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Results for “DELTA FUNCTION”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2010

A connection between spin and statistics based on Galilean invariant delta functions

We define Galilean invariant delta functions by using the Takahashi formulation, which describes particles with arbitrary spin. The direct calculation of the Galilean invariant delta functions in the (N+1)-dimensional Galilean covariant extended manifolds reveals that, for N odd, there exists a surface on which these delta functions vanish. This feature corresponds to the spacelike separation in the relativistic quantum field theory, and it enables us to discuss a connection between spin and statistics in the Galilean covariant theories. These results show that a spin-statistics connection holds for even-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with odd N{>=}5. Likewise, we observe that there is no such connection for odd-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with even N{>=}4. Thus, our results support the claim that there is no connection between spin and statistics in the usual nonrelativistic theory, for which N=4.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1983

Delta function excitation of waves in the earth's ionosphere

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.

Vidmar, R. J.↗
NASA NTRS1981

A new global operator for two-particle delta functions

A new type of global operator to be used in evaluating matrix elements of two-particle delta functions is introduced. It is based, like the Trivedi one-particle operator, on the Poisson equation and is easier to apply than the method of Hiller, Sucher and Feinberg. After a test in the helium isoelectronic sequence, the new method is applied successfully to the interesting problem of hyperfine structure in muonic helium.

Drachman, R. J.↗
DOE OSTI2010

Renormalized interaction of relativistic bosons with delta function potentials

We study the interaction of mutually noninteracting Klein-Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant renormalization. Renormalization is performed nonperturbatively using the orthofermion algebra technique and the principal operator {Phi} is found. The principal operator is then used to obtain the bound state spectrum, in terms of binding energies to single Dirac-delta function centers. The heat kernel method allows us to generalize this procedure to compact and Cartan-Hadamard type Riemannian manifolds. We make use of upper and lower bounds on the heat kernel to constrain the ground state energy from below, thus confirming that our neglect of pair creation is justified for certain ranges of parameters in the problem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1979

Global operators for delta functions - Extension to scattering states and the inclusion of spin

The paper presents an extension of the identities of Hiller, Sucher, and Feinberg for the evaluation of bound-state matrix elements of delta function operators, to scattering states. Attention is given to the technical difficulties encountered in the application of the scattering-state identities and how they can be overcome, including infrared singularities which arise if Coulomb forces are present and the velocity of the incident particle is small. In addition, both the scattering and bound-state identities are generalized to include spin-dependent contact interactions and spin-dependent Hamiltonians. Finally, it is stressed that the identities can be used to improve the accuracy of calculations of interest for diverse physical phenomena, ranging from positron annihilation to hyperfine structure.

Sucher, J.↗
DOE OSTI2022

Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations

We report general three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal magnetohydrodynamics (MHD) limit has been a significant challenge. This work presents numerical solutions of the Hahm–Kulsrud–Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad–Shafranov (GS) solver and the Stepped Pressure Equilibrium Code (SPEC) code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), whereby the solution relaxes to a Taylor state in each region while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution appears to approach the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate agreement between the numerical solutions obtained from the two codes through a convergence study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Solitons supported by localized nonlinearities in periodic media

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single {delta} function or a combination of two {delta} functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the {delta} functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single {delta} function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive {delta} function in the absence of the periodic potential is completely unstable. In addition, we show that the {delta} function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single {delta} function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two {delta} functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the {delta} functions set symmetrically with respect to the minimum or maximum of the underlying potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A white noise approach to the Feynman integrand for electrons in random media

Using the Feynman path integral representation of quantum mechanics it is possible to derive a model of an electron in a random system containing dense and weakly coupled scatterers [see F. Edwards and Y. B. Gulyaev, “The density of states of a highly impure semiconductor,” Proc. Phys. Soc. 83, 495–496 (1964)]. The main goal of this paper is to give a mathematically rigorous realization of the corresponding Feynman integrand in dimension one based on the theory of white noise analysis. We refine and apply a Wick formula for the product of a square-integrable function with Donsker's delta functions and use a method of complex scaling. As an essential part of the proof we also establish the existence of the exponential of the self-intersection local times of a one-dimensional Brownian bridge. As a result we obtain a neat formula for the propagator with identical start and end point. Thus, we obtain a well-defined mathematical object which is used to calculate the density of states [see, e.g., F. Edwards and Y. B. Gulyaev, “The density of states of a highly impure semiconductor,” Proc. Phys. Soc. 83, 495–496 (1964)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Final Results from the Jefferson Lab Qweak Experiment and Constraints on Physics Beyond the Standard Model

