Emergent N = 4 Supersymmetry from N = 1
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
SEARCH · Engineering Papers
Results for “Group Theory and Generalizations”
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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POLCA8 - modelling of cross section variations inside hexagonal assemblies
This paper presents the POLCA8 approach for modelling non-constant cross section distributions inside hexagonal fuel assemblies. The multigroup diffusion equation is modified to account for intranodal cross section variations. The obtained equation is solved in a node-wise manner based on the Fourier expansion method. As a result of varying cross sections, the solution includes a particular part additionally to the homogeneous one. A method for obtaining the particular solution is derived. Numerical tests on a VVER-1000 core are presented showing the impact of cross-section variations to some key parameters for reactor operation. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Universal fine grained asymptotics of free and weakly coupled quantum field theory
We give a rigorous proof that in any free quantum field theory with a finite group global symmetry G, on a compact spatial manifold, at sufficiently high energy, the density of states ρ α (E) for each irreducible representation α of G obeys a universal formula as conjectured by Harlow and Ooguri. We further prove that this continues to hold in a weakly coupled quantum field theory, given an appropriate scaling of the coupling with temperature. This generalizes similar results that were previously obtained in (1 + 1)-D to higher spacetime dimension. We discuss the role of averaging in the density of states, and we compare and contrast with the case of continuous group G, where we prove a universal, albeit different, behavior.
Discrete Symmetries↗
Transition and laminar instability
The linear stability theory was applied to the problem of boundary layer transition in incompressible flow. The theory was put into a form suitable for three-dimensional boundary layers; both the temporal and spatial theories were examined; and a generalized Gaster relation for three-dimensional boundary layers was derived. Numerical examples include the stability characteristics of Falkner-Skan boundary layers, the accuracy of the two-dimensional Gaster relation for these boundary layers, and the magnitude and direction of the group velocity for oblique waves in the Blasius boundary layer. Available experiments which bear on the validity of stability theory and its relation to transition are reviewed and the stability theory is applied to transition prediction. The amplitude method is described in which the wide band disturbance amplitude in the boundary layer is estimated from stability theory and an interaction relation for the initial amplitude density of the most unstable frequency.
Mack, L. M.↗
Loops in 4+1d topological phases
2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form \mathbb{Z}_2 ℤ 2 gauge field (the loop-only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self “exchange” statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The SL(2, \mathbb{Z}_2 ℤ 2 ) symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the “fractional Maxwell theory” and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the \mathbb{Z}_2 ℤ 2 gauge group to \mathbb{Z}_N ℤ N .
Chen, Xie↗
Interacting fractons in 2+1-dimensional quantum field theory
We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Modification to the Hawking temperature of a dynamical black hole by a flow-induced supertranslation
One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the black hole evaporation, where the soft hairs on the horizon are induced by the absorption of a null anisotropic flow, generalizing the shock wave considered in [1, 2]. To do so we introduce two different time-dependent extensions of the diffeomorphism associated with the soft hair, where one is the backreaction of the anisotropic null flow, and the other is a coordinate transformation that produces the Unruh effect and a Doppler shift to the Hawking spectrum. Together, they form an exact BMS charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose surface gravity, i.e. the Hawking temperature, is found to be modified. The modification depends on an exponential average of the anisotropy of the null flow with a decay rate of 4M, suggesting the emergence of a new 2-D degree of freedom on the horizon, which could be a way out of the information loss paradox.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Systematic improvement of x -dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation
We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of 2 + 1 + 1 flavors of highly improved staggered quarks with a physical pion mass at lattice spacing a ≈ 0.09 fm and a box width L ≈ 5.76 fm . We present results for the nucleon H and E generalized parton distributions (GPDs) with average boost momentum P z ≈ 2 GeV at momentum transfers Q 2 = [ 0 , 0.97 ] GeV 2 at skewness ξ = 0 as well as Q 2 ∈ 0.23 GeV 2 at ξ = 0.1 , renormalized in the modified minimal subtraction ( MS ¯ ) scheme at scale μ = 2.0 GeV , with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes. Published by the American Physical Society 2024
