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Results for “infinite dimensional symmetries”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

JIMWLK on a quantum computer

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta 𝑗 ≤ 𝑗 max . We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with 𝑗 max for both pure and mixed Gaussian initial density matrices. For the simplest truncation, 𝑗 max =1/2, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Infinitely many 4D N = 1 SCFTs with a = c

Here, we study a rich set of four-dimensional N = 1 superconformal field theories (SCFTs) with both central charges identical: a = c. We construct them via the diagonal N = 1 gauging of the flavor symmetry G of a collection of N = 2 Argyres–Douglas theories of type D p (G), with or without additional adjoint chiral multiplets. In this way, we construct infinitely many theories that flow to interacting SCFTs with a = c in the infrared. Lastly, we briefly highlight the features of the SCFTs without a = c that arise from generalizing this construction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1975

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Shih, Tso-Shin↗
DOE OSTI2022

Finite-temperature tensor network study of the Hubbard model on an infinite square lattice

Here, the Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network—an infinite projected entangled pair state—evolved in imaginary time by the neighborhood tensor update algorithm working directly in the thermodynamic limit. With U⁡(1)×U⁡(1) symmetry and the bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators, unaffected by boundary effects. The spin correlators—measurable in prospective ultracold atoms experiments attempting to approach the thermodynamic limit—provide evidence of disruption of the antiferromagnetic background with mobile holes in a slightly doped Hubbard model. The charge correlators reveal the presence of hole-doublon pairs near half filling and signatures of hole-hole repulsion on doping. We also obtain specific heat in the slightly doped regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Multi-Galileons in curved space

Using the probe brane construction of higher derivative effective field theories, extended to higher co-dimensions and curved spaces, we construct galileon and DBI theories on de Sitter space with N fields and an so (N) internal symmetry, non-linearly realizing the symmetries of a higher dimensional de Sitter space. In some cases, the theory admits a non-trivial vacuum that spontaneously breaks the so (N) symmetry, and around this vacuum the Goldstone modes have vanishing kinetic terms and become infinitely strongly coupled. This gives an example of a scalar effective field theory with two de Sitter vacua, one of which appears to have Boulware-Deser-like ghosts, and one of which does not.

Cosmological models↗
NASA NTRS1993

Symmetry algebra of a generalized anisotropic harmonic oscillator

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

Castanos, O.↗
NASA NTRS1992

Observations on the Proper Orthogonal Decomposition

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.

Berkooz, Gal↗
DOE OSTI2022

Qubit Regularization and Qubit Embedding Algebras

Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Homological Invariants of Pauli Stabilizer Codes

Abstract We study translationally invariant Pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. Using homological methods, we define a series of invariants called charge modules. We describe their properties and physical meaning. The most complete results are obtained for codes whose charge modules have Krull dimension zero. This condition is interpreted as mobility of excitations. We show that it is always satisfied for translation invariant 2D codes with unique ground state in infinite volume, which was previously known only in the case of uniform, prime qudit dimension. For codes all of whose excitations are mobile we construct a p-dimensional excitation and a $$(D-p-1)$$ ( D - p - 1 ) -form symmetry for every element of thep-th charge module. Moreover, we define a braiding pairing between charge modules in complementary degrees. We discuss examples which illustrate how charge modules and braiding can be computed in practice.

Physics↗
DOE OSTI2021

The R-matrix bootstrap for the 2d O( N ) bosonic model with a boundary

The S-matrix bootstrap is extended to a 1+1d theory with O(N) symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

Vortex studies relating to boundary layer turbulence and noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Futher, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.

Adelman, J. L.↗
NASA NTRS1985

Vortex Studies Relating to Boundary Layer Turbulence and Noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Further, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.

