Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
NASA Technical Reports Server (NTRS)
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
The kinematic algebras from the scattering equations
NASA Astrophysics Data System (ADS)
Monteiro, Ricardo; O'Connell, Donal
2014-03-01
We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant.
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
An algebraic approach to the scattering equations
NASA Astrophysics Data System (ADS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-12-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
Fusion rule algebras from graph theory
NASA Astrophysics Data System (ADS)
Caselle, M.; Ponzano, G.
1989-06-01
We describe a new class of fusion algebras related to graph theory which bear intriguing connections with group algebras. The structure constants and the matrix S, which diagonalizes the fusion rules, are explicitly computed in terms of SU(2) coupling coefficients.
Vertex operator algebras and conformal field theory
Huang, Y.Z. )
1992-04-20
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics.
Imperfect Cloning Operations in Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2015-01-01
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
Excision in algebraic K-theory and Karoubi's conjecture.
Suslin, A A; Wodzicki, M
1990-12-15
We prove that the property of excision in algebraic K-theory is for a Q-algebra A equivalent to the H-unitality of the latter. Our excision theorem, in particular, implies Karoubi's conjecture on the equality of algebraic and topological K-theory groups of stable C*-algebras. It also allows us to identify the algebraic K-theory of the symbol map in the theory of pseudodifferential operators. PMID:11607130
Excision in algebraic K-theory and Karoubi's conjecture.
Suslin, A A; Wodzicki, M
1990-01-01
We prove that the property of excision in algebraic K-theory is for a Q-algebra A equivalent to the H-unitality of the latter. Our excision theorem, in particular, implies Karoubi's conjecture on the equality of algebraic and topological K-theory groups of stable C*-algebras. It also allows us to identify the algebraic K-theory of the symbol map in the theory of pseudodifferential operators. PMID:11607130
Electromagnetic scattering theory
NASA Technical Reports Server (NTRS)
Bird, J. F.; Farrell, R. A.
1986-01-01
Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.
Recent advances in Multi-Channel Algebraic Scattering
Karataglidis, S.; Fraser, P. R.; Amos, K.; Canton, L.; Pisent, G.; Svenne, J. P.; Knijff, D. van der
2011-10-28
For coupled-channel descriptions of low-energy nucleon-induced interactions involving nuclei with particle-unstable exited states, it is necessary to include the widths of the target states. How those widths may affect the elastic scattering cross sections is examined within the framework of the Multi-Channel Algebraic Scattering (MCAS) method.
Algebraic theory of recombination spaces.
Stadler, P F; Wagner, G P
1997-01-01
A new mathematical representation is proposed for the configuration space structure induced by recombination, which we call "P-structure." It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental "genotypes" the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier decomposition of fitness landscapes into a superposition of "elementary landscapes." This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination, the elementary landscapes are exactly the p-spin functions (Walsh functions), that is, the same as the elementary landscapes of the string point mutation spaces (i.e., the hypercube). This supports the notion of a strong homomorphism between string mutation and recombination spaces. However, the effective nearest neighbor correlations on these elementary landscapes differ between mutation and recombination and among different recombination operators. On average, the nearest neighbor correlation is higher for one-point recombination than for uniform recombination. For one-point recombination, the correlations are higher for elementary landscapes with fewer interacting sites as well as for sites that have closer linkage, confirming the qualitative predictions of the Schema Theorem. We conclude that the algebraic approach to fitness landscape analysis can be extended to recombination spaces and provides an effective way to analyze the relative hardness of a landscape for a given recombination operator. PMID:10021760
Algebraic Theories and (Infinity,1)-Categories
NASA Astrophysics Data System (ADS)
Cranch, James
2010-11-01
We adapt the classical framework of algebraic theories to work in the setting of (infinity,1)-categories developed by Joyal and Lurie. This gives a suitable approach for describing highly structured objects from homotopy theory. A central example, treated at length, is the theory of E_infinity spaces: this has a tidy combinatorial description in terms of span diagrams of finite sets. We introduce a theory of distributive laws, allowing us to describe objects with two distributing E_infinity stuctures. From this we produce a theory of E_infinity ring spaces. We also study grouplike objects, and produce theories modelling infinite loop spaces (or connective spectra), and infinite loop spaces with coherent multiplicative structure (or connective ring spectra). We use this to construct the units of a grouplike E_infinity ring space in a natural manner. Lastly we provide a speculative pleasant description of the K-theory of monoidal quasicategories and quasicategories with ring-like structures.
Role of division algebra in seven-dimensional gauge theory
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-03-01
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.
Algebraic K-theory, K-regularity, and -duality of -stable C ∗-algebras
NASA Astrophysics Data System (ADS)
Mahanta, Snigdhayan
2015-12-01
We develop an algebraic formalism for topological -duality. More precisely, we show that topological -duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E ∞ -operad starting from any strongly self-absorbing C ∗-algebra . Then we show that there is a functorial topological K-theory symmetric spectrum construction on the category of separable C ∗-algebras, such that is an algebra over this operad; moreover, is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C ∗-algebras. We also show that -stable C ∗-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of a x+ b-semigroup C ∗-algebras coming from number theory and that of -stabilized noncommutative tori.
Quantum field theories on algebraic curves. I. Additive bosons
NASA Astrophysics Data System (ADS)
Takhtajan, Leon A.
2013-04-01
Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.
Topological insulators and C*-algebras: Theory and numerical practice
Hastings, Matthew B.; Loring, Terry A.
2011-07-15
Research Highlights: > We classify topological insulators using C* algebras. > We present new K-theory invariants. > We develop efficient numerical algorithms based on this technique. > We observe unexpected quantum phase transitions using our algorithm. - Abstract: We apply ideas from C*-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12{sup 3}, averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an 'order parameter' for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C*-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.
Metric Lie 3-algebras in Bagger-Lambert theory
NASA Astrophysics Data System (ADS)
de Medeiros, Paul; Figueroa-O'Farrill, José; Méndez-Escobar, Elena
2008-08-01
We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We classify metric Lie 3-algebras of signature (2, p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product. We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2, p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.
Fourier theory and C∗-algebras
NASA Astrophysics Data System (ADS)
Bédos, Erik; Conti, Roberto
2016-07-01
We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.
Topological insulators and C∗-algebras: Theory and numerical practice
NASA Astrophysics Data System (ADS)
Hastings, Matthew B.; Loring, Terry A.
2011-07-01
We apply ideas from C∗-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12 3, averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an "order parameter" for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C∗-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.
Symmetric linear systems - An application of algebraic systems theory
NASA Technical Reports Server (NTRS)
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Scattering theory for arbitrary potentials
Kadyrov, A.S.; Bray, I.; Stelbovics, A.T.; Mukhamedzhanov, A.M.
2005-09-15
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.
The arithmetic theory of algebraic groups
NASA Astrophysics Data System (ADS)
Platonov, V. P.
1982-06-01
CONTENTS Introduction § 1. Arithmetic groups § 2. Adèle groups § 3. Tamagawa numbers § 4. Approximations in algebraic groups § 5. Class numbers and class groups of algebraic groups § 6. The genus problem in arithmetic groups § 7. Classification of maximal arithmetic subgroups § 8. The congruence problem § 9. Groups of rational points over global fields § 10. Galois cohomology and the Hasse principle § 11. Cohomology of arithmetic groups References
From string theory to algebraic geometry and back
Brinzanescu, Vasile
2011-02-10
We describe some facts in physics which go up to the modern string theory and the related concepts in algebraic geometry. Then we present some recent results on moduli-spaces of vector bundles on non-Kaehler Calabi-Yau 3-folds and their consequences for heterotic string theory.
A Cohomology Theory of Grading-Restricted Vertex Algebras
NASA Astrophysics Data System (ADS)
Huang, Yi-Zhi
2014-04-01
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the correct cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the algebraic completion of a module for the algebra," instead of linear maps from tensor powers of the algebra to a module for the algebra. One subtle complication arising from such functions is that we have to carefully address the issue of convergence when we compose these linear maps with vertex operators. In particular, for each , we have an inverse system of nth cohomologies and an additional nth cohomology of a grading-restricted vertex algebra V with coefficients in a V-module W such that is isomorphic to the inverse limit of the inverse system . In the case of n = 2, there is an additional second cohomology denoted by which will be shown in a sequel to the present paper to correspond to what we call square-zero extensions of V and to first order deformations of V when W = V.
Algebraic isomorphism in two-dimensional anomalous gauge theories
Carvalhaes, C.G.; Natividade, C.P.
1997-08-01
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.
Quantum theory of Thomson scattering
NASA Astrophysics Data System (ADS)
Crowley, B. J. B.; Gregori, G.
2014-12-01
The general theory of the scattering of electromagnetic radiation in atomic plasmas and metals, in the non-relativistic regime, in which account is taken of the Kramers-Heisenberg polarization terms in the Hamiltonian, is described from a quantum mechanical viewpoint. As well as deriving the general formula for the double differential Thomson scattering cross section in an isotropic finite temperature multi-component system, this work also considers closely related phenomena such as absorption, refraction, Raman scattering, resonant (Rayleigh) scattering and Bragg scattering, and derives many essential relationships between these quantities. In particular, the work introduces the concept of scattering strength and the strength-density field which replaces the normal particle density field in the standard treatment of scattering by a collection of similar particles and it is the decomposition of the strength-density correlation function into more familiar-looking components that leads to the final result. Comparisons are made with previous work, in particular that of Chihara [1].
Category of trees in representation theory of quantum algebras
Moskaliuk, N. M.; Moskaliuk, S. S.
2013-10-15
New applications of categorical methods are connected with new additional structures on categories. One of such structures in representation theory of quantum algebras, the category of Kuznetsov-Smorodinsky-Vilenkin-Smirnov (KSVS) trees, is constructed, whose objects are finite rooted KSVS trees and morphisms generated by the transition from a KSVS tree to another one.
Algebraic K-theory of discrete subgroups of Lie groups.
Farrell, F T; Jones, L E
1987-05-01
Let G be a Lie group (with finitely many connected components) and Gamma be a discrete, cocompact, torsion-free subgroup of G. We rationally calculate the algebraic K-theory of the integral group ring ZGamma in terms of the homology of Gamma with trivial rational coefficients. PMID:16593834
Algebraic K-theory of discrete subgroups of Lie groups
Farrell, F. T.; Jones, L. E.
1987-01-01
Let G be a Lie group (with finitely many connected components) and Γ be a discrete, cocompact, torsion-free subgroup of G. We rationally calculate the algebraic K-theory of the integral group ring ZΓ in terms of the homology of Γ with trivial rational coefficients. PMID:16593834
Partial Fractions in Calculus, Number Theory, and Algebra
ERIC Educational Resources Information Center
Yackel, C. A.; Denny, J. K.
2007-01-01
This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.
Forms and algebras in (half-)maximal supergravity theories
NASA Astrophysics Data System (ADS)
Howe, Paul; Palmkvist, Jakob
2015-05-01
The forms in D-dimensional (half-)maximal supergravity theories are discussed for 3 ≤ D ≤ 11. Superspace methods are used to derive consistent sets of Bianchi identities for all the forms for all degrees, and to show that they are soluble and fully compatible with supersymmetry. The Bianchi identities determine Lie superalgebras that can be extended to Borcherds superalgebras of a special type. It is shown that any Borcherds superalgebra of this type gives the same form spectrum, up to an arbitrary degree, as an associated Kac-Moody algebra. For maximal supergravity up to D-form potentials, this is the very extended Kac-Moody algebra E 11. It is also shown how gauging can be carried out in a simple fashion by deforming the Bianchi identities by means of a new algebraic element related to the embedding tensor. In this case the appropriate extension of the form algebra is a truncated version of the so-called tensor hierarchy algebra.
Theory of Graphene Raman Scattering.
Heller, Eric J; Yang, Yuan; Kocia, Lucas; Chen, Wei; Fang, Shiang; Borunda, Mario; Kaxiras, Efthimios
2016-02-23
Raman scattering plays a key role in unraveling the quantum dynamics of graphene, perhaps the most promising material of recent times. It is crucial to correctly interpret the meaning of the spectra. It is therefore very surprising that the widely accepted understanding of Raman scattering, i.e., Kramers-Heisenberg-Dirac theory, has never been applied to graphene. Doing so here, a remarkable mechanism we term"transition sliding" is uncovered, explaining the uncommon brightness of overtones in graphene. Graphene's dispersive and fixed Raman bands, missing bands, defect density and laser frequency dependence of band intensities, widths of overtone bands, Stokes, anti-Stokes anomalies, and other known properties emerge simply and directly. PMID:26799915
NASA Astrophysics Data System (ADS)
Hoppe, Jens
Over the past years, associative algebras have come to play a major role in several areas of theoretical physics. Firstly, it has been realized that Yang Baxter algebras [1] constitute the relevant structure underlying 1+1 dimensional integrable models; in addition, their relation to braid groups, the theory of knots and links, and the exchange algebras of 1+1 dimensional conformal field theories [2] has been quite well understood by now. Secondly, deformations of Poisson structures that appeared in 2+1 dimensional field theories as infinite dimensional symmetry algebras possess underlying associative structures, which have also been studied in some detail (concerning higher spin theories see, e.g., [3, 4] and references therein, concerning the enveloping algebra of sl(2, C) see, e.g., [5], concerning deformations of diffAT2 — the Lie algebra of infinitesimal area preserving diffeomorphisms of the Torus — see [6, 7, 8, 9]). Ideas on how both investigations could eventually converge (i.e., a relation between 2+1 and 1+1 dimensions) have, e.g., been expressed in [10]. As indicated by the two subtitles there will be two parts to my paper: the first one presents a view on something I met long ago [11], and recently got interested in again [5, 7, 9, 12], while the second part introduces some algebraic structures that seem to be interesting, and possibly new.
Non-simply laced Lie algebras via F theory strings
NASA Astrophysics Data System (ADS)
Bonora, L.; Savelli, R.
2010-11-01
In order to describe the appearance in F theory of the non-simply-laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D 2n to B n , of the folding of E 6 to F 4 and that of D 4 to G 2 in terms of junctions and Jordan strings. We also discuss the case of C n , but we are unable in this case to provide a string interpretation.
Do malaria parasites follow the algebra of sex ratio theory?
Schall, Jos J
2009-03-01
The ratio of male to female gametocytes seen in infections of Plasmodium and related haemosporidian parasites varies substantially, both within and among parasite species. Sex ratio theory, a mainstay of evolutionary biology, accounts for this variation. The theory provides an algebraic solution for the optimal sex ratio that will maximize parasite fitness. A crucial term in this solution is the probability of selfing by clone-mates within the vector (based on the clone number and their relative abundance). Definitive tests of the theory have proven elusive because of technical challenges in measuring clonal diversity within infections. Newly developed molecular methods now provide opportunities to test the theory with an exquisite precision. PMID:19201653
"Phonon" scattering beyond perturbation theory
NASA Astrophysics Data System (ADS)
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
On the algebraic K-theory of the complex K-theory spectrum
NASA Astrophysics Data System (ADS)
Ausoni, Christian
2010-03-01
Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.
Light-scattering theory of diffraction.
Guo, Wei
2010-03-01
Since diffraction is a scattering process in principle, light propagation through one aperture in a screen is discussed in the light-scattering theory. Through specific calculation, the expression of the electric field observed at an observation point is obtained and is used not only to explain why Kirchhoff's diffraction theory is a good approximation when the screen is both opaque and sufficiently thin but also to demonstrate that the mathematical and physical problems faced by Kirchhoff's theory are avoided in the light-scattering theory. PMID:20208939
Calculation of exchange energies using algebraic perturbation theory
Burrows, B. L.; Dalgarno, A.; Cohen, M.
2010-04-15
An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion Y{sup +} with an atom X. For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations R. Since the perturbation parameter is essentially 1/R, this method is suitable for large R. In particular, exchange energies are calculated for X{sub 2}{sup +} systems, where X is H, Li, Na, K, Rb, or Cs.
COMMENT: Comment on `Dirac theory in spacetime algebra'
NASA Astrophysics Data System (ADS)
Baylis, William E.
2002-06-01
In contrast to formulations of the Dirac theory by Hestenes and by the present author, the formulation recently presented by Joyce (Joyce W P 2001 J. Phys. A: Math. Gen. 34 1991-2005) is equivalent to the usual Dirac equation only in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation can be solutions either of the Dirac equation in the Hestenes form or of the same equation with the sign of the mass reversed, and in general they are mixtures of the two possibilities. Because of this relationship, Joyce obtains twice as many linearly independent plane-wave solutions for a given momentum eigenvalue as exist in the conventional theory. A misconception about the symmetry of the Hestenes equation and the geometric significance of the algebraic spinors is also briefly discussed.
Experimental confirmation of neoclassical Compton scattering theory
Aristov, V. V.; Yakunin, S. N.; Despotuli, A. A.
2013-12-15
Incoherent X-ray scattering spectra of diamond and silicon crystals recorded on the BESSY-2 electron storage ring have been analyzed. All spectral features are described well in terms of the neoclassical scattering theory without consideration for the hypotheses accepted in quantum electrodynamics. It is noted that the accepted tabular data on the intensity ratio between the Compton and Rayleigh spectral components may significantly differ from the experimental values. It is concluded that the development of the general theory (considering coherent scattering, incoherent scattering, and Bragg diffraction) must be continued.
