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DOE OSTI2021

Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore, remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories, considering the necessary truncation imposed on the Hilbert space of gauge bosons with any finite computing resources. This paper is a first step toward addressing this question in the case of non-Abelian LGTs, which further require the imposition of non-Abelian Gauss’s laws on the Hilbert space, introducing additional computational complexity. Focusing on the case of SU(2) LGT in 1+1 dimensions coupled to one flavor of fermionic matter, a number of different formulations of the original Kogut-Susskind framework are analyzed with regard to the dependence of the dimension of the physical Hilbert space on boundary conditions, system’s size, and the cutoff on the excitations of gauge bosons. The impact of such dependencies on the accuracy of the spectrum and dynamics obtained from a Hamiltonian computation is examined, and the (classical) computational-resource requirements given these considerations are studied. Besides the well-known angular-momentum formulation of the theory, the cases of purely fermionic and purely bosonic formulations (with open boundary conditions), and the Loop-String-Hadron formulation are analyzed, along with a brief discussion of a Quantum-Link-Model formulation of the same theory. Clear advantages are found in working with the Loop-String-Hadron framework which implements non-Abelian Gauss’s laws a priori using a complete set of gauge-invariant operators. Although small lattices are studied in the numerical analysis of this work, and only the simplest algorithms are considered, a range of conclusions will be applicable to larger systems and potentially to higher dimensions. Future studies will extend this investigation to the analysis of resource requirements for quantum simulations of non-Abelian LGT, with the goal of shedding light on the most efficient Hamiltonian formulation of gauge theories of relevance in nature

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Fuzzy gauge theory for quantum computers

Continuous gauge theories, because of their bosonic degrees of freedom, have an infinite-dimensional local Hilbert space. Encoding these degrees of freedom on qubit-based hardware demands some sort of “qubitization” scheme, where one approximates the behavior of a theory while using only finitely many degrees of freedom. We propose a novel qubitization strategy for gauge theories, called “fuzzy gauge theory,” building on the success of the fuzzy σ -model in earlier work. We provide arguments that the fuzzy gauge theory lies in the same universality class as regular gauge theory, in which case its use would obviate the need of any further limit besides the usual spatial continuum limit. Furthermore, we demonstrate that these models are relatively resource-efficient for quantum simulations. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2017

Large gauge transformations and little group for soft photons

Recently, large gauge transformation (LGT), the residual gauge symmetry after gauge fixing that survives at null infinity, has drawn much attention concerning soft theorems and the memory effect. We point out that LGT charges in quantum electrodynamics are in fact one of noncompact generators of the two dimensional Euclidean group. Moreover, by comparing two equivalent descriptions of gauge transformation, we suggest that LGT is simply another way of describing the gauged little group for massless soft photons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Propagator Zeros and Lattice Chiral Gauge Theories

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective Lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional Abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost. Published by the American Physical Society 2024

Physics↗

DOE OSTI2011

On the stability of capacitance-diaphragm gauges with ceramic membranes

Capacitance-diaphragm gauges with ceramic membranes or diaphragms have been on the market for about 15 years. The long-term stability of these devices with full scales from 13 Pa to 133 kPa has been tested in the past decade by the calibration of gauges used by the manufacturer as reference gauges on the production line. These reference gauges were calibrated annually on a primary standard. It was found that the reproducibility of these devices depends on their full scale. For 13 Pa, the annual reproducibility near full scale varied between 0.02% and 0.04%, and for full scales of 133 Pa and higher, it varied between 0.005% and 0.03% of full scale. The reproducibility of the ceramic capacitance-diaphragm gauges for full scales of 133 Pa and 1.3 kPa was significantly lower than the uncertainty of a primary standard applying the static-expansion method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Emergent Halperin–Saslow mode, gauge glass and quenched disorders in quantum Ising magnet TmMgGaO 4

Quenched disorders could bring novel quantum excitations and models to certain quantum magnets. Motivated by recent experiments on the quantum Ising magnet TmMgGaO 4 , we explore the effects of the quenched disorder and the interlayer coupling in this triangular lattice Ising antiferromagnet. It is pointed out that the weak quenched (nonmagnetic) disorder would convert the emergent 2D Berezinskii–Kosterlitz–Thouless (BKT) phase and the critical region into a U(1) gauge glass. There will be an emergent Halperin–Saslow mode associated with this gauge glass. Using the Imry-Ma’s renormalization group result, we explain the fate of the finite-field [Formula: see text] symmetry breaking transition at the low temperatures. The ferromagnetic interlayer coupling would suppress the BKT phase and generate a tiny ferromagnetism. With quenched disorders, this interlayer coupling changes the 2D gauge glass into a 3D gauge glass, and the Halperin–Saslow mode persists. This work merely focuses on addressing a phase regime in terms of emergent U(1) gauge glass behaviors and hope to inspire future works and thoughts in weakly disordered frustrated magnets in general.

