Search results for "Matrix"
showing 10 items of 3205 documents
Partial wave analysis inK-matrix formalism
1995
A description is given of the K-matrix formalism. The formalism, which is normally applied to two-body scattering processes, is generalized to production of two-body channels with finalstate interactions. A multi-channel treatment of production of resonances has been worked out in the P-vector approach of Aitchison. An alternative approach, derived from the P-vector, gives the production amplitude as a product of the T-matrix for a two-body system and a vector Q specifying its production. This formulation, called Q-vector approach here, has also been worked out. Examples of practical importance are given.
Universality of level spacing distributions in classical chaos
2007
Abstract We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limacon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian dis…
Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations
2020
In this study, an improved matrix method based on collocation points is developed to obtain the approximate solutions of systems of high-order pantograph type delay differential equations with variable coefficients. These kinds of systems described by the existence of linear functional argument play a critical role in defining many different phenomena and particularly, arise in industrial applications and in studies based on biology, economy, electrodynamics, physics and chemistry. The technique we have used reduces the mentioned delay system solution with the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Thereby, the approximate solution is…
Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy
2021
Chapter 5 is devoted to asymptotic studies of electron resonant tunneling in a two-dimensional waveguide with two narrows. The narrow diameter plays the role of a small parameter. The asymptotics of basic characteristics of resonant tunneling are presented for electrons with energy between the first and the second thresholds. Moreover, the asymptotics results are compared with numerical ones obtained by approximate calculation of the scattering matrix.
Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine…
2015
We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and MS = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calcul…
Structure of the Odd-A, Shell-Stabilized NucleusNo102253
2005
In-beam {gamma}-ray spectroscopic measurements have been made on {sub 102}{sup 253}No. A single rotational band was identified up to a probable spin of 39/2({Dirac_h}/2{pi}), which is assigned to the 7/2{sup +}[624] Nilsson configuration. The bandhead energy and the moment of inertia provide discriminating tests of contemporary models of the heaviest nuclei. Novel methods were required to interpret the sparse data set associated with cross sections of around 50 nb. These methods included comparisons of experimental and simulated spectra, as well as testing for evidence of a rotational band in the {gamma}{gamma} matrix.
Regularities of Line Strengths in Spectra of NI, FI, and NeII
1998
Recently experimentally determined individual (fine structure) line strengths for the spectra of NI, FI, and NeII are analysed, searching for regu- larities resulting from similarities in the structure of these species. Strengths of spectral lines of the prominent 3S-3p and 3p-3d transition arrays are investigated. The absolute scales of these experimentally derived data are based on independently determined lifetimes for excited levels of NI, FI, and NeII. The simple Coulomb approximation method was applied for calcula- tions of the matrix elements for the "jumping" electron in order to obtain an average trend in line strengths of the studied emitters. In the case of the isoelectronic spec…
Nonquenched Isoscalar Spin-M1Excitations insd-Shell Nuclei
2015
Differential cross sections of isoscalar and isovector spin-M1 (0(+)→1(+)) transitions are measured using high-energy-resolution proton inelastic scattering at E(p)=295 MeV on (24)Mg, (28)Si, (32)S, and (36)Ar at 0°-14°. The squared spin-M1 nuclear transition matrix elements are deduced from the measured differential cross sections by applying empirically determined unit cross sections based on the assumption of isospin symmetry. The ratios of the squared nuclear matrix elements accumulated up to E(x)=16 MeV compared to a shell-model prediction are 1.01(9) for isoscalar and 0.61(6) for isovector spin-M1 transitions, respectively. Thus, no quenching is observed for isoscalar spin-M1 transi…
Trivial S-Matrices, Wigner-Von Neumann Resonances and Positon Solutions of the Integrable Nonlinear Evolution Equations
1996
It is well known that the scattering matrix is different from the unit matrix in the case of 1-dimensional Schrodinger operator with smooth rapidly decreasing nonzero potential. This no more true in the case of the slowly decreasing and oscillating potentials for which the absence of scattering is accompanied by the occurrence of the Wigner-von Neumann resonances embedded in the positive absolutely continuous spectrum. Taken as initial conditions in the KdV like integrable partial differential equations these potentials generate interesting family of explicit solutions. Below we will call them positon or multipositon solutions. The interaction of an arbitrary finite number of positons and s…
Digital simulation of wind field velocity
1998
Abstract In this paper some computational aspects on the generation procedure of n -variate wind velocity vectors are discussed in detail. Decompositions of the power spectral density matrix are also discussed showing the physical significance of eigenquantities of this matrix.