K-theory of the chair tiling via AF-algebras
NASA Astrophysics Data System (ADS)
Julien, Antoine; Savinien, Jean
2016-08-01
We compute the K-theory groups of the groupoid C∗-algebra of the chair tiling, using a new method. We use exact sequences of Putnam to compute these groups from the K-theory groups of the AF-algebras of the substitution and the induced lower dimensional substitutions on edges and vertices.
Scattering theory with path integrals
Rosenfelder, R.
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Solutions in bosonic string field theory and higher spin algebras in AdS
NASA Astrophysics Data System (ADS)
Polyakov, Dimitri
2015-11-01
We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in AdS3. The solutions are expressed in terms of the generating function for the products of Bell polynomials in derivatives of bosonic space-time coordinates Xm(z ) of the open string, the form of which is determined in this work. The products of these polynomials form a natural operator algebra realizations of w∞ (area-preserving diffeomorphisms), enveloping algebra of SU(2) and higher spin algebra in AdS3. The class of string field theory solutions found can, in turn, be interpreted as the "enveloping of enveloping," or the enveloping of AdS3 higher spin algebra. We also discuss the extensions of this class of solutions to superstring theory and their relations to higher spin algebras in higher space-time dimensions.
Introducing Scattering Theory with a Computer
ERIC Educational Resources Information Center
Merrill, John R.
1973-01-01
Discusses a new method of presenting the scattering theory, including classical explanation of cross sections, quantum mechanical expressions for phase shifts, and use of a computer to solve problems. (CC)
The Clifford algebra of physical space and Dirac theory
NASA Astrophysics Data System (ADS)
Vaz, Jayme, Jr.
2016-09-01
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term β \\psi in the usual Dirac factorization of the Klein–Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation.
Theory of waves incoherently scattered
NASA Technical Reports Server (NTRS)
Bauer, P.
1974-01-01
Electromagnetic waves impinging upon a plasma at frequencies larger than the plasma frequency, suffer weak scattering. The scattering arises from the existence of electron density fluctuations. The received signal corresponds to a particular spatial Fourier component of the fluctuations, the wave vector of which is a function of the wavelength of the radiowave. Wavelengths short with respect to the Debye length of the medium relate to fluctuations due to non-interacting Maxwellian electrons, while larger wavelengths relate to fluctuations due to collective Coulomb interactions. In the latter case, the scattered signal exhibits a spectral distribution which is characteristic of the main properties of the electron and ion gases and, therefore, provides a powerful diagnosis of the state of the ionosphere.
Theory of Light Scattering in Axion Electrodynamics
NASA Astrophysics Data System (ADS)
Ochiai, Tetsuyuki
2012-09-01
Taking account of the axion term in the Maxwell Lagrangian, we present a rigorous theory of light scattering in piecewise-constant axion fields. In particular, we focus on axionic substances with confined and/or curved geometries, and the scattering matrices of an axionic slab, cylinder, and sphere are derived analytically. The axion term generates a surface current with off-diagonal optical conductivity, giving rise to a new type of photospin--orbit interaction. As a result, various novel light-scattering phenomena can take place. We demonstrate enhanced Faraday rotation, parity-violating light scattering, and strong perturbation of dipole radiation.
Scattering processes in lattice gauge theories
NASA Astrophysics Data System (ADS)
Alessandrini, V.; Krzywicki, A.
1980-06-01
Scattering between gauge invariant lattice excitations is studied in the framework of a 2+1 dimensional lattice theory with U(1) gauge symmetry. We put the theory in a form analogous to theories of conventional large quantum systems (spin waves in a solid, for example) and we calculate explicitly the cross section for boxiton scattering. The general strategy we have developed goes beyond the simple example of compact QED. Laboratoire associé au CNRS. Postal address: LPTHE, Bâtiment 211, Université Paris-Sud, 91405 Orsay, France.
Clifford Algebra Cℓ 3(ℂ) for Applications to Field Theories
NASA Astrophysics Data System (ADS)
Panicaud, B.
2011-10-01
The multivectorial algebras present yet both an academic and a technological interest. Difficulties can occur for their use. Indeed, in all applications care is taken to distinguish between polar and axial vectors and between scalars and pseudo scalars. Then a total of eight elements are often considered even if they are not given the correct name of multivectors. Eventually because of their simplicity, only the vectorial algebra or the quaternions algebra are explicitly used for physical applications. Nevertheless, it should be more convenient to use directly more complex algebras in order to have a wider range of application. The aim of this paper is to inquire into one particular Clifford algebra which could solve this problem. The present study is both didactic concerning its construction and pragmatic because of the introduced applications. The construction method is not an original one. But this latter allows to build up the associated real algebra as well as a peculiar formalism that enables a formal analogy with the classical vectorial algebra. Finally several fields of the theoretical physics will be described thanks to this algebra, as well as a more applied case in general relativity emphasizing simultaneously its relative validity in this particular domain and the easiness of modeling some physical problems.
Minimal unitary (covariant) scattering theory
Lindesay, J.V.; Markevich, A.
1983-06-01
In the minimal three particle equations developed by Lindesay the two body input amplitude was an on shell relativistic generalization of the non-relativistic scattering model characterized by a single mass parameter ..mu.. which in the two body (m + m) system looks like an s-channel bound state (..mu.. < 2m) or virtual state (..mu.. > 2m). Using this driving term in covariant Faddeev equations generates a rich covariant and unitary three particle dynamics. However, the simplest way of writing the relativisitic generalization of the Faddeev equations can take the on shell Mandelstam parameter s = 4(q/sup 2/ + m/sup 2/), in terms of which the two particle input is expressed, to negative values in the range of integration required by the dynamics. This problem was met in the original treatment by multiplying the two particle input amplitude by THETA(s). This paper provides what we hope to be a more direct way of meeting the problem.
Noyes, H.P.
1990-01-29
We construct discrete space-time coordinates separated by the Lorentz-invariant intervals h/mc in space and h/mc{sup 2} in time using discrimination (XOR) between pairs of independently generated bit-strings; we prove that if this space is homogeneous and isotropic, it can have only 1, 2 or 3 spacial dimensions once we have related time to a global ordering operator. On this space we construct exact combinatorial expressions for free particle wave functions taking proper account of the interference between indistinguishable alternative paths created by the construction. Because the end-points of the paths are fixed, they specify completed processes; our wave functions are born collapsed''. A convenient way to represent this model is in terms of complex amplitudes whose squares give the probability for a particular set of observable processes to be completed. For distances much greater than h/mc and times much greater than h/mc{sup 2} our wave functions can be approximated by solutions of the free particle Dirac and Klein-Gordon equations. Using a eight-counter paradigm we relate this construction to scattering experiments involving four distinguishable particles, and indicate how this can be used to calculate electromagnetic and weak scattering processes. We derive a non-perturbative formula relating relativistic bound and resonant state energies to mass ratios and coupling constants, equivalent to our earlier derivation of the Bohr relativistic formula for hydrogen. Using the Fermi-Yang model of the pion as a relativistic bound state containing a nucleon-antinucleon pair, we find that (G{sub {pi}N}{sup 2}){sup 2} = (2m{sub N}/m{sub {pi}}){sup 2} {minus} 1. 21 refs., 1 fig.
K-theory of locally finite graph C∗-algebras
NASA Astrophysics Data System (ADS)
Iyudu, Natalia
2013-09-01
We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
NASA Astrophysics Data System (ADS)
Ruiz Ruiz, F.
2016-02-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory
Jiang Tongsong
2005-05-01
By means of complex representation and real representation of a quaternion matrix, this paper studies the problem of diagonalization of a quaternion matrix, gives two algebraic methods for diagonalization of quaternion matrices in quaternionic quantum theory.
Magnetization dissipation in ferromagnets from scattering theory
NASA Astrophysics Data System (ADS)
Brataas, Arne; Tserkovnyak, Yaroslav; Bauer, Gerrit E. W.
2011-08-01
The magnetization dynamics of ferromagnets is often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parametrized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain-wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.
NASA Technical Reports Server (NTRS)
Byrnes, C. I.
1980-01-01
It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.
Effective string theory and QCD scattering amplitudes
Makeenko, Yuri
2011-01-15
QCD string is formed at distances larger than the confinement scale and can be described by the Polchinski-Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luescher term, and discuss an application to meson scattering amplitudes in QCD.
Scattering theory for Floquet-Bloch states
NASA Astrophysics Data System (ADS)
Bilitewski, Thomas; Cooper, Nigel R.
2015-03-01
Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasienergy, which is defined only up to the addition of integer multiples of ℏ ω for a Hamiltonian with period T =2 π /ω . We discuss the consequences of this for the interpretation of "elastic" and "inelastic" scattering in cases of physical interest. We illustrate our general results with applications to the scattering of a single particle in a Floquet-Bloch state from a static potential and the scattering of two bosonic particles in Floquet-Bloch states through their interparticle interaction. We analyze examples of these scattering processes that are closely related to the schemes used to generate artificial gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit ω →∞ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stabilize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in the current experimental setup can be switched off by additional confinement of transverse motion.
Surface-integral formulation of scattering theory
Kadyrov, A.S. Bray, I.; Mukhamedzhanov, A.M.; Stelbovics, A.T.
2009-07-15
We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.
Theory of Multiple Coulomb Scattering from Extended Nuclei
DOE R&D Accomplishments Database
Cooper, L. N.; Rainwater, J.
1954-08-01
Two independent methods are described for calculating the multiple scattering distribution for projected angle scattering resulting when very high energy charged particles traverse a thick scatterer. The results are compared with the theories of Moliere and Olbert.
VLF scattering from Red Sprites-Theory
NASA Astrophysics Data System (ADS)
Rodger, C. J.; Wait, J. R.; Dowden, R. L.
1998-05-01
A relatively simple model of Red Sprites as a set of conducting columns reproduces the radio physics properties of VLF sprites. The columnar structure of optical sprites is represented by thin vertical conducting columns (or `Spritelets') in free space, with dimensions taken from optical observations. The scattered field from a set of coupled Spritelets has a complex amplitude pattern which normally includes some deep minima reproducing the `perturbation shadows' seen in some experimental events. It is not uncommon for the back scattered amplitudes to be similar to those for forward scatter in the theoretical model, as in experimental reports. As some sprite events appear to have closely spaced Spritelets, the results presented here indicate that there will be a high degree of electrical shielding. This is an application of the theory presented by[Rodger et al. (1997a)].
Yangian symmetry of scattering amplitudes in Script N = 4 super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Drummond, James; Henn, Johannes; Plefka, Jan
2009-05-01
Tree-level scattering amplitudes in Script N = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar Script N = 4 super Yang-Mills, at least at tree level.
NASA Astrophysics Data System (ADS)
Taormina, Anne
1993-05-01
The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.
Generalized Rayleigh scattering. I. Basic theory.
NASA Astrophysics Data System (ADS)
Ivanov, V. V.
1995-11-01
The classsical problem of multiple molecular (in particular, Rayleigh) scattering in plane-parallel atmospheres is considered from a somewhat broader viewpoint than usual. The general approach and ideology are borrowed from non-LTE line formation theory. The main emphasis is on the depth dependence of the corresponding source matrix rather than on the emergent radiation. We study the azimuth-averaged radiation field of polarized radiation in a semi-infinite atmosphere with embedded primary sources. The corresponding 2x2 phase matrix of molecular scattering is P=(1-W) P_I_+W P_R_, where P_I_ and P_R_ are the phase matrices of the scalar isotropic scattering and of the Rayleigh scattering, respectively, and W is the depolarization parameter. Contrary to the usual assumption that W{in}[0,1], we assume W{in} [0,{infinity}) and call this generalized Rayleigh scattering (GRS). Using the factorization of P which is intimately related to its diadic expansion, we reduce the problem to an integral equation for the source matrix S(τ) with a matrix displacement kernel. In operator form this equation is S={LAMBDA}S+S^*^, where {LAMBDA} is the matrix {LAMBDA}-operator and S^*^ is the primary source term. This leads to a new concept, the matrix albedo of single scattering λ =diag(λ_I_,λ_Q_), where λ_I_ is the usual (scalar) single scattering albedo and λ_Q_=0.7Wλ_I_. Its use enables one to formulate matrix equivalents of many of the results of the scalar theory in exactly the same form as in the scalar case. Of crucial importance is the matrix equivalent of the sqrt(ɛ) law of the scalar theory. Another useful new concept is the λ-plane, i.e., the plane with the axes (λ_I_,λ_Q_). Systematic use of the matrix sqrt(ɛ) law and of the λ-plane proved to be a useful instrument in classifying various limiting and particular cases of GRS and in discussing numerical data on the matrix source functions (to be given in Paper II of the series).
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
2016-07-01
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
Theory of scattering by complex potentials
Thylwe, K.; Froeman, N.
1983-10-15
The scattering problem for a non-relativistic spinless particle under the influence of a complex effective potential, which is spherically symmetric and tends to zero faster than 1/r at infinity, is considered. Certain general relations, which illuminate the influence of the imaginary part of the potential on the scattering process, are derived with the use of the expression for the probability current density. The rigorous phase-integral method developed by N. Froeman and P. O. Froeman is used for obtaining an exact, general formula for the scattering matrix, or equivalently, for the phase shift. The formula is expressed in terms of phase-integral approximations of an arbitrary order and certain quantities defined by convergent series. Estimating the latter quantities and omitting small corrections, an approximate formula is derived for the phase shift, valid for the case that only one complex turning point contributes essentially to the phase shift. Criteria for classifying a scattering problem as such a one-turning-point problem are given. The treatment is made general enough to also cover situations of interest in Regge-pole or complex angular momentum theory.
Cluster Algebras from Dualities of 2d = (2, 2) Quiver Gauge Theories
NASA Astrophysics Data System (ADS)
Benini, Francesco; Park, Daniel S.; Zhao, Peng
2015-11-01
We interpret certain Seiberg-like dualities of two-dimensional = (2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the complexified Fayet-Iliopoulos parameters of the gauge group factors transform under those dualities and observe that they are in fact related to the dual cluster variables of cluster algebras. This implies that there is an underlying cluster algebra structure in the quantum Kähler moduli space of manifolds constructed from the corresponding Kähler quotients. We study the S 2 partition function of the gauge theories, showing that it is invariant under dualities/mutations, up to an overall normalization factor, whose physical origin and consequences we spell out in detail. We also present similar dualities in = (2,2)* quiver gauge theories, which are related to dualities of quantum integrable spin chains.
Classification of operator algebraic conformal field theories in dimensions one and two
NASA Astrophysics Data System (ADS)
Kawahigashi, Yasuyuki
2006-03-01
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of a two-dimensional theory into two chiral theories. We give the first classification result of such chiral theories with representation theoretic invariants. That is, we use the central charge as the first invariant, and if it is less than 1, we obtain a complete classification. Our classification list contains a new net which does not seem to arise from the known constructions such as the coset or orbifold constructions. We also present a classification of full two-dimensional conformal theories. These are joint works with Roberto Longo.
Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry
NASA Astrophysics Data System (ADS)
Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.
2016-09-01
The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.
Equivariant algebraic vector bundles over representations of reductive groups: theory.
Masuda, M; Petrie, T
1991-01-01
Let G be a reductive algebraic group and let B be an affine variety with an algebraic action of G. Everything is defined over the field C of complex numbers. Consider the trivial G-vector bundle B x S = S over B where S is a G-module. From the endomorphism ring R of the G-vector bundle S a construction of G-vector bundles over B is given. The bundles constructed this way have the property that when added to S they are isomorphic to F + S for a fixed G-module F. For such a bundle E an invariant rho(E) is defined that lies in a quotient of R. This invariant allows us to distinguish nonisomorphic G-vector bundles. This is applied to the case where B is a G-module and, in that case, an invariant of the underlying equivariant variety is given too. These constructions and invariants are used to produce families of inequivalent G-vector bundles over G-modules and families of inequivalent G actions on affine spaces for some finite and some connected semisimple groups. PMID:11607220
Effective theories for dark matter nucleon scattering
NASA Astrophysics Data System (ADS)
Hisano, Junji; Nagai, Ryo; Nagata, Natsumi
2015-05-01
We reformulate the calculation of the dark matter-nucleon scattering cross sections based on the method of effective field theories. We assume that the scatterings are induced by the exchange of colored mediators, and construct the effective theories by integrating out the colored particles. All of the leading order matching conditions as well as the renormalization group equations are presented. We consider a Majorana fermion, and real scalar and vector bosons for the dark matter and show the results for each case. The treatment for the twist-2 operators is discussed in detail, and it is shown that the scale of evaluating their nucleon matrix elements does not have to be the hadronic scale. The effects of the QCD corrections are evaluated on the assumption that the masses of the colored mediators are much heavier than the electroweak scale. Our formulation is systematic and model-independent, and thus suitable to be implemented in numerical packages, such as micrOMEGAs and DarkSUSY.
