Purdue University]↗

DOE OSTI2025

𝑁-dimensional maximum-entropy tomography via particle sampling

We propose a modified maximum-entropy (MENT) algorithm for six-dimensional phase space tomography. The algorithm uses particle sampling and low-dimensional density estimation to approximate large sets of high-dimensional integrals in the original MENT formulation. We implement this approach using Markov Chain Monte Carlo (MCMC) sampling techniques and demonstrate convergence of six-dimensional MENT on both synthetic and measured data.

Hoover, Austin [Oak Ridge National Laboratory (ORN↗

DOE OSTI2020

Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows

Here we present a comparative study of the enstrophy budget and mixed mass between two- and three-dimensional flows induced by Richtmyer–Meshkov instability (RMI). Specifically, the individual contributions to the enstrophy budget due to the production from baroclinicity and from vortex stretching (which vanishes in two-dimensional (2D) flow) are delineated. This is enabled by a set of two- and three-dimensional computations at Atwood 0.5 having both narrow- and broad-band perturbations. A further three-dimensional (3D) computation is conducted at Atwood 0.9 using an identical narrowband perturbation to the Atwood 0.5 case to examine the sensitivity to density ratio. The mixed mass is also considered with the goal to obtain insight on how faithfully a simplified calculation performed in two dimensions can capture the mixed mass for an inertial confinement fusion (ICF) or other practical application. It is shown that the late time power law decay of variable density enstrophy is substantially different in two and three dimensions for the narrowband initial perturbation. The baroclinic production term is negligible in three dimensions (aside from the initial shock interaction), as vortex stretching is larger by two orders of magnitude. The lack of vortex stretching considerably reduces the decay rate in both narrowband and broadband perturbations in two dimensions. In terms of mixed mass, the lack of vortex stretching reduces the mixed mass in two dimensions compared to three in all cases. In the broadband cases, the spectral bandwidth in the 2D case is wider; hence, there is a longer time period of sustained linear growth which reduces the normalized mixed mass further.

42 ENGINEERING↗

DOE OSTI2024

Synthesis and characterization of low-dimensional N-heterocyclic carbene lattices

The covalent interaction of N-heterocyclic carbenes (NHCs) with transition metal atoms gives rise to distinctive frontier molecular orbitals (FMOs). These emergent electronic states have spurred the widespread adoption of NHC ligands in chemical catalysis and functional materials. Although formation of carbene-metal complexes in self-assembled monolayers on surfaces has been explored, design and electronic structure characterization of extended low-dimensional NHC-metal lattices remains elusive. Here, in this work, we demonstrate a modular approach to engineering one-dimensional (1D) metal-organic chains and two-dimensional (2D) Kagome lattices using the FMOs of NHC–Au–NHC junctions to create low-dimensional molecular networks exhibiting intrinsic metallicity. Scanning tunneling spectroscopy and first-principles density functional theory reveal the contribution of C–Au–C π-bonding states to dispersive bands that imbue 1D- and 2D-NHC lattices with exceptionally small work functions.

Qie, Boyu↗

DOE OSTI2021

Instantaneous Three-Dimensional Temperature Measurements via Ultrafast Laser Spectroscopy with Structured Light

Detonations and flames are characterized by three-dimensional (3D) temperature fields, yet state-of- the-art temperature measurement techniques yield information at a point or along a line. The goal of the research documented here was to combine ultrafast laser spectroscopy and structured illumination to deliver an unprecedented measurement capability—three-dimensional, instantaneous temperature measurements in a gas-phase volume. To achieve this objective, different parts of the proposed technique were developed and tested independently. Structured illumination was used to image particulate matter (soot) in a turbulent flame at multiple planes using a single laser pulse and a single camera. Emission spectroscopy with structured detection was demonstrated for emission- based measurements of explosives with enhance dimensionality. Finally, an instrument for multi- planar laser-based temperature measurement technique was developed. Structured illumination techniques will continue to be developed for multi-dimensional and multi-parameter measurements. These new measurement capabilities will be important for heat transfer and fluid dynamic research areas.