Physics↗

DOE OSTI2022

Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Gauge properties of the guiding center variational symplectic integrator

Recently, variational symplectic algorithms have been developed for the long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the t → 0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and Φ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Hadronization dynamics from the spectral representation of the gauge invariant quark propagator

We study the Dirac decomposition of the gauge invariant quark propagator, whose imaginary part describes the hadronization of a quark as this interacts with the vacuum, and relate each of its coefficients to a specific sum rule for the chiral-odd and chiral-even quark spectral functions. Working at first in light-like axial gauge, we obtain a new sum rule for the spectral function associated to the gauge fixing vector, and show that its second moment is in fact equal to zero. Then, we demonstrate that the first moment of the chiral-odd quark spectral function is equal in any gauge to the so-called inclusive jet mass, which is related to the mass of the particles produced in the hadronization of a quark. Finally, we present a gauge-dependent formula that connects the second moment of the chiral-even quark spectral function to invariant mass generation and final state rescattering in the hadronization of a quark.

Costa, Caroline S. R.↗

DOE OSTI2020

Lattice Gauge Theory and Two Dimensional Quantum Gravity

We construct a two dimensional SU(2) lattice gauge theory containing a single adjoint scalar field which, when tuned to a critical point associated to spontaneous breaking of center symmetry, possesses a long distance effective theory which describes two dimensional quantum gravity. The metric is emergent in the theory and depends on the gauge fields with the diffeomorphism symmetry of the continuum metric theory arising from lattice gauge symmetry. Apart from the intrinsic interest in formulating gravity as a lattice gauge theory the construction holds some advantages over traditional numerical approaches eg. dynamical triangulations since it uses only conventional cubic lattices and Wilson gauge links.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1974

RF gauging efforts with liquid hydrogen and liquid oxygen as applicable to subcritical space vehicle systems

The RF gauging concept is based on the interaction between a fluid dielectric medium in an enclosed metallic cavity and electromagnetic fields set up within that cavity. In RF gauging systems, the fundamental measurement relies on the interpretation of changes in the resonant RF frequencies of an enclosed tank as the mass of the propellant contained in the tank is changed. In addition to a discussion of the basic principles of operation of these systems, the study presents a description of the current breadboard implementation with typical test arrangements, along with supporting test data. The experimental testing of the RF gauging technique for liquid cryogen mass gauging indicates that this technique is a feasible approach to liquid oxygen and liquid hydrogen gauging under all attitude or reduced gravity environments.

Thompson, H. E.↗

NASA NTRS1976

Zero-G flight test of a gauging system. Volume 1: Summary

The capability of a nucleonic gauging system to gauge the content of a reduced-scale storable liquid tank in a zero-g environment as provided by a KC-135 Zero-G Aircraft was demonstrated. Although the propellant-ullage interface never achieved the stable, zero-g equilibrium configuration, the gauging system gauged liquid quantity over all tank loadings to a total system accuracy the order of two percent. It was also determined that the gauging system presented no undue safety hazard to operating personnel in either ground and/or flight testing.

Source record↗

NASA NTRS1984

Measurement of high temperature strain by the laser-speckle strain gauge

By using the laser-speckle strain gauge, the strain of metal at the temperature lower than 250 C is measured. The principle of the gauge is to measure the expansion or contraction of the fine structures of surface by detecting the resultant speckle displacement in an optoelectronic way, whereby the effect of rigid-body motion is automatically cancelled out with the aid of a differential detection system. A transportable apparatus was built and a comparison experiment performed with a resistance strain gauge at room temperature. It has a strain sensitivity of .00002, a gauge length smaller than 1 mm, and no upper limit in a range of strain measurement. In the measurement of high-temperature strain it is free from the need for a dummy gauge and insensitive to an electric drift effect. As examples of strain measurement at high-temperature, thermal expansion and contraction of a top of a soldering iron are measured. The interval of the measurement can be made at shortest 1.6 sec. and the change in the strain is clearly followed until the ultimate stationary temperature is reached.