Chen Famin; Wu Yongshi
2010-11-15
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
Regular perturbation theory of relativistic corrections: II. Algebraic approximation
NASA Astrophysics Data System (ADS)
Rutkowski, A.; Kozłowski, R.; Rutkowska, D.
2001-01-01
A four-component equivalent of the Schrödinger equation, describing both the nonrelativistic electron and the nonrelativistic positron, is introduced. The difference between this equation and the Dirac equation is treated as a perturbation. The relevant perturbation equations and formulas for corrections to the energy are derived. Owing to the semibounded character of the Schrödinger Hamiltonian of the unperturbed equation the variational perturbation method is formulated. The Hylleraas functionals become then either upper or lower bounds to the respective exact corrections to the energy. In order to demonstrate the usefulness of this approach to the problem of the variational optimization of nonlinear parameters, the perturbation corrections to wave functions for the of hydrogenlike atoms have been approximated in terms of exponential basis functions. The Dirac equation in this algebraic approximation is solved iteratively starting with the solution of the Schrödinger equation.
Towards a loop representation of connection theories defined over a super Lie algebra
Urrutia, L.F. |
1996-02-01
The purpose of this contribution is to review some aspects of the loop space formulation of pure gauge theories having the connection defined over a Lie algebra. The emphasis is focused on the discussion of the Mandelstam identities, which provide the basic constraints upon both the classical and the quantum degrees of freedom of the theory. In the case where the connection is extended to be valued on a super Lie algebra, some new results are presented which can be considered as first steps towards the construction of the Mandelstam identities in this situation, which encompasses such interesting cases as supergravity in 3+1 dimensions together with 2+1 super Chern-Simons theories, for example. Also, these ideas could be useful in the loop space formulation of fully supersymmetric theories. {copyright} {ital 1996 American Institute of Physics.}
Towards a loop representation of connection theories defined over a super Lie algebra
Urrutia, Luis F.
1996-02-20
The purpose of this contribution is to review some aspects of the loop space formulation of pure gauge theories having the connection defined over a Lie algebra. The emphasis is focused on the discussion of the Mandelstam identities, which provide the basic constraints upon both the classical and the quantum degrees of freedom of the theory. In the case where the connection is extended to be valued on a super Lie algebra, some new results are presented which can be considered as first steps towards the construction of the Mandelstam identities in this situation, which encompasses such interesting cases as supergravity in 3+1 dimensions together with 2+1 super Chern-Simons theories, for example. Also, these ideas could be useful in the loop space formulation of fully supersymmetric theories.
An algebraic PT-symmetric quantum theory with a maximal mass
NASA Astrophysics Data System (ADS)
Rodionov, V. N.; Kravtsova, G. A.
2016-03-01
In this paper, we draw attention to the fact that the studies by V.G. Kadyshevsky devoted to the creation of the geometric quantum field theory with a fundamental mass have had great development recently, as regards a non-Hermitian algebraic approach to construction of the quantum theory. The central idea of such theories is to construct a new scalar product in which the average values of non-Hermitian Hamiltonians are real. Many studies in this field include both purely mathematical ones and those containing the discussion of experimental results. We consider the development of an algebraic relativistic pseudo-Hermitian quantum theory with a maximal mass and discuss its experimentally important corollaries.
NASA Astrophysics Data System (ADS)
Orantin, N.
2007-09-01
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.
K-Theory of Crossed Products of Tiling C*-Algebras by Rotation Groups
NASA Astrophysics Data System (ADS)
Starling, Charles
2015-02-01
Let Ω be a tiling space and let G be the maximal group of rotations which fixes Ω. Then the cohomology of Ω and Ω/ G are both invariants which give useful geometric information about the tilings in Ω. The noncommutative analog of the cohomology of Ω is the K-theory of a C*-algebra associated to Ω, and for translationally finite tilings of dimension 2 or less, the K-theory is isomorphic to the direct sum of cohomology groups. In this paper we give a prescription for calculating the noncommutative analog of the cohomology of Ω/ G, that is, the K-theory of the crossed product of the tiling C*-algebra by G. We also provide a table with some calculated K-groups for many common examples, including the Penrose and pinwheel tilings.
Algebraic Characterization of the Vacuum in Light-Front Field Theory
NASA Astrophysics Data System (ADS)
Herrmann, Marc; Polyzou, Wayne
2016-03-01
In the light-front formulation of quantum field theory, the vacuum vector of an interacting field theory has a relatively simple relationship to the vacuum of a free field theory. This is a benefit over the usual equal-time formulation where the interacting vacuum vector has infinite norm with respect to the Hilbert space of the free field theory. By describing the vacuum as a positive linear functional on an operator algebra constructed from free fields with two distinct masses, it can be demonstrated that the complications associated with adding dynamics to the vacuum of a free theory are not present in the construction of the light-front vacuum. Instead, the complications are moved into defining a subalgebra of the light-front algebra which corresponds to the physically relevant algebra of local fields. These results can then be applied to interacting fields by first describing them in terms of asymptotic in or out fields. However, in order to treat local operators products, the vacuum functional may need to be modified to include states with zero eigenvalue of the generator of translations in the direction along the light front, x- =1/√(2) >x0-x3. This work supported by DOE contract No. DE-FG02-86ER40286.
LieART-A Mathematica application for Lie algebras and representation theory
NASA Astrophysics Data System (ADS)
Feger, Robert; Kephart, Thomas W.
2015-07-01
We present the Mathematica application "LieART" (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included as online supplementary material (see Appendix A).
Scattering asymptotic conditions in Euclidean relativistic quantum theory
NASA Astrophysics Data System (ADS)
Aiello, Gordon J.; Polyzou, W. N.
2016-03-01
We discuss the formulation of the scattering asymptotic condition as a strong limit in Euclidean quantum theories satisfying the Osterwalder-Schrader axioms. When used with the invariance principle this provides a constructive method to compute scattering observables directly in the Euclidean formulation of the theory, without an explicit analytic continuation.
Scale-adaptive tensor algebra for local many-body methods of electronic structure theory
Liakh, Dmitry I
2014-01-01
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dappiaggi, Claudio; Nosari, Gabriele; Pinamonti, Nicola
2016-06-01
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
Multigluon scattering in open superstring theory
Stieberger, Stephan; Taylor, Tomasz R.
2006-12-15
We discuss the amplitudes describing N-gluon scattering in type I superstring theory, on a disk world sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit ({alpha}{sup '}{yields}0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N=4, 5, and N=6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals--generalized Euler integrals--which for N{>=}6 correspond to multiple hypergeometric series (generalized Kampe de Feriet functions). Their {alpha}{sup '} expansions lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O({alpha}{sup '2}), originate from the well-known {alpha}{sup '2} TrF{sup 4} effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N. We argue that such a procedure can be extended to all orders in {alpha}{sup '}. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multijet production at the Large Hadron Collider (LHC)
On the Algebraic K Theory of the Massive D8 and M9-Branes
NASA Astrophysics Data System (ADS)
Vancea, Ion V.
In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable compact manifold W in a massive Type IIA supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d=11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K0(C(Z)x{¯ {k}*}G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.
The theory of Enceladus and Dione: An application of computerized algebra in dynamical astronomy
NASA Technical Reports Server (NTRS)
Jefferys, W. H.; Ries, L. M.
1974-01-01
A theory of Saturn's satellites Enceladus and Dione is discussed which is literal (all constants of integration appear explicitly), canonically invariant (the Hori-Lie method is used), and which correctly handles the eccentricity-type resonance between the two satellites. Algebraic manipulations are designed to be performed using the TRIGMAN formula manipulation language, and computer programs were developed so that, with minor modifications, they can be used on the Mimas-Tethys and Titan-Hyperion systems.
Theory of ghost scattering with incoherent light sources
NASA Astrophysics Data System (ADS)
Cheng, Jing
2016-04-01
Inspired by the idea of ghost imaging, we propose a ghost scattering scheme to study light scattering with incoherent light sources through the nonlocal correlation measurement of the differential scattering cross-section fluctuations in two different optical paths. We present a rigorous formal theory to describe the ghost scattering process. Also we have derived a simple and closed-form ghost scattering formula within the first-order Born approximation which is particularly suited for weak scatterers. We find that the scattering information of a test scatterer can be obtained by using only a single-pixel detector in the corresponding optical path through the nonlocal correlation measurement with the help of another reference path.
Representations of Conformal Nets, Universal C*-Algebras and K-Theory
NASA Astrophysics Data System (ADS)
Carpi, Sebastiano; Conti, Roberto; Hillier, Robin; Weiner, Mihály
2013-05-01
We study the representation theory of a conformal net {{A}} on S 1 from a K-theoretical point of view using its universal C*-algebra {C^*({A})}. We prove that if {{A}} satisfies the split property then, for every representation π of {{A}} with finite statistical dimension, {π(C^*({A}))} is weakly closed and hence a finite direct sum of type I∞ factors. We define the more manageable locally normal universal C*-algebra {C_ln^*({A})} as the quotient of {C^*({A})} by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if {{A}} is completely rational with n sectors, then {C_ln^*({A})} is a direct sum of n type I∞ factors. Its ideal {{K}_{A}} of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of {C^*({A})} with finite statistical dimension act on {{K}_{A}}, giving rise to an action of the fusion semiring of DHR sectors on {K_0({K}_{A})}. Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra.
NASA Astrophysics Data System (ADS)
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
NASA Astrophysics Data System (ADS)
Méliot, Pierre-Loïc
2010-12-01
In this thesis, we investigate the asymptotics of random partitions chosen according to probability measures coming from the representation theory of the symmetric groups S_n and of the finite Chevalley groups GL(n,F_q) and Sp(2n,F_q). More precisely, we prove laws of large numbers and central limit theorems for the q-Plancherel measures of type A and B, the Schur-Weyl measures and the Gelfand measures. Using the RSK algorithm, it also gives results on longest increasing subsequences in random words. We develop a technique of moments (and cumulants) for random partitions, thereby using the polynomial functions on Young diagrams in the sense of Kerov and Olshanski. The algebra of polynomial functions, or observables of Young diagrams is isomorphic to the algebra of partial permutations; in the last part of the thesis, we try to generalize this beautiful construction.
On the similarity of theories of anelastic and scattering attenuation
Wennerberg, L.; Frankel, A.
1989-01-01
We point out basic parallels between theories of anelastic and scattering attenuation. We consider approximations to scattering effects presented by O'Doherty and Anstey (1971), Sato (1982), and Wu (1982). We use the linear theory of anelasticity. We note that the frequency dependence of Q can be related to a distribution of scales of physical properties of the medium. The frequency dependence of anelastic Q is related to the distribution of relaxation times in exactly the same manner as the frequency dependence of scattering Q is related to the distribution of scatterer sizes. Thus, the well-known difficulty of separating scattering from intrinsic attenuation is seen from this point of view as a consequence of the fact that certain observables can be interpreted by identical equations resulting from either of two credible physical theories describing fundamentally different processes. -from Authors
Electromagnetic scattering by magnetic spheres: Theory and algorithms
NASA Astrophysics Data System (ADS)
Milham, Merill E.
1994-10-01
The theory for the scattering of magnetic spheres is developed by means of scaling functions. This theory leads in a natural way to the development of scattering algorithms which use exponential scaling to overcome computational overflow problems. The design and testing of the algorithm is described. Fortran codes which implement the algorithmic design are presented and examples of code use are given. Listings of the code are included.
Multiple Scattering Theory for Inelastic Processes
NASA Astrophysics Data System (ADS)
Braun, V. M.; Shabelski, Yu. M.
The review is devoted to the description of inelastic interactions of composite systems in the framework of the multiple scattering approach. Quasielastic scattering and multiple hadron production processes are considered for hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at high energies. We show that important information on inelastic processes follows on very general grounds from the classification of various intermediate states in the elastic amplitude, as similarly AGK cutting rules arise for reggeon diagrams. Attention is mainly given to the appropriate technique, which is illustrated with several examples of increasing complexity. The general formalism for the inelastic screening corrections is presented and its particular applications to various reactions. The review does not aim at the systematic study of numerous versions of the multiple scattering calculus confronting each other and to the extensive experimental data. Instead, we concentrate on a few simple examples to make clear the underlying physics and to work out the needed machinery employed in practical calculations.
Theory of Thomson scattering in inhomogeneous media
NASA Astrophysics Data System (ADS)
Kozlowski, P. M.; Crowley, B. J. B.; Gericke, D. O.; Regan, S. P.; Gregori, G.
2016-04-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.
Theory of Thomson scattering in inhomogeneous media.
Kozlowski, P M; Crowley, B J B; Gericke, D O; Regan, S P; Gregori, G
2016-01-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems. PMID:27068215
Theory of Thomson scattering in inhomogeneous media
Kozlowski, P. M.; Crowley, B. J. B.; Gericke, D. O.; Regan, S. P.; Gregori, G.
2016-01-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems. PMID:27068215
Scattering theory with localized non-Hermiticities
Znojil, Miloslav
2008-07-15
In the context of the recent interest in solvable models of scattering mediated by non-Hermitian Hamiltonians (cf. H. F. Jones, Phys. Rev. D 76, 125003 (2007)) we show that the well-known variability of the ad hoc choice of the metric {theta} which defines the physical Hilbert space of states can help us to clarify several apparent paradoxes. We argue that with a suitable {theta}, a fully plausible physical picture of the scattering can be recovered. Quantitatively, our new recipe is illustrated on an exactly solvable toy model.
On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
NASA Astrophysics Data System (ADS)
He, Yang-Hui
2002-09-01
In this writing we shall address certain beautiful inter-relations between the construction of 4-dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such as orbifolds, symplectic quotients and quiver representations, as well as the physics, such as gauged linear sigma models, geometrical engineering, Hanany-Witten setups and D-brane probes. We investigate aspects of world-volume gauge dynamics using D-brane resolutions of various Calabi-Yau singularities, notably Gorenstein quotients and toric singularities. Attention will be paid to the general methodology of constructing gauge theories for these singular backgrounds, with and without the presence of the NS-NS B-field, as well as the T-duals to brane setups and branes wrapping cycles in the mirror geometry. Applications of such diverse and elegant mathematics as crepant resolution of algebraic singularities, representation of finite groups and finite graphs, modular invariants of affine Lie algebras, etc. will naturally arise. Various viewpoints and generalisations of McKay's Correspondence will also be considered. The present work is a transcription of excerpts from the first three volumes of the author's PhD thesis which was written under the direction of Prof. A. Hanany - to whom he is much indebted - at the Centre for Theoretical Physics of MIT, and which, at the suggestion of friends, he posts to the ArXiv pro hac vice; it is his sincerest wish that the ensuing pages might be of some small use to the beginning student.
The theory of Enceladus and Dione - An application of computerized algebra in dynamical astronomy
NASA Technical Reports Server (NTRS)
Jefferys, W. H.; Ries, L. M.
1975-01-01
The orbits of the satellites of the outer planets are poorly known, due to lack of attention over the past half century. We have been developing a new theory of Saturn's satellites Enceladus and Dione which is literal (all constants of integration appear explicitly), canonically invariant (the Hori-Lie method is used), and which correctly handles the eccentricity-type resonance between the two satellites. The algebraic manipulations are being performed using the TRIGMAN formula manipulation language, and the programs have been developed so that with minor modifications they can be used on the Mimas-Tethys and Titan-Hyperion systems.
A modified Lax-Phillips scattering theory for quantum mechanics
NASA Astrophysics Data System (ADS)
Strauss, Y.
2015-07-01
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
A modified Lax-Phillips scattering theory for quantum mechanics
Strauss, Y.
2015-07-15
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Scatter Theories and Their Application to Lunar Radar Return
NASA Technical Reports Server (NTRS)
Hayre, H. S.
1961-01-01
The research work being done under this NASA grant is divided into the following three categories: (1) An estimate of the radar return for the NASA Aerobee rocket shot at White Sands Missile Range. (WSMR) (2) Development of new scatter theories, modification and correlation of existing scatter theories, and application of the theories to moon-echo data for estimation of the surface features of the moon. (3) Acoustic modeling of the lunar surface and correlation of the theoretical with both full scale and acoustical experimental results.
ERIC Educational Resources Information Center
Store, Jessie Chitsanzo
2012-01-01
There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…
Multiple-scattering theory for electromagnetic waves
Wang, X. ); Zhang, X. ); Yu, Q.; Harmon, B.N. )
1993-02-15
In this paper, a multiple-scattering formalism for electromagnetic waves is presented. Its application to the three-dimensional periodic dielectric structures is given in a form similar to the usual Korringa-Kohn-Rostoker form of scalar waves. Using this approach, the band-structure results of touching spheres of diamond structure in a dielectric medium with dielectric constant 12.96 are calculated. The application to disordered systems under the coherent-potential approximation is discussed.
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
Reassessment of the theory of stimulated Raman scattering
NASA Technical Reports Server (NTRS)
Fralick, G. C.; Deck, R. T.
1985-01-01
A modification of the standard theory of stimulated Raman scattering (SRS) first proposed by Sparks (1974, 1975) is analyzed and shown to incorporate a possibly important physical effect; however, its original formulation is incorrect. The analysis is based on an exact numerical integration of the coupled equations of the modified theory, the results of which are compared with both the conventional theory of SRS and with one set of experimental data. A reformulation of the modified theory is suggested that leads to a gain which is in somewhat better agreement with the data than is the conventional theory.