42 ENGINEERING↗

DOE OSTI2021

Preliminary Implementation of Two-Dimensional Cartesian Solver in CTF-R

Sub-channel codes are one of the the modeling and simulation tools used for thermal-hydraulic analysis of nuclear reactors. A few examples of such sub-channel codes are the COolant Boiling in Rod Arrays (COBRA) family of codes. The approximations that are used to simplify the fluid conservation equations into sub-channel form, mainly that of axially-dominated flow, lead to noticeable limitations on sub-channels solvers for problems with significant flow in lateral directions. In this report, a two-dimensional Cartesian solver is developed and implemented within CTF-R, which is the residual solver in the North Carolina State University version of COBRA-TF (CTF). The new solver will enable CTF to simulate flow that is not axially-dominated. The appropriate Cartesian forms of the conservation equations are derived and implemented in the solver. Once the conservation equations are established, the process of constructing the matrix system was altered to solve a two-dimensional staggered grid system. A simple case was used to test that the two-dimensional Cartesian solver is accurate. The test problem does not include any source terms or flow in the lateral direction. The results show that the solver was able to run the simple case and converge to a steady-state solution. Future work will focus on testing existing capabilities by using test cases that include transients and equation cross-terms. Future work will also include adding additional capabilities such as enabling the solver to include cases with source terms and three dimensional cases.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Modeling of Macroscopic Dynamics in Three-Dimensional Plasma Configurations (Final Technical Report)

A numerical simulation-based study to investigate the stability properties of inherently three-dimensional plasma magnetic configurations is presented. These configurations, called stellarators and heliotrons, use external helical coils to provide the twisting magnetic field that is required to confine ionized plasma particles. In contrast to the tokamak configuration, which nominally has the property of axisymmetry, electrical current does not need to be induced in stellarator and heliotron plasma. Experiments have shown that these three-dimensional configurations are remarkably robust to macroscopic instability, even when driven to relatively high levels of plasma pressure. Our understanding of how the plasma is able to withstand macroscopic instability will be enhanced by the work proposed here. The effort will generalize existing numerical modeling capability, and it will apply the new capability to model macroscopic dynamics in these three-dimensional configurations. The development work has been applied to the NIMROD simulation code (https://nimrodteam.org) that was originally based on axisymmetric problem domains. It has been generalized to accommodate the three-dimensional shaping of the plasma volume in stellarators and heliotrons. Its use of equilibrium data has also been generalized, and the implementation allows different numerical representation of the magnetic field. Analysis has been performed to inform the selection of numerical methods, and a method to accelerate the iterative solution of the necessary algebraic systems has been developed and implemented. Verification of the new NIMSTELL code on benchmark problems has also been an important part of the effort.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Development of electro-optical quantum transducers based on three-dimensional superconducting cavities

Quantum transducers enable the conversion of quantum information and signals between different physical platforms. Based on the pioneering works in three-dimensional superconducting cavity technology developed at Fermilab, we are advancing the development of three-dimensional microwave-optical transducers and exploring their applications in quantum information processing and sensing. We present our progress in the design, fabrication, and characterization of three-dimensional microwave cavities integrated with bulk lithium niobate resonators. The material characterization using three-dimensional cavities based on a resonant-type method allows for understanding of complex permittivity and loss mechanism of electro-optic materials at cryogenic temperatures. We also evaluate the potential of the high-efficiency quantum transducers in enhancing the performance of quantum sensors for applications such as dark matter detection, compared to conventional homodyne detection approaches. This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC0207CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. This work is funded by the DOE's Early Career Research Program. This research used resources of the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Superconducting Quantum Materials and Systems Center (SQMS) under Contract No. DE-AC02-07CH11359.

Zorzetti, Silvia↗

DOE OSTI2024

Defects and Defect Engineering of Two-Dimensional Transition Metal Dichalcogenide (2D TMDC) Materials

As layered materials, transition metal dichalcogenides (TMDCs) are promising two-dimensional (2D) materials. Interestingly, the characteristics of these materials are transformed from bulk to monolayer. The atomically thin TMDC materials can be a good alternative to group III–V and graphene because of their emerging tunable electrical, optical, and magnetic properties. Although 2D monolayers from natural TMDC materials exhibit the purest form, they have intrinsic defects that limit their application. However, the synthesis of TMDC materials using the existing fabrication tools and techniques is also not immune to defects. Additionally, it is difficult to synthesize wafer-scale TMDC materials for a multitude of factors influencing grain growth mechanisms. While defect engineering techniques may reduce the percentage of defects, the available methods have constraints for healing defects at the desired level. Thus, this holistic review of 2D TMDC materials encapsulates the fundamental structure of TMDC materials, including different types of defects, named zero-dimensional (0D), one-dimensional (1D), and two-dimensional (2D). Moreover, the existing defect engineering methods that relate to both formation of and reduction in defects have been discussed. Finally, an attempt has been made to correlate the impact of defects and the properties of these TMDC materials.

2D materials↗