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Energy-momentum tensor in a classical model of the electron
We show that the leading nonanalytic terms in the small-𝑡 expansion of the energy-momentum tensor form factors of an electrically charged particle in QED can be correctly derived in a classical model of the electron by Białynicki-Birula. Based on the lucidity of the employed exactly solvable model, we comment also on the recently proposed concept of a regularized proton 𝐷-term.
Reducing Computation and Communication in Scientific Computing: Connecting Theory to Practice.
This report summarizes the work produced as part of a Truman Fellowship appointment and its associated LDRD project. The overall goal of the project was to develop better algorithms and implementations for key computational kernels within the field of scientific computing by designing them to be communication efficient, moving as little data as possible. The primary problem of interest was dense matrix multiplication; other computations that were addressed include sparse matrix-matrix multiplication, QR factorization, solving symmetric linear systems, and the symmetric eigendecomposition. The project also involved the study of computations at the intersection of scientific computing and data analysis, including nonnegative matrix factorization for discovering latent factors, Tucker tensor decomposition for data compression, and sampling methods for similarity search.
Unsupervised and Supervised Learning Frameworks for Knowledge Extraction [Slides]
Abstract not provided.
Pressure Inside Hadrons: Criticism, Conjectures, and All That
The interpretation of the energy-momentum tensor form factor D(t) of hadrons in terms of pressure and shear force distributions is discussed, concerns raised in the literature are reviewed, and ways to reconcile the concerns with the interpretation are indicated.
A globally well-posed finite element algorithm for aerodynamics applications
A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.
A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics
A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.
On infinite tensor networks, complementary recovery and type II factors
We initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case, we decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network. As a specific example, we describe this inductive limit for the holographic Harlow-Pastawski-Preskill-Yoshida code model and relate its algebraic and error-correction features. We find that the local algebras in this model are given by the hyperfinite type II$_\infty$ factor. Next, we discuss other networks that build upon this framework and comment on a connection between type II factors and stabilizer circuits. We conclude with a discussion of multiscale entanglement renormalization ansatz networks in which complementary recovery is broken. We argue that this breaking possibly permits a limiting type III von Neumann algebra, making them more suitable ansätze for approximating subregions of quantum field theories.
Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small $\mathcal{x}$
The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $s\gg Q^2 \gg q^2_⊥$ with $\frac{1}{Q^2}$ accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h\frac{⊥}{1}$. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.
1/Q 2 power corrections to TMD factorization for Drell-Yan hadronic tensor
I calculate $\frac{1}{Q^2}$ power corrections to unpolarized Drell-Yan hadronic tensor for electromagnetic (EM) current at large N c and demonstrate the EM gauge invariance at this level.
Efficient computation of the N-th rank QED polarization tensor: Universal worldline structure of form factors
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Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small-x
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Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x
The Drell-Yan hadronic tensor for electromagnetic (EM) current in the Sudakov region s?Q2?q2? is obtained with 1Q2 accuracy. In the leading order in Nc the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: f1 responsible for total DY cross section, and Boer-Mulders function h?1. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.
Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data
We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.
Tensor-GMRES method for large sparse systems of nonlinear equations
This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.
Factorization breaking of A d T for polarized deuteron targets in a relativistic framework
We discuss the possible factorization of the tensor asymmetry $A^T_d$ measured for polarized deuteron targets within a relativistic framework. We define a reduced asymmetry and find that factorization holds only in plane wave impulse approximation and if $p$-waves are neglected. Our numerical results show a strong factorization breaking once final state interactions are included. We also compare the $d$-wave content of the wave functions with the size of the factored, reduced asymmetry and find that there is no systematic relationship of this quantity to the d-wave probability of the various wave functions.
Quadrupole forces between quark and gluon subsystems inside higher-spin particles
We generalize the mechanical interpretation of the forces between quark and gluon subsystems, previously studied for the nucleon, to arbitrary higher-spin particles. For spin-0 and spin-1/2 particles, this force is characterized by the nonconserved $\overline{𝑐}$(𝑡) form factor. However, such an interpretation has not yet been established for higher-spin particles due to the intricate structure of the nonconserved energy-momentum tensor (EMT) form factors. By performing a multipole expansion, we identify the physically meaningful combinations of the nonconserved covariant EMT form factors and provide them with a clear mechanical interpretation.
Tensor properties of the nucleon
We report in the present talk recent results of the tensor properties of the nucleon within the framework of the chiral quark-soliton model. The tensor and anomalous tensor magnetic form factors are calculated for the momentum transfer up to Q{sup 2}{<=}1 GeV{sup 2} and at a renormalization scale of 0.36 GeV{sup 2}. The main results are summarized as follows: the flavor tensor charges of the nucleon are yielded as {delta}u = 1.08, {delta}d = -0.31, {delta}s -0.01, while the up and down anomalous tensor magnetic moments are evaluated as {kappa}{sub T}{sup u} = 3.56 and {kappa}{sub T}{sup d} = 1.83, respectively. The strange anomalous tensor magnetic moment turns out to be {kappa}{sub T}{sup s} 0.2{approx}-0.2, compatible with zero. We discuss their physical implications, comparing them in particular with those from the lattice QCD.