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
A Theory of Radar Scattering by the Moon
NASA Technical Reports Server (NTRS)
Senior, T. B. A.; Siegel, K. M.
1959-01-01
A theory is described in which the moon is regarded as a "quasi-smooth" scatterer at radar frequencies. A scattered pulse is then composed of a number of individual returns each of which is provided by a single scattering area. In this manner it is possible to account for all the major features of the pulse, and the evidence in favor of the theory is presented. From a study of the measured power received at different frequencies, it is shown that the scattering area nearest to the earth is the source of a specular return, and it is then possible to obtain information about the material of which the area is composed. The electromagnetic constants are derived and their significance discussed.
Scattering theory approach to electrodynamic Casimir forces
Rahi, Sahand Jamal; Kardar, Mehran; Emig, Thorsten; Graham, Noah; Jaffe, Robert L.
2009-10-15
We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.
Multiphoton-scattering theory and generalized master equations
NASA Astrophysics Data System (ADS)
Shi, Tao; Chang, Darrick E.; Cirac, J. Ignacio
2015-11-01
We develop a scattering theory to investigate the multiphoton transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S matrix of the asymptotic in and out states. For the case of few incident photons in the waveguide, we also rederive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; and (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the fourth one, we show how a quantum emitter can generate entanglement of outgoing photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.
New optimal polynomial theory for NN-scattering
Rijken, T A; Signell, P
1980-01-01
A new optimal polynomial theory for nucleon-nucleon scattering is presented. For the first time in nucleon-nucleon scattering, the derivative amplitudes originally introduced by Fubini, Furlan, and Rosetti are applied. Based on the properties of these amplitudes we introduce K-matrix functions which have suitable analyticity properties as functions of cos theta, where theta is the center of mass scattering angle. The K-matrix functions enable introduction of a new set of functions for which the optimal mapping techniques of Cutkosky, Deo and Ciulli can be applied. Results are shown for proton-proton phase shift analyses at 210 and 330 MeV.
Unified theory of near-field analysis and measurement - Scattering and inverse scattering
NASA Astrophysics Data System (ADS)
Wacker, P. F.
1981-03-01
The scanning procedures of unified theory of near-field analysis and measurement are adapted to the determination of scattering patterns of electromagnetic and scalar systems from measurements made in the near, intermediate, or far field, with emphasis on high accuracy and efficient data processing. The scanning procedures include spherical, improved plane polar, and many types of plane rectangular, plane radial, and circular cylindrical scanning. Application of group representation to inverse scattering analysis is discussed.
Theory of direct scattering of neutral and charged atoms
NASA Technical Reports Server (NTRS)
Franco, V.
1979-01-01
The theory for direct elastic and inelastic collisions between composite atomic systems formulated within the framework of the Glauber approximation is presented. It is shown that the phase-shift function is the sum of a point Coulomb contribution and of an expression in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase shift function. The scattering amplitude is reexpressed, the pure Coulomb scattering in the case of elastic collisions between ions is isolated, and the exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account some multiple collisions. The approximate optical profile function terms corresponding to interactions involving one and two electrons are obtained in forms of Meijer G functions and as a one-dimensional integral, and for collisions involving one or two neutral atoms, the scattering amplitude is further reduced to a simple closed-form expression.
Steady-state current transfer and scattering theory.
Ben-Moshe, Vered; Rai, Dhurba; Skourtis, Spiros S; Nitzan, Abraham
2010-08-01
The correspondence between the steady-state theory of current transfer and scattering theory in a system of coupled tight-binding models of one-dimensional wires is explored. For weak interwire coupling both calculations give nearly identical results, except at singular points associated with band edges. The effect of decoherence in each of these models is studied using a generalization of the Liouville-von Neuman equation suitable for steady-state situations. An example of a single impurity model is studied in detail, leading to a lattice model of scattering off target that affects both potential scattering and decoherence. For an impurity level lying inside the energy band, the transmission coefficient diminishes with increasing dephasing rate, while the opposite holds for impurity energy outside the band. The efficiency of current transfer in the coupled wire system decreases with increasing dephasing. PMID:20707524
Topics in electromagnetic, acoustic, and potential scattering theory
NASA Astrophysics Data System (ADS)
Nuntaplook, Umaporn
With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of
Theory of raman scattering from molecules adsorbed at semiconductor surfaces
NASA Astrophysics Data System (ADS)
Ueba, H.
1983-09-01
A theory is presented to calculate the Raman polarizability of an adsorbed molecule at a semiconductor surface, where the electronic excitation in the molecular site interacts with excitons (elementary excitations in the semiconductor) through non-radiative energy transfer between them, in an intermediate state in the Raman scattering process. The Raman polarizability thus calculated is found to exhibit a peak at the energy corresponding to a resonant excitation of excitons, thereby suggesting the possibility of surface enhanced Raman scattering on semiconductor surfaces. The mechanism studied here can also give an explanation of a recent observation of the Raman excitation profiles of p-NDMA and p-DMAAB adsorbed on ZnO or TiO 2, where those profiles were best described by assuming a resonant intermediate state of the exciton transition in the semiconductors. It is also demonstrated that in addition to vibrational Raman scattering, excitonic Raman scattering of adsorbed molecules will occur in the coupled molecule-semiconductor system, where the molecular returns to its ground electronic state by leaving an exciton in the semiconductor. A spectrum of the excitonic Raman scattering is expected to appear in the background of the vibrational Raman band and to be characterized by the electronic structure of excitons. A desirable experiment is suggested for an examination of the theory.
Scattering Theory Calculations of Casimir Energies at High Curvature
NASA Astrophysics Data System (ADS)
Graham, Noah; Emig, Thorsten; Forrow, Aden; Jaffe, Robert; Kardar, Mehran; Maghrebi, Mohammad; Rahi, Jamal; Shpunt, Alex
2013-03-01
Scattering theory provides a powerful tool for capturing the response of an object to electromagnetic charge and field fluctuations. Techniques based on scattering theory have made possible a wide range of new calculations of Casimir energies. In this approach, the Casimir interaction energy for a collection of objects can be expressed in terms of the scattering T-matrices for each object individually, combined with universal translation matrices describing the objects' relative positions and orientations. These translation matrices are derived from an expansion of the free Green's function in an appropriate coordinate system, independent of the details of the objects themselves. This method proves particularly valuable for geometries involving high curvature, such as edges and tips. I will describe this approach in general terms and then give results from several problems to which it has been applied successfully. I will also discuss new developments in scattering theory that have been motivated by these problems. I would like to request that this abstract be part of a session on Casimir physics. Supported by the National Science Foundation, the US Department of Energy, the Defense Advanced Research Projects Agency, and the Deutsche Forschungsgemeinschaft
NASA Astrophysics Data System (ADS)
Putnam, Ian F.
2010-03-01
We investigate the C*-algebras associated to aperiodic structures called model sets obtained by the cut-and-project method. These C*-algebras are Morita equivalent to crossed product C*-algebras obtained from dynamics on a disconnected version of the internal space. This construction may be made from more general data, which we call a hyperplane system. From a hyperplane system, others may be constructed by a process of reduction and we show how the C*-algebras involved are related to each other. In particular, there are natural elements in the Kasparov KK-groups for the C*-algebra of a hyperplane system and that of its reduction. The induced map on K-theory fits in a six-term exact sequence. This provides a new method of the computation of the K-theory of such C*-algebras which is done completely in the setting of non-commutative geometry.
Effective Field Theories from Soft Limits of Scattering Amplitudes.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist. PMID:26196613
Four loop scattering in the Nambu-Goto theory
NASA Astrophysics Data System (ADS)
Conkey, Peter; Dubovsky, Sergei
2016-05-01
We initiate the study of multiloop scattering amplitudes in the Nambu-Goto theory on the worldsheet of a non-critical string. We start with a brute force calculation of two loop four particle scattering. Somewhat surprisingly, even though non-trivial UV counterterms are present at this order, on-shell amplitudes remain polynomial in the momenta of colliding particles. We show that this can be understood as a consequence of existence of certain close by (semi)integrable models. Furthermore, these arguments can be extended to obtain the answer for three and four loop scattering, bypassing the brute force calculation. The resulting amplitudes develop non-polynomial (logarithmic) dependence on the momenta starting at three loops.
Radar scattering from the summer polar mesosphere: Theory and observations
Cho, J.Y.N.
1993-01-01
The anomalously large radar reflectivities observed in the summer polar mesosphere have eluded satisfactory explanation until now. The author proposes that the following chain of causality is responsible for the so-called polar mesosphere summer echoes (PMSE): The uniquely low temperature in the summer mesopause produce ice aerosols. Because the aerosols exist in a plasma, they become electrically charged. The ambient electrons become coupled to the aerosols through electric fields and their effective diffusivity is retarded due to the large size of the aerosols. The reduction in diffusivity allows electron density inhomogeneities to be maintained at the radar Bragg scales. The radar waves are then scattered by the inhomogeneities. The above concept is supported by developing a quantitative theory of ambipolar diffusion in the mesosphere. The results to isotropic turbulence and Fresnel radar scatter are applied to show that the observed radar reflectivities can be explained by the theory. It is shown that the presence of realistic charged aerosols are sufficient to explain PMSE. The author also shows that dressed aerosol radar scatter can only apply to echoes detected by UHF radars. The data is taken with the Sondrestrom 1.29-GHz radar and attribute it to dressed aerosol scatter. The author used the Cornell University portable radar interferometer (CUPRI) to observe the mesosphere while rockets carrying in situ sensors were flown through two PMSE occurrences and a noctilucent cloud/PMSE event. The first simultaneous height comparison between noctilucent clouds and PMSE show that the radar scattering region was near or slightly above the visible cloud layer. The author also infers from aspect sensitivity measurements and Doppler spectrograms that there were two distinct types of PMSE: Enhanced turbulent scatter and partial (Fresnel) reflection from steep edges in the electron density. Both mechanisms require an anomalously low electron diffusion coefficient.
A microscopic, coupled-channel theory of pion scattering
Kagarlis, M.A.; Johnson, M.B.; Fortune, H.T.
1995-05-15
The authors develop a new and comprehensive coordinate-space theory of pion-nucleus scattering to facilitate disentangling the conventional aspects of pion scattering from the non-conventional ones relevant to issues of hadron dynamics. They work in coordinate space in order to both unify and extend the relatively extensive and successful analyses of exclusive pion-nucleus reactions previously made within a similar framework. They construct the optical potential microscopically in shell-model framework by summing particle-hole pair configurations, leading naturally to a coupled-channel formulation. The theory includes a complete treatment of all spin-isospin components of the pion-nucleon scattering amplitude, and Fermi averaging is done explicitly. The authors present numerical results showing the significance of Fermi motion and spin dependence on charge-exchange angular distributions: Single and double spin flip are shown to play dominant and generally unappreciated roles in charge-exchange reactions, and corrections for Fermi motion are shown to be needed in order to quantitatively separate medium effects from conventional multiple scattering. 72 refs., 11 figs.
Effective Field Theories from Soft Limits of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-01
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
Theory and phenomenology of coherent neutrino-nucleus scattering
McLaughlin, Gail
2015-07-15
We review the theory and phenomenology of coherent elastic neutrino-nucleus scattering (CEνNS). After a brief introduction, we summarize the places where CEνNS is already in use and then turn to future physics opportunities from CEνNS. CEνNS has been proposed as a way to limit or discover beyond the standard model physics, measure the nuclear-neutron radius and constrain the Weinberg angle.
Benchmark calculations of thermal reaction rates. I - Quantal scattering theory
NASA Technical Reports Server (NTRS)
Chatfield, David C.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
The thermal rate coefficient for the prototype reaction H + H2 yields H2 + H with zero total angular momentum is calculated by summing, averaging, and numerically integrating state-to-state reaction probabilities calculated by time-independent quantum-mechanical scattering theory. The results are very carefully converged with respect to all numerical parameters in order to provide high-precision benchmark results for confirming the accuracy of new methods and testing their efficiency.
Hybrid theory and calculation of e-N2 scattering
NASA Technical Reports Server (NTRS)
Chandra, N.; Temkin, A.
1976-01-01
A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.
ERIC Educational Resources Information Center
Senarat, Somprasong; Tayraukham, Sombat; Piyapimonsit, Chatsiri; Tongkhambanjong, Sakesan
2013-01-01
The purpose of this research is to develop a multidimensional computerized adaptive test for diagnosing the cognitive process of grade 7 students in learning algebra by applying multidimensional item response theory. The research is divided into 4 steps: 1) the development of item bank of algebra, 2) the development of the multidimensional…
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L_{max} = (l,m)_{max}, while scattering matrices, which determine spectral properties, are truncated at L_{tr} = (l,m)_{tr} where phase shifts δl>l_{tr} are negligible. Historically, L_{max} is set equal to L_{tr}, which is correct for large enough L_{max} but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L_{max} > L_{tr} with δl>l_{tr} set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R^{3} process with rank N(l_{tr} + 1)^{2}] and includes higher-L contributions via linear algebra [R^{2} process with rank N(l_{max} +1)^{2}]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1_{0} CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L_{max} for a given L_{tr}.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang andmore » Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.« less
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
NASA Astrophysics Data System (ADS)
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-01
The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.
An effective field theory for forward scattering and factorization violation
NASA Astrophysics Data System (ADS)
Rothstein, Ira Z.; Stewart, Iain W.
2016-08-01
Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where | t| ≪ s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude's rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to
NASA Technical Reports Server (NTRS)
Schwenke, David W.; Mladenovic, Mirjana; Zhao, Meishan; Truhlar, Donald G.; Sun, Yan
1988-01-01
The computational steps in calculating quantum mechanical reactive scattering amplitudes by the L2 generalized Newton variational principle are discussed with emphasis on computational strategies and recent improvements that make the calculations more efficient. Special emphasis is placed on quadrature techniques, storage management strategies, use of symmetry, and boundary conditions. It is concluded that an efficient implementation of these procedures provides a powerful algorithm for the accurate solution of the Schroedinger equation for rearrangements.
Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds.
Farrell, F T; Jones, L E
1986-08-01
Among other results, we rationally calculate the algebraic K-theory of any discrete cocompact subgroup of a Lie group G, where G is either O(n, 1), U(n, 1), Sp(n, 1), or F(4), in terms of the homology of the double coset space Gamma\\G/K, where K is a maximal cocompact subgroup of G. We obtain the formula K(n)(ZGamma) [unk] [unk] congruent with [unk](i=0) (infinity)H(i)(Gamma\\G/K; [unk](n-i)), where [unk](j) is a stratified system of Q vector spaces over Gamma\\G/K and the vector space [unk](j)(GammagK) corresponding to the double coset GammagK is isomorphic to K(J)(Z(Gamma [unk] gKg(-1))) [unk] Q. Note Gamma [unk] gKg(-1) is a finite subgroup of Gamma. Earlier, a similar formula for discrete cocompact subgroups Gamma of the group of rigid motions of Euclidean space was conjectured by F. T. Farrell and W. C. Hsiang and proven by F. Quinn. PMID:16593733
Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds
Farrell, F. T.; Jones, L. E.
1986-01-01
Among other results, we rationally calculate the algebraic K-theory of any discrete cocompact subgroup of a Lie group G, where G is either O(n, 1), U(n, 1), Sp(n, 1), or F4, in terms of the homology of the double coset space Γ\\G/K, where K is a maximal cocompact subgroup of G. We obtain the formula Kn(ZΓ) [unk] [unk] ≅ [unk]i=0∞Hi(Γ\\G/K; [unk]n-i), where [unk]j is a stratified system of Q vector spaces over Γ\\G/K and the vector space [unk]j(ΓgK) corresponding to the double coset ΓgK is isomorphic to KJ(Z(Γ [unk] gKg-1)) [unk] Q. Note Γ [unk] gKg-1 is a finite subgroup of Γ. Earlier, a similar formula for discrete cocompact subgroups Γ of the group of rigid motions of Euclidean space was conjectured by F. T. Farrell and W. C. Hsiang and proven by F. Quinn. PMID:16593733
Hard-core lattice bosons: new insights from algebraic graph theory
NASA Astrophysics Data System (ADS)
Squires, Randall W.; Feder, David L.
2014-03-01
Determining the characteristics of hard-core lattice bosons is a problem of long-standing interest in condensed matter physics. While in one-dimensional systems the ground state can be formally obtained via a mapping to free fermions, various properties (such as correlation functions) are often difficult to calculate. In this work we discuss the application of techniques from algebraic graph theory to hard-core lattice bosons in one dimension. Graphs are natural representations of many-body Hamiltonians, with vertices representing Fock basis states and edges representing matrix elements. We prove that the graphs for hard-core bosons and non-interacting bosons have identical connectivity; the only difference is the existence of edge weights. A formal mapping between the two is therefore possible by manipulating the graph incidence matrices. We explore the implications of these insights, in particular the intriguing possibility that ground-state properties of hard-core bosons can be calculated directly from those of non-interacting bosons.