Astronomy & Astrophysics↗
The anomaly that was not meant IIB
Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Water-enhanced bifunctional metal-acid catalyst for C=C bond hydrogenation
Water-assisted proton shuttling can promote hydrogenation of polar functional groups, and it is generally believed that such an effect can be hardly applied to hydrogenation of C═C bonds due to the latter's weak interaction with water. Here, we report density functional theory calculations and metadynamics simulations, through which we show a dynamic bifunctional metal–acid site that can be transformed, when interacting with water, into an active configuration for unexpected water-enhanced proton shuttling to C═C bonds. In particular, we investigated B(OH)3 anchored to a Ni catalyst for hydrogenation of cyclohexene in an organic solvent, which showed in experiments an increased rate by 100 times when adding a small amount of water. Metadynamics simulations suggest that a B(OH)3–H2O cluster can form on Ni(111), which promotes the proton transfer in the first hydrogenation step, while the second hydrogenation is still driven by metal-mediated direct H-transfer. The recovery process of B(OH)3–H2O also involves a proton shuttling step. We find that the boric species on the surface serves as an electron reservoir and carries the negative charge to balance the positive charge in the proton transfer steps. This work thus provides fundamental insights into this dynamic transformation process of the metal–acid interface, which can in principle be applied to many other bifunctional systems for hydrogenating non-polar unsaturated groups by engineering the interfacial charge separation.
Sun, Shoutian↗
First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.
Michael I Mishchenko↗
A note on the analytic structure of celestial amplitudes
Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on “ordinary” amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of great interest and need to be better understood. In this paper, we critically examine the analytic structure of celestial amplitudes in a massless low-energy effective field theory. We find that, fixed-order loop contributions, which generate multipoles on the negative β-plane, in general do not provide an accurate description of the analytic structure of celestial amplitudes. By resumming over the leading logarithmic contributions using renormalization group equations (RGEs), we observe much richer analytic structures, which generally contain branch cuts. It is also possible to generate multipoles or shifted single poles if the RGEs satisfy certain relations. Including sub-leading logarithmic contributions is expected to introduce additional corrections to the picture. However, without a new approach, it is difficult to make a general statement since the analytic form of the Mellin transform is challenging to obtain.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Many-body localization transition with correlated disorder
We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. Rather than starting from a microscopic model, we analyze the transition within a strong-randomness renormalization group (RG) framework. We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Furthermore, assuming the MBL transition is described by the recently developed renormalization-group scheme, we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.
1-dimensional systems↗
Reduced-order modeling of neutron transport separated in energy by Minimax Proper Generalized Decomposition
In this article, we demonstrate a Petrov-Galerkin Proper Generalized Decomposition (PGD) known as Minimax PGD for modeling neutron transport separated in energy. To compare the Minimax with the classical Galerkin PGD, we assess both on a model problem of UO{sub 2} or Mixed Oxide (MOX) fuel pins in an infinite lattice with 3 industry-standard energy meshes. We find the Minimax PGD achieves a superior decomposition to Galerkin PGD, both with and without update of the energy modes. This suggests Minimax PGD may be more computationally efficient, provided this reduction in modes (to achieve a given accuracy) outweighs the cost of solving the necessary adjoint problems. In either case, we note that PGD offers an a priori Reduced-Order Model (ROM) which may be dramatically cheaper to solve than the full-order model, especially in problems with fine to ultrafine energy meshes. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Long-Range Interaction between Molecules with Electronic Degeneracy: Beyond the Born–Oppenheimer Approximation
Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.
ab initio calculations↗
Effect of discontinuities on the group delay of a microwave transmission line
The problem is considered of the effect of reflections from discontinuities at each end of a transmission line on the group delay at microwave frequencies. Previous work is briefly reviewed and a general analysis is made. Graphical data are presented based upon the formulas developed. Experimental results are given which confirm the theory.
Beatty, R. W.↗
Effective field theory of 6D SUSY RG Flows
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Many-Body Effects in FeN4 Center Embedded in Graphene
We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.
36 MATERIALS SCIENCE↗