Adelman, J. L.↗
DOE OSTI2023

Strain engineering a persistent spin helix with infinite spin lifetime

Persistent spin textures (PSTs) in solid-state materials arise from a unidirectional spin-orbit field in momentum space and offer a route to deliver long carrier spin lifetimes sought for future quantum microelectronic devices. Nonetheless, few three-dimensional materials are known to host PSTs owing to crystal symmetry and chemical requirements. There are even fewer examples demonstrated experimentally. Here we report that high-quality persistent spin textures can be obtained in the polar point groups containing an odd number of mirror operations. We use representation theory analysis and electronic structure calculations to formulate general discovery principles to identify PSTs hidden in known complex ternary layered and perovskite structures with large electric polarizations. We then show some of these materials exhibit PSTs without requiring any special crystalline symmetries. This finding removes the limitation imposed by mirror-symmetry protected PSTs that has limited compound discovery. Our general design approach enables the pursuit of persistent spin helices in materials exhibiting the C 3 v crystal class adopted by many quantum materials exhibiting large Rashba coefficients.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Local Distortions and Metal–Semiconductor–Metal Transition in Quasi-One-Dimensional Nanowire Compounds AV 3 Q 3 O δ (A = K, Rb, Cs and Q = Se, Te)

Metal cluster compounds have garnered renewed interest in the search for novel superconductors and topological semimetals owing to structural instabilities of metal-cluster geometries and broken symmetries. Here we synthesized needle-like crystals of the V-cluster-based quasi-one-dimensional (Q1D) materials AV 3 Q 3 O δ (A = K, Rb, Cs, Q= Se, Te) which can also be viewed as being composed of parallel nanowires. We examine how changes in their average and local structure control their electronic properties. All compounds crystallize in the TIFe 3 Te 3 -type structure (P6 3 /m space group) with infinite (V 3 )Q 3 ) - double-walled columnar chains separated by A + cations. Our single-crystal and synchrotron powder diffraction studies indicate oxygen atoms partially occupy the center site of the V 6 octahedral metal cluster cages in KV 3 Te 3 O 0.33 , RbV 3 Te 3 O 0.32 , and CsV 3 Te 3 O 0.35 , whereas KV 3 Se 3 is structurally oxygen-free. Our synchrotron X-ray pair distribution function (PDF) analyses indicate that the oxygen-free V 6 cluster octahedra in KV 3 Se 3 are highly distorted perpendicular to the chain direction even at room temperature, reducing the symmetry of the average structure from hexagonal P6 3 /m to monoclinic P2 1 /m. Our theoretical calculation supports this P2 1 /m distortion and suggests the structure further distorts to P2 1 or P2 1 /c at lower temperatures. In contrast, the oxygen-centered V-cluster in KV 3 Te 3 O 0.33 exhibits a V-3-triangle-trimerization along the chain direction. This feature is discernible from the local PDF and is consistent with lattice dynamical calculations based on density functional theory. Resistivity measurements indicate that KV 3 Se 3 exhibits metallic behavior, whereas a dramatic metal-semiconductor-metal transition emerges in KV 3 Te 3 O 6.33 , RbV 3 Te 3 O 0.32 , and CsV 3 Te 3 O 0.35 because of oxygen disorder and changes in local structure captured from our electronic structure analyses of the Fermi surface. Our investigation of the AV 3 Q 3 O 6 family demonstrates the importance of understanding local changes in structure driven by electronic instabilities, which can guide the search for new quantum materials in other low-dimensional cluster-compound materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Multivariable pseudospectrum in C $\ast$ -algebras

Here we look at various forms of spectrum and associated pseudospectrum that can be defined for noncommuting d-tuples of Hermitian elements of a C $\ast$ -algebra. In particular, we focus on the forms of multivariable pseudospectra that are finding applications in physics. The emphasis is on theoretical calculations of examples, in particular for noncommuting pairs and triple of operators on infinite dimensional Hilbert space. In particular, we look at the universal pair of projections in a C $\ast$ -algebra, the usual position and momentum operators, and triples of tridiagonal operators. We prove a relation between the quadratic pseudospectrum and Clifford pseudospectra, as well as results about how symmetries in a tuple of operators can lead to a symmetry in the various pseudospectra.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Constraints on long-range forces in de Sitter space

The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

AdS-CFT Correspondence↗
DOE OSTI2023

(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons

The (2+1)-dimensional continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground-state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground-state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. Here, these are two different U(1) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton and lineon-elasticity dualities for the Lifshitz theory, and scalar and vector charge gauge theories.

2-dimensional systems↗
DOE OSTI2022

Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For d-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for d ≤ 4, while dipole symmetry cannot be spontaneously broken for d ≤ 2. For T = 0, we show that charge symmetry cannot be spontaneously broken for d ≤ 2 if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