S-duality and the prepotential of N={2}^{star } theories (II): the non-simply laced algebras
NASA Astrophysics Data System (ADS)
Billó, M.; Frau, M.; Fucito, F.; Lerda, A.; Morales, J. F.
2015-11-01
We derive a modular anomaly equation satisfied by the prepotential of the N={2}^{star } supersymmetric theories with non-simply laced gauge algebras, including the classical B r and C r infinite series and the exceptional F 4 and G 2 cases. This equation determines the exact prepotential recursively in an expansion for small mass in terms of quasi-modular forms of the S-duality group. We also discuss the behaviour of these theories under S-duality and show that the prepotential of the SO(2 r + 1) theory is mapped to that of the Sp(2 r) theory and viceversa, while the exceptional F 4 and G 2 theories are mapped into themselves (up to a rotation of the roots) in analogy with what happens for the N=4 supersymmetric theories. These results extend the analysis for the simply laced groups presented in a companion paper.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
NASA Astrophysics Data System (ADS)
Khudaverdian, H. M.
2014-03-01
We consider differential operators acting on densities of arbitrary weights on manifold M identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special subalgebra of functions on extended manifold . On one hand there is a canonical lift of projective structures on M to affine structures on extended manifold . On the other hand the restriction of algebra of all functions on extended manifold to this special subalgebra of functions implies the canonical scalar product. This leads in particular to classification of second order operators with use of Kaluza-Klein-like mechanisms.
Theory of high-energy electron scattering by composite targets
Coester, F.
1988-01-01
The emphasis of these expository lectures is on the role of relativistic invariance and the unity of the theory for medium and high energies. Sec. 2 introduces the kinematic notation and provides an elementary derivation of the general cross section. The relevant properties of the Poincare group and the transformation properties of current operators and target states are described in Sec 3. In Sec. 4 representations of target states with kinematic light-front symmetry are briefly discussed. The focus is on two applications. An impulse approximation of inclusive electron nucleus scattering at both medium and high energies. A parton model of the proton applied to deep inelastic scattering of polarized electrons by polarized protons. 19 refs.
WLWL scattering in Higgsless models: Identifying better effective theories
NASA Astrophysics Data System (ADS)
Belyaev, Alexander S.; Chivukula, R. Sekhar; Christensen, Neil D.; He, Hong-Jian; Kurachi, Masafumi; Simmons, Elizabeth H.; Tanabashi, Masaharu
2009-09-01
The three-site model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this paper we analyze how well the three-site model performs as a general exemplar of Higgsless models in describing WLWL scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. We show that the size of the four-point vertex for the (unphysical) Nambu-Goldstone modes and the degree to which the sum rules are saturated by contributions from the lowest-lying Kaluza-Klein resonances both provide good measures of the extent to which a highly deconstructed theory can accurately describe the low-energy physics of a continuum 5D Higgsless model. After comparing the three-site model to flat and warped continuum models, we analyze extensions of the three-site model to a longer open linear moose with an additional U(1) group and to a ring (“breaking electroweak symmetry strongly” or “hidden local symmetry”) model with three sites and three links. Both cases may be readily analyzed in the framework of the general sum rules. We demonstrate that WLWL scattering in the ring model can very closely approximate scattering in the continuum models, provided that the hidden local symmetry parameter a is chosen to mimic ρ-meson dominance of ππ scattering in QCD. The hadron and lepton collider phenomenology of both extended models is briefly discussed, with a focus on the complementary information to be gained from precision measurements of the Z' line shape and ZWW coupling at a high-energy lepton collider.
Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory
NASA Astrophysics Data System (ADS)
Hoefel, Eduardo; Livernet, Muriel
2012-08-01
Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.
Oblique Alfvén Solitons and Inverse Scattering Theory
NASA Astrophysics Data System (ADS)
Wheeler, H. R., IV; Reynolds, M. A.; Hamilton, R.
2014-12-01
Solitary wave structures observed by the Ulysses spacecraft in the solar wind were analyzed using both inverse scattering theory as well as direct numerical integration of the derivative nonlinear Schrödinger (DNLS) equation. Several of these structures were found to be consistent with soliton solutions of the DNLS equation. Such solitary structures have been commonly observed in the space plasma environment and may, in fact, be long-lived solitons. While the generation of these solitons may be due to an instability mechanism, e.g., the mirror instability, they may be observable far from the source region due to their coherent nature.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Application of a scattering theory of VHF transequatorial propagation
NASA Astrophysics Data System (ADS)
Ferguson, J. A.
1984-08-01
Numerical application is made of the theory of scattering by long, curved, field-aligned irregularities of ionization density in the F-region developed by Ferguson and Booker (1983). Using an intermediate-scale regime of irregularities with an outer scale equal to the scale height of the F-region and an inner scale equal to the ion gyroradius, combined with a small-scale regime with an outer scale equal to the ionic gyroradius and an inner scale equal to the electron gyroradius, calculations are made corresponding to (1) equatorial spread-F in the VHF and UHF bands, (2) long-range transequatorial propagation of the type observed by Nielson, and (3) short-range transequatorial propagation of the type observed by Cohen and Bowles. The same ionospheric model yields field-strengths of the right order of magnitude in all three cases. The theory also predicts a focusing phenomenon that should be looked for experimentally.
Classical theory of rotational rainbow scattering from uncorrugated surfaces.
Khodorkovsky, Yuri; Averbukh, Ilya Sh; Pollak, Eli
2010-08-01
A classical perturbation theory is developed to study rotational rainbow scattering of molecules from uncorrugated frozen surfaces. Considering the interaction of the rigid rotor with the translational motion towards the surface to be weak allows for a perturbative treatment, in which the known zeroth order motion is that of a freely rotating molecule hitting a surface. Using perturbation theory leads to explicit expressions for the angular momentum deflection function with respect to the initial orientational angle of the rotor that are valid for any magnitude of the initial angular momentum. The rotational rainbows appear as peaks both in the final angular momentum and rotational energy distributions, as well as peaks in the angular distribution, although the surface is assumed to be uncorrugated. The derived analytic expressions are compared with numerical simulation data. Even when the rotational motion is significantly coupled to the translational motion, the predictions of the perturbative treatment remain qualitatively correct. PMID:21399336
NASA Technical Reports Server (NTRS)
Weatherford, Charles A.
1993-01-01
One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.
Electron Scattering from Neon Via Effective Range Theory
NASA Astrophysics Data System (ADS)
Fedus, Kamil
2014-12-01
Elastic cross-sections for electron scattering on neon from 0 energy up to 16 eV are analyzed by an analytical approach to the modified effective range theory (MERT). It is shown that energy and angular variations of elastic differential, integral and momentum transfer cross-sections can be accurately parameterized by six MERT coefficients up to the energy threshold for the first Feshbach resonance. MERT parameters are determined empirically by numerical comparison with large collection of available experimental data of elastic total (integral) cross-sections. The present analysis is validated against numerous electron beams and swarm experiments. The comparison of derived MERT parameters with those found for other noble gases, helium, argon and krypton, is done. The derived scattering length (for the s-partial wave) in neon, 0.227 a 0, agrees well with recent theories; it is small but, differently from Ar and Kr, still positive. Analogue parameters for the p-wave and the d-wave are negative and positive respectively for all the four gases compared.
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
NASA Astrophysics Data System (ADS)
Dzheparov, F. S.; Lvov, D. V.
2016-02-01
Multiple small-angle neutron scattering by a high-density system of inhomogeneities has been considered. A combined approach to the analysis of multiple small-angle neutron scattering has been proposed on the basis of the synthesis of the Zernike-Prince and Moliére formulas. This approach has been compared to the existing multiple small-angle neutron scattering theory based on the eikonal approximation. This comparison has shown that the results in the diffraction limit coincide, whereas differences exist in the refraction limit because the latter theory includes correlations between successive scattering events. It has been shown analytically that the existence of correlations in the spatial position of scatterers results in an increase in the number of unscattered neutrons. Thus, the narrowing of spectra of multiple small-angle neutron scattering observed experimentally and in numerical simulation has been explained.
NASA Astrophysics Data System (ADS)
Milham, Merrill E.
1994-10-01
In this report, relevant parts of the scattering theory for magnetic spheres are presented. Mass extinction coefficients, and the lognormal size distribution are defined. The theory and algorithms for integrating scattering parameters over size distributions are developed. The integrations are carried out in terms of dimensionless scattering, and size distribution parameters, which are simply related to the usual mass scattering coefficients. Fortran codes, which implement the algorithmic design, are presented, and examples of code use are given. Code listings are included.
Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.
Meair, Jonathan; Jacquod, Philippe
2013-02-27
We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance. PMID:23343784
Siegert pseudostate formulation of scattering theory: General three-dimensional case
NASA Astrophysics Data System (ADS)
Krainov, Lev O.; Batishchev, Pavel A.; Tolstikhin, Oleg I.
2016-04-01
This paper generalizes the Siegert pseudostate (SPS) formulation of scattering theory to arbitrary finite-range potentials without any symmetry in the three-dimensional (3D) case. The orthogonality and completeness properties of 3D SPSs are established. The SPS expansions for scattering states, outgoing-wave Green's function, scattering matrix, and scattering amplitude, that is, all major objects of scattering theory, are derived. The theory is illustrated by calculations for several model potentials. The results enable one to apply 3D SPSs as a purely discrete basis capable of representing both discrete and continuous spectra in solving various stationary and time-dependent quantum-mechanical problems.
Unified connected theory of few-body reaction mechanisms in N-body scattering theory
NASA Technical Reports Server (NTRS)
Polyzou, W. N.; Redish, E. F.
1978-01-01
A unified treatment of different reaction mechanisms in nonrelativistic N-body scattering is presented. The theory is based on connected kernel integral equations that are expected to become compact for reasonable constraints on the potentials. The operators T/sub +-//sup ab/(A) are approximate transition operators that describe the scattering proceeding through an arbitrary reaction mechanism A. These operators are uniquely determined by a connected kernel equation and satisfy an optical theorem consistent with the choice of reaction mechanism. Connected kernel equations relating T/sub +-//sup ab/(A) to the full T/sub +-//sup ab/ allow correction of the approximate solutions for any ignored process to any order. This theory gives a unified treatment of all few-body reaction mechanisms with the same dynamic simplicity of a model calculation, but can include complicated reaction mechanisms involving overlapping configurations where it is difficult to formulate models.
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.; Cabrera, B.; Cerdeño, D. G.; Mandic, V.; Rogers, H. E.; Agnese, R.; Anderson, A. J.; Asai, M.; Balakishiyeva, D.; Barker, D.; et al
2015-05-18
We examine the consequences of the effective field theory (EFT) of dark matter-nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. Here. we demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. In conclusion, we discussmore » the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.« less
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.
2015-05-01
We examine the consequences of the effective field theory (EFT) of dark matter–nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implicationsmore » of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.« less
Imaging Internal Structure of Long Bones Using Wave Scattering Theory.
Zheng, Rui; Le, Lawrence H; Sacchi, Mauricio D; Lou, Edmond
2015-11-01
An ultrasonic wavefield imaging method is developed to reconstruct the internal geometric properties of long bones using zero-offset data acquired axially on the bone surface. The imaging algorithm based on Born scattering theory is implemented with the conjugate gradient iterative method to reconstruct an optimal image. In the case of a multilayered velocity model, ray tracing through a smooth medium is used to calculate the traveled distance and traveling time. The method has been applied to simulated and real data. The results indicate that the interfaces of the top cortex are accurately imaged and correspond favorably to the original model. The reconstructed bottom cortex below the marrow is less accurate mainly because of the low signal-to-noise ratio. The current imaging method has successfully recovered the top cortical layer, providing a potential tool to investigate the internal structures of long bone cortex for osteoporosis assessment. PMID:26299684
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.; Cabrera, B.; Cerdeno, D. G.; Mandic, V.; Rogers, H. E.; Agnese, R.; Anderson, A. J.; Asai, M.; Balakishiyeva, D.; Barker, D.; Basu Thakur, R.; Bauer, D. A.; Billard, J.; Borgland, A.; Brandt, D.; Brink, P. L.; Bunker, R.; Caldwell, D. O.; Calkins, R.; Chagani, H.; Chen, Y.; Cooley, J.; Cornell, B.; Crewdson, C. H.; Cushman, Priscilla B.; Daal, M.; Di Stefano, P. C.; Doughty, T.; Esteban, L.; Fallows, S.; Figueroa-Feliciano, E.; Godfrey, G. L.; Golwala, S. R.; Hall, Jeter C.; Harris, H. R.; Hofer, T.; Holmgren, D.; Hsu, L.; Huber, M. E.; Jardin, D. M.; Jastram, A.; Kamaev, O.; Kara, B.; Kelsey, M. H.; Kennedy, A.; Leder, A.; Loer, B.; Lopez Asamar, E.; Lukens, W.; Mahapatra, R.; McCarthy, K. A.; Mirabolfathi, N.; Moffatt, R. A.; Morales Mendoza, J. D.; Oser, S. M.; Page, K.; Page, W. A.; Partridge, R.; Pepin, M.; Phipps, A.; Prasad, K.; Pyle, M.; Qiu, H.; Rau, W.; Redl, P.; Reisetter, A.; Ricci, Y.; Roberts, A.; Saab, T.; Sadoulet, B.; Sander, J.; Schnee, R. W.; Scorza, S.; Serfass, B.; Shank, B.; Speller, D.; Toback, D.; Upadhyayula, S.; Villano, A. N.; Welliver, B.; Wilson, J. S.; Wright, D. H.; Yang, X.; Yellin, S.; Yen, J. J.; Young, B. A.; Zhang, J.
2015-05-01
We examine the consequences of the effective eld theory (EFT) of dark matter-nucleon scattering or current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral di*erences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.
2015-05-01
We examine the consequences of the effective field theory (EFT) of dark matter–nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.; Cabrera, B.; Cerdeño, D. G.; Mandic, V.; Rogers, H. E.; Agnese, R.; Anderson, A. J.; Asai, M.; Balakishiyeva, D.; Barker, D.; Basu Thakur, R.; Bauer, D. A.; Billard, J.; Borgland, A.; Brandt, D.; Brink, P. L.; Bunker, R.; Caldwell, D. O.; Calkins, R.; Chagani, H.; Chen, Y.; Cooley, J.; Cornell, B.; Crewdson, C. H.; Cushman, P.; Daal, M.; Di Stefano, P. C. F.; Doughty, T.; Esteban, L.; Fallows, S.; Figueroa-Feliciano, E.; Godfrey, G. L.; Golwala, S. R.; Hall, J.; Harris, H. R.; Hofer, T.; Holmgren, D.; Hsu, L.; Huber, M. E.; Jardin, D. M.; Jastram, A.; Kamaev, O.; Kara, B.; Kelsey, M. H.; Kennedy, A.; Leder, A.; Loer, B.; Lopez Asamar, E.; Lukens, P.; Mahapatra, R.; McCarthy, K. A.; Mirabolfathi, N.; Moffatt, R. A.; Morales Mendoza, J. D.; Oser, S. M.; Page, K.; Page, W. A.; Partridge, R.; Pepin, M.; Phipps, A.; Prasad, K.; Pyle, M.; Qiu, H.; Rau, W.; Redl, P.; Reisetter, A.; Ricci, Y.; Roberts, A.; Saab, T.; Sadoulet, B.; Sander, J.; Schnee, R. W.; Scorza, S.; Serfass, B.; Shank, B.; Speller, D.; Toback, D.; Upadhyayula, S.; Villano, A. N.; Welliver, B.; Wilson, J. S.; Wright, D. H.; Yang, X.; Yellin, S.; Yen, J. J.; Young, B. A.; Zhang, J.
2015-05-18
We examine the consequences of the effective field theory (EFT) of dark matter-nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. Here. we demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. In conclusion, we discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Virtual Compton scattering off the nucleon in chiral perturbation theory
Hemmert, T.R.; Holstein, B.R.; Knoechlein, G.; Scherer, S.
1997-03-01
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg`s power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry, and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compare our expansion with the multipole expansion by Guichon, Liu, and Thomas. We establish the connection of our calculation with the generalized polarizabilities of the nucleon where it is possible. {copyright} {ital 1997} {ital The American Physical Society}
Covariant Spectator Theory of np scattering: Isoscalar interaction currents
Gross, Franz L.
2014-06-01
Using the Covariant Spectator Theory (CST), one boson exchange (OBE) models have been found that give precision fits to low energy $np$ scattering and the deuteron binding energy. The boson-nucleon vertices used in these models contain a momentum dependence that requires a new class of interaction currents for use with electromagnetic interactions. Current conservation requires that these new interaction currents satisfy a two-body Ward-Takahashi (WT), and using principals of {\\it simplicity\\/} and {\\it picture independence\\/}, these currents can be uniquely determined. The results lead to general formulae for a two-body current that can be expressed in terms of relativistic $np$ wave functions, ${\\it \\Psi}$, and two convenient truncated wave functions, ${\\it \\Psi}^{(2)}$ and $\\widehat {\\it \\Psi}$, which contain all of the information needed for the explicit evaluation of the contributions from the interaction current. These three wave functions can be calculated from the CST bound or scattering state equations (and their off-shell extrapolations). A companion paper uses this formalism to evaluate the deuteron magnetic moment.