Yamaguchi, I.↗

NASA NTRS1986

Response of hot element flush wall gauges in oscillating laminar flow

The time dependent response characteristics of flush-mounted hot element gauges used as instruments to measure wall shear stress in unsteady periodic air flows were investigated. The study was initiated because anomalous results were obtained from the gauges in oscillating turbulent flows for the phase relation of the wall shear stress variation, indicating possible gauge response problems. Flat plate laminar oscillating turbulent flows characterized by a mean free stream velocity with a superposed sinusoidal variation were performed. Laminar rather than turbulent flows were studied, because a numerical solution for the phase angle between the free stream velocity and the wall shear stress variation that is known to be correct can be obtained. The focus is on comparing the phase angle indicated by the hot element gauges with corresponding numerical prediction for the phase angle, since agreement would indicate that the hot element gauges faithfully follow the true wall shear stress variation.

Giddings, T. A.↗

NASA NTRS1989

High-Temperature Strain-And-Temperature Gauge

Two-element gauge used alternately in two different bridge circuits to measure both temperature and strain. Three-lead strain-and-temperature gauge developed for use at temperatures up to 750 degree F (390 degree C) on fiber-reinforced carbon/carbon composite material having coefficient of thermal expansion of 0.8 ppm/degree F. Unlike most temperature-compensated gauges, gauge gives accurate results even during rapid heating and cooling cycles. Similar gauges produced for materials with different coefficients of thermal expansion.

Wnuk, S. P.↗

NASA NTRS1995

Global precipitation estimates based on a technique for combining satellite-based estimates, rain gauge analysis, and NWP model precipitation information

The 'satellite-gauge model' (SGM) technique is described for combining precipitation estimates from microwave satellite data, infrared satellite data, rain gauge analyses, and numerical weather prediction models into improved estimates of global precipitation. Throughout, monthly estimates on a 2.5 degrees x 2.5 degrees lat-long grid are employed. First, a multisatellite product is developed using a combination of low-orbit microwave and geosynchronous-orbit infrared data in the latitude range 40 degrees N - 40 degrees S (the adjusted geosynchronous precipitation index) and low-orbit microwave data alone at higher latitudes. Then the rain gauge analysis is brougth in, weighting each field by its inverse relative error variance to produce a nearly global, observationally based precipitation estimate. To produce a complete global estimate, the numerical model results are used to fill data voids in the combined satellite-gauge estimate. Our sequential approach to combining estimates allows a user to select the multisatellite estimate, the satellite-gauge estimate, or the full SGM estimate (observationally based estimates plus the model information). The primary limitation in the method is imperfections in the estimation of relative error for the individual fields. The SGM results for one year of data (July 1987 to June 1988) show important differences from the individual estimates, including model estimates as well as climatological estimates. In general, the SGM results are drier in the subtropics than the model and climatological results, reflecting the relatively dry microwave estimates that dominate the SGM in oceanic regions.

Huffman, George J.↗

NASA NTRS1999

Optimal Scales for Comparing Satellite and Rain-Gauge Rainfall Estimates for Verification Purposes

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. The comparison of the two requires that some quantitative measure be supplied for the amount of disagreement that can be tolerated due to the differences in sampling. As part of an effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed and its parameters fit to radar data from a field experiment conducted near the Inter-Tropical Convergence Zone (ITCZ) in the eastern Atlantic (GATE). Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. It can therefore be used to study some of the issues involved with comparing rain-gauge averages to satellite averages. Its implications for the best time and space scales for comparing the two will be discussed.

Bell, Thomas L.↗

NASA NTRS2002

Development and Design of Zero-g Liquid Quantity Gauge for Solar Thermal Vehicle

The development and design of a cryogenic liquid quantity gauge for zero-gravity (zero-g) applications are described. The gauge, named the compression mass gauge (CMG), operates on the principle of slightly changing the volume of the tank by an oscillating bellows. The resulting pressure change is measured and used to predict the volume of vapor in the tank, from which the volume of liquid is computed. For each gauging instance, pressures are measured for several different bellows frequencies to enable minor real-gas effects to be quantified and thereby to obtain a gauging accuracy of 11 percent of tank volume. The CMG has been selected by NASA's Future-X program for a flight demonstration on the United States Air Force-Boeing Solar Orbit Transfer Vehicle Space Experiment (SOTVSE). This report reviews the design trade studies needed for the CMG to satisfy the SOTVSE limitations on its power, volume, and mass and also describes the mechanical design of the CMG.

Dodge, Franklin T.↗