The $Q_{weak}$ $\vec{e}p$ elastic scattering experiment used to extract an asymmetry at $Q^2$ = 0.0248 $GeV^2$ will be described. The final result was -226.5 ± 9.3 ppb- the most precise ep asymmetry ever measured. Some of the backgrounds and corrections applied in the experiment will be explained and quantified, and some of the experimental challenges will be described. Several methods used to extract consistent values of the proton's weak charge $Q^p_w$ from our asymmetry measurement will be outlined. We also show the multi-TeV mass reach for beyond-the-Standard-Model physics obtained from our determination of the proton's weak charge, and discuss our sensitivity to specific examples of new physics like compositeness. From the proton's weak charge, a result for the fundamental standard model parameter $sin^2θ_W$ is obtained at the energy scale of our experiment. We compare that to the few other determinations of $sin^2θ_W$ available in the literature, as well as the predicted behaviour based on SM input.

Smith, Gregory↗
DOE OSTI2019

Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects

A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible realizations of this phenomenon in typical condensed matter systems requires dealing with the presence of defects. We examine the effect of delta-function point defects residing on a curved surface S. In particular, we solve the scattering problem for a multi-delta-function potential in plane, which requires a proper regularization of divergent terms entering its scattering amplitude, and include the effects of nontrivial geometry of S by treating it as a perturbation of the plane. This allows us to obtain analytic expressions for the geometric scattering amplitude for a surface consisting of one or more Gaussian bumps. In general the presence of the delta-function defects enhances the geometric scattering effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Massive celestial fermions

In an effort to further the study of amplitudes in the celestial CFT (CCFT), we construct conformal primary wavefunctions for massive fermions. Upon explicitly calculating the wavefunctions for Dirac fermions, we deduce the corresponding transformation of momentum space amplitudes to celestial amplitudes. The shadow wavefunctions are shown to have opposite spin and conformal dimension 2 - Δ. The Dirac conformal primary wave- functions are delta function normalizable with respect to the Dirac inner product provided they lie on the principal series with conformal dimension Δ = 1 + iλ for λ ∈ $\mathbb{R}$. It is shown that there are two choices of a complete basis: single spin J=$\frac{1}{2}$ or J=-$\frac{1}{2}$ and λ ∈ $\mathbb{R}$ or multiple spin J=±$\frac{1}{2}$ and λ $\mathbb{R}$ +∪0 . The massless limit of the Dirac conformal primary wavefunctions is shown to agree with previous literature. The momentum generators on the celestial sphere are derived and, along with the Lorentz generators, form a representation of the Poincaré algebra. Finally, we show that the massive spin-1 conformal primary wavefunctions can be constructed from the Dirac conformal primary wavefunctions using the standard Clebsch-Gordan coefficients. We use this procedure to write the massive spin-$\frac{3}{2}$, Rarita-Schwinger, conformal primary wavefunctions. This provides a prescription for constructing all massive fermionic and bosonic conformal primary wavefunctions starting from spin-$\frac{1}{2}$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are initially made in the frequency domain and provide Fourier-harmonic modes for the gauge-invariant master functions that satisfy inhomogeneous versions of the Regge-Wheeler and Zerilli equations. These gravitational master equations have specific singular sources containing both delta function and derivative-of-delta function terms. We demonstrate in this paper successful application of the method of extended homogeneous solutions, developed recently by Barack, Ori, and Sago, to handle source terms of this type. The method allows transformation back to the time domain, with exponential convergence of the partial mode sums that represent the field. This rapid convergence holds even in the region of r traversed by the point mass and includes the time-dependent location of the point mass itself. We present numerical results of mode calculations for certain orbital parameters, including highly accurate energy and angular momentum fluxes at infinity and at the black hole event horizon. We then address the issue of reconstructing the metric perturbation amplitudes from the master functions, the latter being weak solutions of a particular form to the wave equations. The spherical harmonic amplitudes that represent the metric in Regge-Wheeler gauge can themselves be viewed as weak solutions. They are in general a combination of (1) two differentiable solutions that adjoin at the instantaneous location of the point mass (a result that has order of continuity C{sup -1} typically) and (2) (in some cases) a delta function distribution term with a computable time-dependent amplitude.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