ERIC Educational Resources Information Center
Bair, Sherry L.; Rich, Beverly S.
2011-01-01
This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…
Theory and Measurement of Partially Correlated Persistent Scatterers
NASA Astrophysics Data System (ADS)
Lien, J.; Zebker, H. A.
2011-12-01
Interferometric synthetic aperture radar (InSAR) time-series methods can effectively estimate temporal surface changes induced by geophysical phenomena. However, such methods are susceptible to decorrelation due to spatial and temporal baselines (radar pass separation), changes in orbital geometries, atmosphere, and noise. These effects limit the number of interferograms that can be used for differential analysis and obscure the deformation signal. InSAR decorrelation effects may be ameliorated by exploiting pixels that exhibit phase stability across the stack of interferograms. These so-called persistent scatterer (PS) pixels are dominated by a single point-like scatterer that remains phase-stable over the spatial and temporal baseline. By identifying a network of PS pixels for use in phase unwrapping, reliable deformation measurements may be obtained even in areas of low correlation, where traditional InSAR techniques fail to produce useful observations. PS identification is challenging in natural terrain, due to low reflectivity and few corner reflectors. Shanker and Zebker [1] proposed a PS pixel selection technique based on maximum-likelihood estimation of the associated signal-to-clutter ratio (SCR). In this study, we further develop the underlying theory for their technique, starting from statistical backscatter characteristics of PS pixels. We derive closed-form expressions for the spatial, rotational, and temporal decorrelation of PS pixels as a function of baseline and signal-to-clutter ratio. We show that previous decorrelation and critical baseline expressions [2] are limiting cases of our result. We then describe a series of radar scattering simulations and show that the simulated decorrelation matches well with our analytic results. Finally, we use our decorrelation expressions with maximum-likelihood SCR estimation to analyze an area of the Hayward Fault Zone in the San Francisco Bay Area. A series of 38 images of the area were obtained from C
Pseudorational Impulse Responses — Algebraic System Theory for Distributed Parameter Systems
NASA Astrophysics Data System (ADS)
Yamamoto, Yutaka
This paper gives a comprehensive account on a class of distributed parameter systems, whose impulse response is called pseudorational. This notion was introduced by the author in 1980's, and is particularly amenable for the study of systems with bounded-time memory. We emphasize algebraic structures induced by this class of systems. Some recent results on coprimeness issues and H∞ control are discussed and illustrated.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
High-energy scatterings in infinite-derivative field theory and ghost-free gravity
NASA Astrophysics Data System (ADS)
Talaganis, Spyridon; Mazumdar, Anupam
2016-07-01
In this paper, we will consider scattering diagrams in the context of infinite-derivative theories. First, we examine a finite-order, higher-derivative scalar field theory and find that we cannot eliminate the growth of scattering diagrams for large external momenta. Then, we employ an infinite-derivative scalar toy model and obtain that the external momentum dependence of scattering diagrams is convergent as the external momenta become very large. In order to eliminate the external momentum growth, one has to dress the bare vertices of the scattering diagrams by considering renormalised propagator and vertex loop corrections to the bare vertices. Finally, we investigate scattering diagrams in the context of a scalar toy model which is inspired by a ghost-free and singularity-free infinite-derivative theory of gravity, where we conclude that infinite derivatives can eliminate the external momentum growth of scattering diagrams and make the scattering diagrams convergent in the ultraviolet.
Field-theoretical description of deep inelastic scattering
Geyer, B.; Robaschik, D.; Wieczorek, E.
1980-01-01
The most important theoretical notions concerning deep inelastic scattering are reviewed. Topics discussed are the model-independent approach, which is based on the general principles of quantum field theory, the application of quantum chromodynamics to deep inelastic scattering, approaches based on the quark--parton model, the light cone algebra, and conformal invariance, and also investigations in the framework of perturbation theory.
Yoshida, Ken-ichi; Itoh, Tamitake; Biju, Vasudevanpillai; Ishikawa, Mitsuru; Ozaki, Yukihiro
2009-02-15
We examined an electromagnetic (EM) theory of surface-enhanced resonance Raman scattering (SERRS) using single Ag nanoaggregates. The SERRS-EM theory is characterized by twofold EM enhancement induced by the coupling of plasmon resonance with both excitation and emission of Raman scattering plus fluorescence. The total emission cross-section spectra of enhanced Raman scattering and enhanced fluorescence were calculated using the following parameters: the spectrum of enhancement factor induced by plasmon resonance, resonance Raman scattering overlapped with fluorescence, and excitation wavelengths. The calculations well agreed with experimental total emission cross-section spectra, thus providing strong indications that the SERRS-EM theory is quantitatively correct.
Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media
Tong Zhisong; Korotkova, Olga
2010-09-15
The theory of scattering of scalar stochastic fields from deterministic and random media is generalized to the electromagnetic domain under the first-order Born approximation. The analysis allows for determining the changes in spectrum, coherence, and polarization of electromagnetic fields produced on their propagation from the source to the scattering volume, interaction with the scatterer, and propagation from the scatterer to the far field. An example of scattering of a field produced by a {delta}-correlated partially polarized source and scattered from a {delta}-correlated medium is provided.
Modern integral equation techniques for quantum reactive scattering theory
Auerbach, S.M.
1993-11-01
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Average wavefunction method for multiple scattering theory and applications
Singh, H.
1985-01-01
A general approximation scheme, the average wavefunction approximation (AWM), applicable to scattering of atoms and molecules off multi-center targets, is proposed. The total potential is replaced by a sum of nonlocal, separable interactions. Each term in the sum projects the wave function onto a weighted average in the vicinity of a given scattering center. The resultant solution is an infinite order approximation to the true solution, and choosing the weighting function as the zeroth order solution guarantees agreement with the Born approximation to second order. In addition, the approximation also becomes increasingly more accurate in the low energy long wave length limit. A nonlinear, nonperturbative literature scheme for the wave function is proposed. An extension of the scheme to multichannel scattering suitable for treating inelastic scattering is also presented. The method is applied to elastic scattering of a gas off a solid surface. The formalism is developed for both periodic as well as disordered surfaces. Numerical results are presented for atomic clusters on a flat hard wall with a Gaussian like potential at each atomic scattering site. The effect of relative lateral displacement of two clusters upon the scattering pattern is shown. The ability of AWM to accommodate disorder through statistical averaging over cluster configuration is illustrated. Enhanced uniform back scattering is observed with increasing roughness on the surface. Finally, the AWM is applied to atom-molecule scattering.
NASA Astrophysics Data System (ADS)
Hong, Sang-Hoon; Wdowinski, Shimon
2012-01-01
Common vegetation scattering theories indicate that short wavelength Synthetic Aperture Radar (SAR) observations (X- and C-band) measure mainly vegetation canopies as the short-wavelength radar signal interacts mostly with upper sections of the vegetation. Furthermore, these theories also suggest that SAR cross- polarization (cross-pol) observations reflect only volume scattering. Consequently most SAR decomposition techniques assume that the cross-pol signal represents solely volume scattering. However, short-wavelength and cross-pol observations from the Everglades wetlands, south Florida, suggest that a significant portion of the SAR signal scatters from the surface and not only from the upper sections of the vegetation. The indication for surface scattering in wetland environment is derived from phase observable processed using interferometric techniques. The interferometric SAR (InSAR) observations reveal coherent phase signal in all polarizations and all wavelengths, reflecting water level changes beneath the vegetation. This coherent phase signal cannot be explained by neither volume scattering nor radar signal interaction with the upper sections of the vegetations, because canopies and branches are frequently move by wind. The only way that such coherent signal can be maintained and represents surface water level changes is when a multiple bounce from the vegetation and surface occurs. The simplest multi-bounce scattering mechanism that generate cross-pol signal occurs by rotated dihedrals. Thus, we use the rotated dihedral mechanism to explain the InSAR wetland observations and to revise the current vegetation scattering theories to accounts also for double bounce component in cross-pol observations.
Path integral formulation of scattering theory with application to scattering by black holes
Zhang, T.R.
1985-01-01
The computational power of Feynman path integrals was exploited. Path-integration formalism for the quantum mechanics scattering and classical wave scattering was generalized. Firstly, the standard WKB approximation was generalized to the cases where the critical points of the action functional are degenerate. Three typical semiclassical scattering features served as examples for a classification of degenerate critical points: conservation laws, rainbows, glories. Secondly, the method developed for non-relativistic quantum mechanics scattering was used in the case of classical wave scattering. Scattering by Schwarzschild black holes was chosen as an example, and WKB cross sections for scalar, vector, and tensor fields were worked out. Finally, 2s-th Bessel function behavior of WKB cross section for helicity-s polarized glory scattering in curved space time was proved.
NASA Astrophysics Data System (ADS)
McLenaghan, Raymond G.; Smirnov, Roman G.; The, Dennis
2004-03-01
We develop a new approach to the study of Killing tensors defined in pseudo-Riemannian spaces of constant curvature that is ideologically close to the classical theory of invariants. The main idea, which provides the foundation of the new approach, is to treat a Killing tensor as an algebraic object determined by a set of parameters of the corresponding vector space of Killing tensors under the action of the isometry group. The spaces of group invariants and conformal group invariants of valence two Killing tensors defined in the Minkowski plane are described. The group invariants, which are the generators of the space of invariants, are applied to the problem of classification of orthogonally separable Hamiltonian systems defined in the Minkowski plane. Transformation formulas to separable coordinates expressed in terms of the parameters of the corresponding space of Killing tensors are presented. The results are applied to the problem of orthogonal separability of the Drach superintegrable potentials.
General theory of scalar wave scattering by a composite particle, one particle imbedded in another
NASA Astrophysics Data System (ADS)
Park, Byong Chon; Kim, Jin Seung
2016-04-01
A general theory of scalar wave scattering by a composite particle, consisting of a smaller particle completely imbedded in a larger particle, is developed to give the coefficients of scattering and transmission in the form of recurrence formulae. Iterative application of the formulae yields the coefficients in the forms of power series of the coefficients obtained in single particle scattering theories, and each term of the power series can be interpreted as a multiple scattering of the wave between the two component particles in increasingly higher order.
Perturbation theory for isotropic velocity-dependent potentials: scattering case
NASA Astrophysics Data System (ADS)
Jaghoub, Mahmoud
2010-02-01
The time-independent Schr"odinger equation with an isotropic velocity-depen-dent potential is considered. Treating the velocity-dependent interaction as a small perturbation we develop analytical formulae for the changes in the scattering phase shifts and wave functions. It is shown that only the zeroth order solution and the perturbing potential are needed to determine the phase shift and wave function corrections. No prior knowledge of the unperturbed scattering states continuum is required. In order to test the validity of our approach we applied it to an exactly solvable model for nucleon-nucleon scattering. The results of the perturbation formalism compare quite well with the those of the exactly solvable model. The developed formalism can be applied in problems concerning pion-nucleon, nucleon-nucleon and electron-atom scattering. It may also be useful in studying the scattering of electrons in semiconductor heterostructures. )
Theory of magnetic circular dichroism of nonresonant x-ray Raman scattering
NASA Astrophysics Data System (ADS)
Takahashi, Manabu; Hiraoka, Nozomu
2015-09-01
We develop a theory of magnetic circular dichroism (MCD) of hard x-ray Raman scattering (XRS) to analyze the MCD signal at iron L edge from pure ferromagnetic iron. The obtained formula of scattering amplitude has terms corresponding to the charge (Thomson) scattering process, and the orbital and spin scattering processes in the elastic x-ray magnetic scattering. The total scattering intensity is almost independent of incident photon helicity since it is mainly produced by the charge scattering. The weak MCD signals are caused primarily by interference between the charge scattering amplitude and each of the orbital and spin scattering amplitudes. The shape of the MCD spectra depends on angle αM between the wave vector of the incident photon and the magnetization vector. At αM=0∘ , the spin scattering is suppressed so that the MCD spectrum becomes analogous to that observed in the x-ray absorption spectroscopy. At αM=135∘ , the orbital scattering is suppressed, and the spin scattering plays central roles in producing the MCD signal. The magnitude of the MCD signal turns out to be proportional to the spin density of states projected onto the 3 d states in the unoccupied state. Consequently, the value of the integrated MCD signal is proportional to the spin moment in the 3 d states at the scattering site. The calculated MCD spectra with the help of a band structure calculation well reproduce the observed spectra.
Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.
NASA Astrophysics Data System (ADS)
Auerbach, Scott Michael
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering
DOE R&D Accomplishments Database
Tang, K. T.; Karplus, M.
1970-10-01
A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.
NASA Astrophysics Data System (ADS)
Nakatsuka, Takao; Nishimura, Jun
2008-08-01
The Molière theory of multiple Coulomb scattering is improved to take account of ionization loss by applying a differential formulation of the theory. Distributions for the deflection angle θ⃗ , as well as for any linear combination between θ⃗ and the lateral displacement r⃗ , under the ionization process are derived by a series expansion with the same universal functions f(n)(ϑ) of Molière, except that the values for both the expansion parameter B and the scale angle θM are corrected from those under the fixed-energy process. We find that Goudsmit-Saunderson angular distribution with ionization is also expressed by the same characteristic parameters B and θM derived above by the Molière theory. The transport mechanism of Molière process of multiple Coulomb scattering and the stochastic property of Molière series expansion are also investigated and discussed.
Electromagnetic scattering from two dielectric spheres: Comparison between theory and experiment
NASA Astrophysics Data System (ADS)
Kattawar, G. W.; Dean, C. E.
1982-08-01
A comparison is made between theoretical and experimental results for cooperative scattering between two spheres. The overall agreement between theory and experiment is quite good. Also a large side scattering resonance which was measured to be 44 times larger than that due to a single sphere was calculated to be actually 47.6 times larger.
Singularity in the Laboratory Frame Angular Distribution Derived in Two-Body Scattering Theory
ERIC Educational Resources Information Center
Dick, Frank; Norbury, John W.
2009-01-01
The laboratory (lab) frame angular distribution derived in two-body scattering theory exhibits a singularity at the maximum lab scattering angle. The singularity appears in the kinematic factor that transforms the centre of momentum (cm) angular distribution to the lab angular distribution. We show that it is caused in the transformation by the…
Generator algebra of the asymptotic Poincare group in the general theory of relativity
Solovev, V.O.
1986-06-01
This paper obtains the Poisson brackets of the generators of the Hamiltonian formalism for general relativity with allowance for surface terms of aritrary form. For Minkowski space, there exists the asymptotic Poincare group, which is the semi-direct product of the Poincare group and an infinite subgroup for which the algebra of generators with surface terms closes. A criterion invariant with respect to the choice of the coordinate system on the hypersurfaces is obtained for realization of the Poincare group in asymptotically flat space-time. The ''background'' flat metric on the hypersurfaces and Poincare group that preserve it are determined nonuniquely; however, the numerical values of the generators do not depend on the freedom of this choice on solutions of the constraint equations. For an asymptotically Galilean metric, the widely used boundary cnoditins are determined more accurately. A prescription is given for application of the Arnowitt-Deser-Misner decomposition in the case of a slowly decreasing contribution from coordinate and time transformations.
NASA Astrophysics Data System (ADS)
Connes, Alain; Kreimer, Dirk
This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop
Yao, Jie; Lesage, Anne-Cécile; Hussain, Fazle; Bodmann, Bernhard G.; Kouri, Donald J.
2014-12-15
The reversion of the Born-Neumann series of the Lippmann-Schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem. One limitation of the current inversion methods based on the reversion of the Born-Neumann series is that the velocity potential should have compact support. However, this assumption cannot be satisfied in certain cases, especially in seismic inversion. Based on the idea of distorted wave scattering, we explore an inverse scattering method for velocity potentials without compact support. The strategy is to decompose the actual medium as a known single interface reference medium, which has the same asymptotic form as the actual medium and a perturbative scattering potential with compact support. After introducing the method to calculate the Green’s function for the known reference potential, the inverse scattering series and Volterra inverse scattering series are derived for the perturbative potential. Analytical and numerical examples demonstrate the feasibility and effectiveness of this method. Besides, to ensure stability of the numerical computation, the Lanczos averaging method is employed as a filter to reduce the Gibbs oscillations for the truncated discrete inverse Fourier transform of each order. Our method provides a rigorous mathematical framework for inverse acoustic scattering with a non-compact support velocity potential.
The Retrieval of Ozone Profiles from Limb Scatter Measurements: Theory
NASA Technical Reports Server (NTRS)
Flittner, D. E.; Herman, B. M.; Bhartia, P. K.; McPeters, R. D.; Hilsenrath, E.
1999-01-01
An algorithm is presented for retrieving vertical profiles of O3 concentration using measurements of UV and visible light scattered from the limb of the atmosphere. The UV measurements provide information about the O3 profile in the upper and middle stratosphere, while only visible wavelengths are capable of probing the lower stratospheric O3 profile. Sensitivity to the underlying scene reflectance is greatly reduced by normalizing measurements at a tangent height high in the atmosphere (approximately 55 km), and relating measurements taken at lower altitudes to this normalization point. To decrease the effect of scattering by thin aerosols/clouds that may be present in the field of view, these normalized measurements are then combined by pairing wavelengths with strong and weak O3 absorption. We conclude that limb scatter can be used to measure O3 between 15 km and 50 km with 2-3 km vertical resolution and better than 10% accuracy.
Scattering by ensembles of small particles experiment, theory and application
NASA Technical Reports Server (NTRS)
Gustafson, B. A. S.
1980-01-01
A hypothetical self consistent picture of evolution of prestellar intertellar dust through a comet phase leads to predictions about the composition of the circum-solar dust cloud. Scattering properties of thus resulting conglomerates with a bird's-nest type of structure are investigated using a micro-wave analogue technique. Approximate theoretical methods of general interest are developed which compared favorably with the experimental results. The principal features of scattering of visible radiation by zodiacal light particles are reasonably reproduced. A component which is suggestive of (ALPHA)-meteoroids is also predicted.
Hybrid Theory of Electron-Hydrogenic Systems Elastic Scattering
NASA Technical Reports Server (NTRS)
Bhatia, A. K.
2007-01-01
Accurate electron-hydrogen and electron-hydrogenic cross sections are required to interpret fusion experiments, laboratory plasma physics and properties of the solar and astrophysical plasmas. We have developed a method in which the short-range and long-range correlations can be included at the same time in the scattering equations. The phase shifts have rigorous lower bounds and the scattering lengths have rigorous upper bounds. The phase shifts in the resonance region can be used to calculate very accurately the resonance parameters.
Batishchev, Pavel A.; Tolstikhin, Oleg I.
2007-06-15
The Siegert pseudostate (SPS) formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura [Phys. Rev. A, 58, 2077 (1998)] for s-wave scattering in a spherically symmetric finite-range potential, is generalized to nonzero angular momenta. The orthogonality and completeness properties of SPSs are established and SPS expansions for the outgoing-wave Green's function, physical states, and scattering matrix are obtained. The present formulation completes the theory of SPSs in the one-channel case, making its application to three-dimensional problems possible. The results are illustrated by calculations for several model potentials.
Application of Mie theory to assess structure of spheroidal scattering in backscattering geometries
Chalut, Kevin J.; Giacomelli, Michael G.; Wax, Adam
2010-01-01
Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure. PMID:18677348
A dynamical formulation of one-dimensional scattering theory and its applications in optics
Mostafazadeh, Ali
2014-02-15
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrödinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility. -- Highlights: • Proposes a dynamical theory of scattering in one dimension. • Derives and solves dynamical equations for scattering data. • Gives a new inverse scattering prescription. • Constructs optical potentials with desired scattering properties.
Comparison of the domain of validity of several approximate surface scatter theories
NASA Astrophysics Data System (ADS)
Choi, Narak; Harvey, James E.
2012-10-01
A new generalized Harvey-Shack (GHS) surface scatter theory is numerically compared to the classical small perturbation method (SPM), the Kirchhoff approximation method (KM) and the rigorous method of moment (MoM) for one-dimensional ideally conducting surfaces whose surface power spectral density function is Gaussian or abc-function. In spite of its simple analytic form, our numerical comparison shows that the new GHS theory is valid (with reasonable accuracy) over a broader range of surface parameter space than either of the two classical surface scatter theories.
Acoustic swimbladder resonance spectroscopy: Fundamentals in scattering theory
NASA Astrophysics Data System (ADS)
Francis, David T. I.; Foote, Kenneth G.
2003-04-01
A history of the physics of acoustic resonance is given. The primary, low-frequency, resonant scattering model for air bubbles in water [Minnaert (1933)] is reviewed. Subsequent applications to swimbladdered fish, including models by Andreeva (1964), Love (1978), and Feuillade and Nero (1998), among others, are developed. Reference is made to exemplary measurements of backscattering by Holliday (1972) and Loevik and Hovem (1979), and of forward scattering, or absorption, by Weston (1967) and Diachok (2000), among others. High-frequency resonances are also described, with presentation of both analytical and numerical results for the immersed air bubble. Comparison of these validates the numerical, boundary-element method (BEM). The BEM allows high-frequency resonances to be studied for swimbladders of realistic shapes under pressure and for typical wave-number-swimbladder length products of order 10-40. Implications of high-frequency swimbladder resonance for auditory function in fish are mentioned. [Work supported by ONR.
Zhou, Yun Pollak, Eli; Miret-Artés, Salvador
2014-01-14
A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.
Higher-order M-theory corrections and the Kac Moody algebra E10
NASA Astrophysics Data System (ADS)
Damour, Thibault; Nicolai, Hermann
2005-07-01
It has been conjectured that the classical dynamics of M-theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E10/K(E10), where K(E10) is the maximal compact subgroup of the hyperbolic Kac Moody group E10. We here provide further evidence for this conjecture by showing that the leading higher-order corrections, quartic in the curvature and related 3-form-dependent terms, correspond to negative imaginary roots of E10. The conjecture entails certain predictions for which higher-order corrections are allowed: in particular corrections of type RM(DF)N are compatible with E10 only for M + N = 3k + 1. Furthermore, the leading parts of the R4, R7, ... terms are predicted to be associated with singlets under the {\\mathfrak{sl}}_{10} decomposition of E10. Although singlets are extremely rare among the 4400 752 653 representations of {\\mathfrak{sl}}_{10} appearing in E10 up to level ell <= 28, there are indeed singlets at levels ell = 10 and ell = 20 which do match with the R4 and the expected R7 corrections. Our analysis indicates a far more complicated behaviour of the theory near the cosmological singularity than suggested by the standard homogeneous ansätze.
Theory of polariton-mediated Raman scattering in microcavities.
León Hilario, L M; Bruchhausen, A; Lobos, A M; Aligia, A A
2007-04-30
We calculate the intensity of the polariton-mediated inelastic light scattering in semiconductor microcavities. We treat the exciton-photon coupling nonperturbatively and incorporate lifetime effects in both excitons and photons, and a coupling of the photons to the electron-hole continuum. Taking the matrix elements as fitting parameters, the results are in excellent agreement with measured Raman intensities due to optical phonons that are resonant with the upper polariton branches in II-VI microcavities with embedded CdTe quantum wells. PMID:21690956
NASA Astrophysics Data System (ADS)
Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert
Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.
Elastic Proton Scattering of Medium Mass Nuclei from Coupled-Cluster Theory
Hagen, G.; MichelN.,
2012-01-01
Using coupled-cluster theory and interactions from chiral effective field theory, we compute overlap functions for transfer and scattering of low-energy protons on the target nucleus 40Ca. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions. Using known asymptotic forms for one-nucleon overlap functions we derive a simple and intuitive way of computing scattering observables such as elastic scattering phase shifts and cross sections. As a first application and proof of principle, we compute phase shifts and differential interaction cross sections at energies of 9.6 and 12.44 MeV and compare with experimental data. Our computed diffraction minima are in fair agreement with experimental results, while we tend to overestimate the cross sections at large scattering angles.
Time Delay for Dispersive Systems in Quantum Scattering Theory
NASA Astrophysics Data System (ADS)
Tiedra de Aldecoa, Rafael
We consider time delay and symmetrized time delay (defined in terms of sojourn times) for quantum scattering pairs {H0 = h(P), H}, where h(P) is a dispersive operator of hypoelliptic-type. For instance, h(P) can be one of the usual elliptic operators such as the Schrödinger operator h(P) = P2 or the square-root Klein-Gordon operator h(P) = √ {1 + P2}. We show under general conditions that the symmetrized time delay exists for all smooth even localization functions. It is equal to the Eisenbud-Wigner time delay plus a contribution due to the non-radial component of the localization function. If the scattering operator S commutes with some function of the velocity operator ∇h(P), then the time delay also exists and is equal to the symmetrized time delay. As an illustration of our results, we consider the case of a one-dimensional Friedrichs Hamiltonian perturbed by a finite rank potential. Our study puts into evidence an integral formula relating the operator of differentiation with respect to the kinetic energy h(P) to the time evolution of localization operators.
Sahoo, Tapas; Pollak, Eli
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.
Covariant spectator theory of np scattering: Deuteron quadrupole moment
Gross, Franz
2015-01-26
The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to np scattering data. Included in the calculation are a new class of isoscalar np interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experiential result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently from _{X}EFT predictions to order N^{3}LO.
Covariant spectator theory of np scattering: Deuteron quadrupole moment
Gross, Franz
2015-01-26
The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to np scattering data. Included in the calculation are a new class of isoscalar np interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experiential result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently frommore » XEFT predictions to order N3LO.« less
Theory for computing the field scattered from a smooth inflected surface
NASA Technical Reports Server (NTRS)
Barger, R. L.; Dominek, A. K.
1986-01-01
A theory is described for computing the reflected or scattered field from a smooth body with inflection points. These inflections occur in certain directions at each surface point for which the total (Gaussian) curvature is zero or negative. For surface illumination in one of these critical directions, the usual reflection formulas obtained by the high-frequency approximation are inapplicable, and a shadow zone exists in the reflected field. Scattering into the shadow zone is treated, as well as specular reflection. This theory should have a variety of applications such as for certain optics problems, computer graphics modeling of three-dimensional shapes, and the design and analysis of specialized microwave reflector antennas.
NASA Astrophysics Data System (ADS)
Links, Jon; Moghaddam, Amir; Zhang, Yao-Zhong
2013-08-01
We demonstrate the occurrence of free quasi-particle excitations obeying generalized exclusion statistics in a BCS model with asymmetric pair scattering. The results are derived from an exact solution of the Hamiltonian, which was obtained via the algebraic Bethe ansatz utilizing the representation theory of an underlying Yangian algebra. The free quasi-particle excitations are associated with highest weight states of the Yangian algebra, corresponding to a class of analytic solutions of the Bethe ansatz equations.
NASA Astrophysics Data System (ADS)
Setare, M. R.; Adami, H.
2016-08-01
The Chern-Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz-Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Shaped beam scattering from a single lymphocyte cell by generalized Lorenz-Mie theory
NASA Astrophysics Data System (ADS)
Wang, Jia Jie; Han, Lu; Han, Yi Ping; Gouesbet, Gerard; Wu, Xuecheng; Wu, Yingchun
2014-01-01
With the aim of improving the measurement capabilities of laser-based diagnostic instruments for cells, an eccentric stratified dielectric sphere model illuminated by an arbitrary shaped beam is applied to the modeling of light scattering by a single nucleated cell within the framework of the generalized Lorenz-Mie theory (GLMT). A particular attention is paid to the study of scattering properties of a lymphocyte cell from an arbitrary incident Gaussian beam. Numerical results concerning the influence of shaped beam parameters (beam waist radius, incident angle, location of beam center) as well as of cellular parameters (ratio of nucleus size to cell size, location of the nucleus within the cell) on the scattering properties are presented and discussed, with comparisons to the scattering behaviors from a concentric stratified sphere model. The results reveal that the forward scattering intensities are mainly determined by the cell size regardless of the nucleus/cell ratio, while sideward scattering signals are sensitive to the change of cell internal structure. As the beam waist radius varies, the scattering patterns in the present cases are similar to each other, although the absolute intensities are different. Additionally, location of the nucleus within the cell, incident angle of the beam as well as location of the beam waist center play significant effects on the light scattering intensity distributions.
Scattering of an electromagnetic plane wave by a Luneburg lens. I. Ray theory.
Lock, James A
2008-12-01
For a plane wave incident on either a Luneburg lens or a modified Luneburg lens, the magnitude and phase of the transmitted electric field are calculated as a function of the scattering angle in the context of ray theory. It is found that the ray trajectory and the scattered intensity are not uniformly convergent in the vicinity of edge ray incidence on a Luneburg lens, which corresponds to the semiclassical phenomenon of orbiting. In addition, it is found that rays transmitted through a large-focal-length modified Luneburg lens participate in a far-zone rainbow, the details of which are exactly analytically soluble in ray theory. Using these results, the Airy theory of the modified Luneburg lens is derived and compared with the Airy theory of the rainbows of a homogeneous sphere. PMID:19037388
The theory of surface-enhanced Raman scattering
NASA Astrophysics Data System (ADS)
Lombardi, John R.; Birke, Ronald L.
2012-04-01
By considering the molecule and metal to form a conjoined system, we derive an expression for the observed Raman spectrum in surface-enhanced Raman scattering. The metal levels are considered to consist of a continuum with levels filled up to the Fermi level, and empty above, while the molecule has discrete levels filled up to the highest occupied orbital, and empty above that. It is presumed that the Fermi level of the metal lies between the highest filled and the lowest unfilled level of the molecule. The molecule levels are then coupled to the metal continuum both in the filled and unfilled levels, and using the solutions to this problem provided by Fano, we derive an expression for the transition amplitude between the ground stationary state and some excited stationary state of the molecule-metal system. It is shown that three resonances contribute to the overall enhancement; namely, the surface plasmon resonance, the molecular resonances, as well as charge-transfer resonances between the molecule and metal. Furthermore, these resonances are linked by terms in the numerator, which result in SERS selection rules. These linked resonances cannot be separated, accounting for many of the observed SERS phenomena. The molecule-metal coupling is interpreted in terms of a deformation potential which is compared to the Herzberg-Teller vibronic coupling constant. We show that one term in the sum involves coupling between the surface plasmon transition dipole and the molecular transition dipole. They are coupled through the deformation potential connecting to charge-transfer states. Another term is shown to involve coupling between the charge-transfer transition and the molecular transition dipoles. These are coupled by the deformation potential connecting to plasmon resonance states. By applying the selection rules to the cases of dimer and trimer nanoparticles we show that the SERS spectrum can vary considerably with excitation wavelength, depending on which plasmon and
Mitri, Farid
2014-11-01
The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent. PMID:25389166
Lorenz-Mie theory for 2D scattering and resonance calculations
NASA Astrophysics Data System (ADS)
Gagnon, Denis; Dubé, Louis J.
2015-10-01
This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell’s equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.
Elements of QED-NRQED effective field theory: NLO scattering at leading power
NASA Astrophysics Data System (ADS)
Dye, Steven P.; Gonderinger, Matthew; Paz, Gil
2016-07-01
The proton radius puzzle, i.e. the large discrepancy in the extraction of the proton charge radius between regular and muonic hydrogen, challenges our understanding of the structure of the proton. It can also be an indication of a new force that couples to muons, but not to electrons. An effective field theory analysis using nonrelativistic quantum electrodynamics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. The muonic hydrogen result can be tested by a muon-proton scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in Switzerland. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still nonrelativistic. The interaction between the muons and protons can be described by a hybrid QED-NRQED effective field theory. We present some elements of this effective field theory. In particular we consider O (Z α ) scattering up to power m2/M2 , where m (M ) is the muon (proton) mass and Z =1 for a proton, and O (Z2α2) scattering at leading power. We show how the former reproduces Rosenbluth scattering up to power m2/M2 and the latter the relativistic scattering off a static potential. Proton structure corrections at O (Z2α2) will be considered in a subsequent paper.
Matrix operator theory of radiative transfer. I - Rayleigh scattering.
NASA Technical Reports Server (NTRS)
Plass, G. N.; Kattawar, G. W.; Catchings, F. E.
1973-01-01
An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.
Semiclassical multi-phonon theory for atom-surface scattering: Application to the Cu(111) system
NASA Astrophysics Data System (ADS)
Daon, Shauli; Pollak, Eli
2015-05-01
The semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)] is further developed to include the full multi-phonon transitions in atom-surface scattering. A practically applicable expression is developed for the angular scattering distribution by utilising a discretized bath of oscillators, instead of the continuum limit. At sufficiently low surface temperature good agreement is found between the present multi-phonon theory and the previous one-, and two-phonon theory derived in the continuum limit in our previous study [Daon, Pollak, and Miret-Artés, J. Chem. Phys. 137, 201103 (2012)]. The theory is applied to the measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. We find that the present multi-phonon theory substantially improves the agreement between experiment and theory, especially at the higher surface temperatures. This provides evidence for the importance of multi-phonon transitions in determining the angular distribution as the surface temperature is increased.
Semiclassical multi-phonon theory for atom-surface scattering: Application to the Cu(111) system.
Daon, Shauli; Pollak, Eli
2015-05-01
The semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)] is further developed to include the full multi-phonon transitions in atom-surface scattering. A practically applicable expression is developed for the angular scattering distribution by utilising a discretized bath of oscillators, instead of the continuum limit. At sufficiently low surface temperature good agreement is found between the present multi-phonon theory and the previous one-, and two-phonon theory derived in the continuum limit in our previous study [Daon, Pollak, and Miret-Artés, J. Chem. Phys. 137, 201103 (2012)]. The theory is applied to the measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. We find that the present multi-phonon theory substantially improves the agreement between experiment and theory, especially at the higher surface temperatures. This provides evidence for the importance of multi-phonon transitions in determining the angular distribution as the surface temperature is increased. PMID:25956085
Semiclassical multi-phonon theory for atom-surface scattering: Application to the Cu(111) system
Daon, Shauli; Pollak, Eli
2015-05-07
The semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)] is further developed to include the full multi-phonon transitions in atom-surface scattering. A practically applicable expression is developed for the angular scattering distribution by utilising a discretized bath of oscillators, instead of the continuum limit. At sufficiently low surface temperature good agreement is found between the present multi-phonon theory and the previous one-, and two-phonon theory derived in the continuum limit in our previous study [Daon, Pollak, and Miret-Artés, J. Chem. Phys. 137, 201103 (2012)]. The theory is applied to the measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. We find that the present multi-phonon theory substantially improves the agreement between experiment and theory, especially at the higher surface temperatures. This provides evidence for the importance of multi-phonon transitions in determining the angular distribution as the surface temperature is increased.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
NASA Technical Reports Server (NTRS)
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
1995-01-01
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Scattering of an electromagnetic plane wave by a Luneburg lens. II. Wave theory.
Lock, James A
2008-12-01
The partial wave scattering and interior amplitudes for the interaction of an electromagnetic plane wave with a modified Luneburg lens are derived in terms of the exterior and interior radial functions of the scalar radiation potentials evaluated at the lens surface. A Debye series decomposition of these amplitudes is also performed and discussed. The effective potential inside the lens for the transverse electric polarization is qualitatively examined, and the approximate lens size parameters of morphology-dependent resonances are determined. Finally, the physical optics model is used to calculate wave scattering in the vicinity of the ray theory orbiting condition in order to demonstrate the smoothing of ray theory discontinuities by the diffraction of scattered waves. PMID:19037389
Low-energy p-d scattering and {sup 3}He in pionless effective field theory
Koenig, Sebastian; Hammer, H.-W.
2011-06-15
We calculate low-energy proton-deuteron scattering in the framework of pionless effective field theory. In the quartet channel, we calculate the elastic scattering phase shift up to next-to-next-to-leading order in the power counting. In the doublet channel, we perform a next-to-leading-order calculation. We obtain good agreement with the available phase-shift analyses down to the scattering threshold. The phase shifts in the region of nonperturbative Coulomb interactions are calculated by using an optimized integration mesh. Moreover, the Coulomb contribution to the {sup 3}He-{sup 3}H binding energy difference is evaluated in first-order perturbation theory. We comment on the implications of our results for the power counting of subleading three-body forces.
Topics in Nonsupersymmetric Scattering Amplitudes in Gauge and Gravity Theories
NASA Astrophysics Data System (ADS)
Nohle, Joshua David
In Chapters 1 and 2, we introduce and review the duality between color and kinematics in Yang-Mills theory uncovered by Bern, Carrasco and Johansson (BCJ). In Chapter 3, we provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions. In Chapter 4, we extend the four-point one-loop nonsupersymmetric pure Yang-Mills discussion of Chapter 3 to include fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature. In Chapter 5, we switch from the topic of color-kinematics duality to discuss the recently renewed interest in the soft behavior of gravitons and gluons. Specifically, we discuss the subleading low-energy behavior. Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at
Scattering theory for the Klein-Gordon equation with nondecreasing potentials
Cruz, Maximino; Arredondo R, Juan H.
2008-11-15
The Klein-Gordon equation is considered in the case of nondecreasing potentials. The energy inner product is nonpositive on a subspace of infinite dimension, not consisting entirely of eigenvectors of the associated operator. A scattering theory for this case is developed and asymptotic completeness for generalized Moeller operators is proven.
Shaped beam scattering by an aggregate of particles using generalized Lorenz-Mie theory
NASA Astrophysics Data System (ADS)
Briard, Paul; Wang, Jia jie; Han, Yi Ping
2016-04-01
In this paper, the light scattering by an aggregate of particles illuminated by an arbitrary shaped beam is analyzed within the framework of generalized Lorenz-Mie theory (GLMT). The theoretical derivations of aggregated particles illuminated by an arbitrary shaped beam are revisited, with special attention paid to the computation of beam shape coefficients of a shaped beam for aggregated particles. The theoretical treatments as well as a home-made code are then verified by making comparisons between our numerical results and those calculated using a public available T-Matrix code MSTM. Good agreements are achieved which partially indicate the correctness of both codes. Additionally, more numerical results are presented to study the scattered fields of aggregated particles illuminated by a focused Gaussian beam. Several large enhancements in the scattered intensity distributions are found which are believed to be due to the Bragg's scattering by a linear chain of spheres.
Bettelheim, F A; Paunovic, M
1979-01-01
Light-scattering intensities in the I parallel and I+ mode were obtained on thin sections of three human lenses. Random density and orientation fluctuation theory, without cross correlation, was employed to evaluate light-scattering parameters. Both the density correlation distances, as well as the orientation correlation distances, were related to structural elements in the lens fiber cell that have been observed by other investigators with different techniques. The magnitude of these fluctuations were evaluated, and it was demonstrated that the density fluctuations are the main contributors to light scattering in normal human lenses. Changes in the light-scattering parameters were evaluated as a function of position within the lens. The changes observed agree with the biochemical data in the literature that reflects that an aging process occurs when one proceeds from the periphery of the lens toward the center. PMID:262413
NASA Astrophysics Data System (ADS)
Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.
2010-12-01
In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for Ca40,42,44,48 with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+Ca40,42,44,48 systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.
Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.
2010-12-15
In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for {sup 40,42,44,48}Ca with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+{sup 40,42,44,48}Ca systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.
Mechanism of elastic and inelastic proton scattering on a {sup 15}C nucleus in diffraction theory
Ibraeva, E. T.; Zhusupov, M. A.; Imambekov, O.
2012-11-15
The amplitudes for elastic and inelastic proton scattering on the neutron-rich nucleus {sup 15}C (to its J{sup {pi}} = 5/2{sup +} level in the latter case) in inverse kinematics were calculated within Glauber diffraction theory. First- and second-order terms were taken into account in the multiple-scattering operator. The {sup 15}C wave function in the multiparticle shell model was used. This made it possible to calculate not only respective differential cross sections but also the contribution of proton scattering on nucleons occurring in different shells. The differential cross sections for elastic and inelastic scattering were calculated at the energies of 0.2, 0.6, and 1 GeV per nucleon.
Array algebra estimation in signal processing
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.
Choi, B.H.; Poe, R.T.
1985-08-01
We present a systematic formulation of the atom--surface scattering dynamics which includes the vibrational states of the atoms in the solid (phonons). The properties of the total scattering wave function of the system, a representation of the interaction potential matrix, and the characteristics of the independent physical solutions are all derived from the translational invariance of the full Hamiltonian. The scattering equations in the integral forms as well as the related Green functions were also obtained. The configurational representations of the Green functions, in particular, are quite different from those of the conventional scattering theory where the collision partners are spatially localized. Various versions of the integral expression of scattering, transition, and reactance matrices were also obtained. They are useful for introducing approximation schemes. From the present formulation, some specific theoretical schemes which are more realistic compared to those that have been employed so far and at the same time capable of yielding effective ab initio computation are derived in the following paper. The time reversal invariance and the microscopic reversibility of the atom--surface scattering were discussed. The relations between the in and outgoing scattering wave functions which are satisfied in the atom--surface system and important in the transition matrix methods were presented. The phonon annihilation and creation, and the adsorption and desorption of the atom are related through the time reversal invariance, and thus the microscopic reversibility can be tested by the experiment.
A non-paraxial scattering theory for specifying and analyzing fabrication errors in optical surfaces
NASA Astrophysics Data System (ADS)
Vernold, Cynthia Louise
There are three fundamental mechanisms in optical systems that contribute to image degradation: aperture diffraction, geometrical aberrations caused by residual design errors, and scattering effects due to optical fabrication errors. Diffraction effects, as well as optical design errors and fabrication errors that are laterally large in nature (generally referred to as figure errors), are accurately modeled using conventional ray trace analysis codes. However, these ray-trace codes fall short of providing a complete picture of image degradation; they routinely ignore fabrication-induced errors with spatial periods that are too small to be considered figure errors. These errors are typically referred to as mid-spatial-frequency (ripple) and high- spatial-frequency (micro-roughness) surface errors. These overlooked, but relevant, fabrication-induced errors affect image quality in different ways. Mid-spatial- frequency errors produce small-angle scatter that tends to widen the diffraction-limited image core (i.e. for a system with a circular exit pupil, this is the central lobe of the Airy pattern), and in doing so, reduces the optical resolution of a system. High-spatial-frequency errors tend to scatter energy out of the image core into a wide-angle halo, causing a reduction in image contrast. Micro-roughness and ripple are inherent aspects of the less conventional, small-tool-based optical fabrication approaches. It is especially important in these cases to specify these errors accurately during the design phase of a project, and deterministically monitor and control them during the fabrication phase of a project. Surprisingly, most current approaches to this issue employ some guessing and ``gut feel'' based on past experience, because accurate theories and analysis tools are not readily available. This dissertation takes the first step towards solving this problem by describing a Fourier-based approach for classifying and quantifying surface errors that can be
Hybrid theory and calculation of e-N2 scattering. [quantum mechanics - nuclei (nuclear physics)
NASA Technical Reports Server (NTRS)
Chandra, N.; Temkin, A.
1975-01-01
A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.
Li, Jing; Hong, Wenxue
2014-12-01
The feature extraction and feature selection are the important issues in pattern recognition. Based on the geometric algebra representation of vector, a new feature extraction method using blade coefficient of geometric algebra was proposed in this study. At the same time, an improved differential evolution (DE) feature selection method was proposed to solve the elevated high dimension issue. The simple linear discriminant analysis was used as the classifier. The result of the 10-fold cross-validation (10 CV) classification of public breast cancer biomedical dataset was more than 96% and proved superior to that of the original features and traditional feature extraction method. PMID:25868233
NASA Technical Reports Server (NTRS)
Fung, A. K.; Dome, G.; Moore, R. K.
1977-01-01
The paper compares the predictions of two different types of sea scatter theories with recent scatterometer measurements which indicate the variations of the backscattering coefficient with polarization, incident angle, wind speed, and azimuth angle. Wright's theory (1968) differs from that of Chan and Fung (1977) in two major aspects: (1) Wright uses Phillips' sea spectrum (1966) while Chan and Fung use that of Mitsuyasu and Honda, and (2) Wright uses a modified slick sea slope distribution by Cox and Munk (1954) while Chan and Fung use the slick sea slope distribution of Cox and Munk defined with respect to the plane perpendicular to the look direction. Satisfactory agreements between theory and experimental data are obtained when Chan and Fung's model is used to explain the wind and azimuthal dependence of the scattering coefficient.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
ERIC Educational Resources Information Center
Hagerty, Gary; Smith, Stanley; Goodwin, Danielle
2010-01-01
In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…
New family of Maxwell like algebras
NASA Astrophysics Data System (ADS)
Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.
2016-08-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
He3 and pd scattering to next-to-leading order in pionless effective field theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared; Egolf, David A.; Kerin, John; König, Sebastian; Springer, Roxanne P.
2014-06-01
We study the three-body systems of He3 and pd scattering and demonstrate, both analytically and numerically, that a new pd three-body force is needed at next-to-leading order in pionless effective field theory. We also show that at leading order these observables require no new three-body force beyond what is necessary to describe nd scattering. We include electromagnetic effects by iterating only diagrams that involve a single photon exchange in the three-body sector.
Electron-deuteron scattering based on the Chiral Effective Field Theory
NASA Astrophysics Data System (ADS)
Rozpȩdzik, Dagmara
2014-06-01
Based on the Chiral Effective Field Theory (ChEFT) dynamical picture of the two-pion exchange (TPE) contributions to the nuclear current operator which appear at higher order chiral expansions were considered. Their role in the electron-deuteron scattering reactions was studied and chiral predictions were compared with those obtained in the conventional framework. Results for cross section and various polarization observables are presented. The bound and scattering states were calculated with five different chiral nucleon-nucleon (NN) potentials which leads to the so-called theoretical uncertainty bands for the predicted results.
West, R.; Tsang, Leung; Winebrenner, D.P. )
1993-03-01
Dense medium radiative transfer theory is applied to a three-layer model consisting of two scattering layers overlying a homogeneous half space with a size distribution of particles in each layer. A model with a distribution of sizes gives quite different results than those obtained from a model with a single size. The size distribution is especially important in the low frequency limit when scattering is strongly dependent on particle size. The size distribution and absorption characteristics also affect the extinction behavior as a function of fractional volume. Theoretical results are also compared with experimental data. The sizes, permittivities, and densities used in the numerical illustrations are typical values for snow.
NASA Technical Reports Server (NTRS)
Flesia, C.; Schwendimann, P.
1992-01-01
The contribution of the multiple scattering to the lidar signal is dependent on the optical depth tau. Therefore, the radar analysis, based on the assumption that the multiple scattering can be neglected is limited to cases characterized by low values of the optical depth (tau less than or equal to 0.1) and hence it exclude scattering from most clouds. Moreover, all inversion methods relating lidar signal to number densities and particle size must be modified since the multiple scattering affects the direct analysis. The essential requests of a realistic model for lidar measurements which include the multiple scattering and which can be applied to practical situations follow. (1) Requested are not only a correction term or a rough approximation describing results of a certain experiment, but a general theory of multiple scattering tying together the relevant physical parameter we seek to measure. (2) An analytical generalization of the lidar equation which can be applied in the case of a realistic aerosol is requested. A pure analytical formulation is important in order to avoid the convergency and stability problems which, in the case of numerical approach, are due to the large number of events that have to be taken into account in the presence of large depth and/or a strong experimental noise.
Density functional theory for low-energy electron-molecule scattering
NASA Astrophysics Data System (ADS)
Burke, Kieron; Wasserman, Adam
2004-09-01
Time-dependent density functional theory (TDDFT) is becoming popular as an approach to time-dependent electronic problems[1]. In the weak field regime, TDDFT predicts electronic transition frequencies and optical spectra of atoms, molecules, clusters, and solids, with an accuracy comparable to high-level wavefunction calculations at a fraction of the computational cost[2]. For large systems, TDDFT is the method of choice. Given the importance of correlation effects in low-energy electron-molecule scattering, extracting scattering amplitudes from TDDFT appears desirable. I will review this background, and outline how this can be done[3]. Detailed results will be shown by Wasserman in another talk. [1] Time-Dependent Density Functional Theory, M.A.L. Marques and E.K.U. Gross, Annu. Rev. Phys. Chem. 55, 427 (2004). [2] Time-dependent density functional theory in quantum chemistry, F. Furche and K. Burke, to appear in 1st vol. of Annu. Rev. of Computational Chemistry (2004) [3] Electron-molecule scattering from time-dependent density functional theory A. Wasserman, N.T. Maitra, and K. Burke, submitted (see http:dft.rutgers.edu/pubs/publist.html).
NASA Astrophysics Data System (ADS)
Margerin, Ludovic; Planès, Thomas; Mayor, Jessie; Calvet, Marie
2016-01-01
Coda-wave interferometry is a technique which exploits tiny waveform changes in the coda to detect temporal variations of seismic properties in evolving media. Observed waveform changes are of two kinds: traveltime perturbations and distortion of seismograms. In the last 10 yr, various theories have been published to relate either background velocity changes to traveltime perturbations, or changes in the scattering properties of the medium to waveform decorrelation. These theories have been limited by assumptions pertaining to the scattering process itself-in particular isotropic scattering, or to the propagation regime-single-scattering and/or diffusion. In this manuscript, we unify and extend previous results from the literature using a radiative transfer approach. This theory allows us to incorporate the effect of anisotropic scattering and to cover a broad range of propagation regimes, including the contribution of coherent, singly scattered and multiply scattered waves. Using basic physical reasoning, we show that two different sensitivity kernels are required to describe traveltime perturbations and waveform decorrelation, respectively, a distinction which has not been well appreciated so far. Previous results from the literature are recovered as limiting cases of our general approach. To evaluate numerically the sensitivity functions, we introduce an improved version of a spectral technique known as the method of `rotated coordinate frames', which allows global evaluation of the Green's function of the radiative transfer equation in a finite domain. The method is validated through direct pointwise comparison with Green's functions obtained by the Monte Carlo method. To illustrate the theory, we consider a series of scattering media displaying increasing levels of scattering anisotropy and discuss the impact on the traveltime and decorrelation kernels. We also consider the related problem of imaging variations of scattering properties based on intensity
J-matrix method of scattering in one dimension: The nonrelativistic theory
Alhaidari, A.D. Bahlouli, H.; Abdelmonem, M.S.
2009-12-15
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.
Mechanisms of ultrasonic modulation of multiply scattered incoherent light based on diffusion theory
NASA Astrophysics Data System (ADS)
Zhu, Li-Li; Li, Hui
2015-01-01
An analytic equation interpreting the intensity of ultrasound-modulated scattering light is derived, based on diffusion theory and previous explanations of the intensity modulation mechanism. Furthermore, an experiment of ultrasonic modulation of incoherent light in a scattering medium is developed. This analytical model agrees well with experimental results, which confirms the validity of the proposed intensity modulation mechanism. The model supplements the existing research on the ultrasonic modulation mechanism of scattering light. Project supported by the National Natural Science Foundation of China (Grant No. 61178089), the Key Program of Science and Technology of Fujian Province, China (Grant No. 2011Y0019), and the Educational Department of Fujian Province, China (Grant No. JA13074).