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At least 1,693 records · Page 94
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DOE OSTI2010

Analysis of Mode III Elastodynamic Cracked Plane using the Fractal Two-Level Finite Element Method

In this study, the fractal two-level finite element method, which has mainly been used for static cracked plane problems, is applied to the cracked plane problem. Using the transformation process in the proposed method, the infinite dimension of the finite element matrices that are assembled for a singular region is made finite in terms of the dynamics stress intensity factors directly, and thus the computational time can be reduced significantly. The Newmark time integration scheme is then used to obtain the dynamic stress intensity factors. The results from the proposed method are in reasonable agreement with those of classical methods. The main drawback of the time integration scheme is that numerical oscillations are induced in some cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Application of Thermoporometry to Evaluate the Mesoporosity of Cement Pastes

In the context of temporary near-surface or reversible deep geological storage of intermediate-level radioactive waste (ILW), most wastes package concepts comprise an external container made of fiber reinforced concrete, receiving several primary waste packages. Self-irradiation of encapsulating and/or embedding matrices can lead to continuous production of hydrogen which, for obvious safety reasons, must be removed from the container. Previous studies have demonstrated that gas transport depends on two interdependent factors: the water saturation and the microstructural properties of the material. Most techniques used to investigate cement paste porosity require drying of the cement paste prior to the test, which can modify the material microstructure and does not permit the localization of the aqueous phase in the material with various degrees of saturations. This paper focuses on the characterization of pores in cement paste by thermoporometry. The technique, based on the thermodynamic conditions of the melting-solidification reactions of a condensate inside a porous body, provides a simple method for determining the pore size distribution in saturated cement pastes. The results obtained on cement pastes of different formulations with different types of cement are discussed in term of material microstructure and compared with those obtained by other techniques.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2010

On Exceptional Superconformal Algebras

We obtain realizations of superconformal algebras K(2), K'(4) and the exceptional N = 6 superconformal algebra in matrices over a Weyl algebra of size 2x2, 4x4 and 8x8, respectively. A general construction of these realizations is based on the spin representations of the orthogonal Lie algebras. We give explicit descriptions of these matrix realizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Analytically Solvable Quantum Hamiltonians and Relations to Orthogonal Polynomials

Quantum systems consisting of a linear chain of n harmonic oscillators coupled by a quadratic nearest-neighbour interaction are considered. We investigate when such a system is analytically solvable, in the sense that the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This leads to a relation with Jacobi matrices of systems of discrete orthogonal polynomials. Our study is first performed in the case of canonical quantization. Then we consider these systems under Wigner quantization, leading to solutions in terms of representations of Lie superalgebras. Finally, we show how such analytically solvable Hamiltonians also play a role in another application, that of spin chains used as communication channels in quantum computing. In this context, the analytic solvability leads to closed form expressions for certain transition amplitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

A note on the nonexistence of sum of squares certificates for the Bessis-Moussa-Villani conjecture

The algebraic reformulation of the Bessis-Moussa-Villani conjecture is equivalent to a family of dimension-free tracial inequalities involving positive semidefinite matrices. Sufficient conditions for these to hold in the form of algebraic identities involving polynomials in noncommuting variables have been given by Klep and Schweighofer ['Sums of Hermitian squares and the BMV conjecture', J. Stat. Phys. 133, 739 (2008)]. Later the existence of these certificates has been settled for all but one case, which is resolved in this note.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Inverse scattering transform for the nonlinear Schroedinger system on a zigzag-runged ladder lattice

A detailed description of four-component nonlinear Schroedinger system on zigzag-runged ladder lattice is given. In order to support the equivalence between the two pairs of field amplitudes, we introduce the two sets of auxiliary linear problems, allowing one to develop the inverse scattering technique in the most adequate symmetrical form. The two complementary sets of discrete Marchenko equations are derived and their multisoliton solutions for the true reflectionless field amplitudes are found. The dispersion relations for the diagonal elements of reduced monodromy matrices are obtained. We explicitly present the simplest realization of soliton dynamics corresponding to the time-independent intersite coupling parameters and zero Peierls phases and show that the two-site structure of the lattice unit cell is strictly manifested as the two splitted branches of soliton excitations. In the general case of time-dependent intersite coupling parameters and nonzero Peierls phases, the theory is capable to model the dynamics of parametrically driven nonlinear ladder systems subjected to external magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Matrix Structure Exploitation in Generalized Eigenproblems Arising in Density Functional Theory

In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap matrices and solving the associated generalized eigenproblems Ax = {lambda}Bx constitute the two most time-consuming fractions of each iteration. Two promising directions, implementing the new methodology, are presented that will ultimately improve the performance of the generalized eigensolver and save computational time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

A theoretical approach to the photochemical activation of matrix isolated aluminum atoms and their reaction with methane

The photochemical activation of Al atoms in cryogenic matrices to induce their reaction with methane has been experimentally studied before. Here, a theoretical study of the nonadiabatic transition probabilities for the ground ({sup 2}P:3s{sup 2}3p{sup 1}) and the lowest excited states ({sup 2}S:3s{sup 2}4s{sup 1} and {sup 2}D:3s{sup 2}3d{sup 1}) of an aluminum atom interacting with a methane molecule (CH{sub 4}) was carried out through ab initio Hartree-Fock self-consistent field calculations. This was followed by a multiconfigurational study of the correlation energy obtained by extensive variational and perturbational configuration interaction analyses using the CIPSI program. The {sup 2}D state is readily inserted into a C-H bond, this being a prelude to a sequence of avoided crossings with the initially repulsive (to CH{sub 4}) lower lying states {sup 2}P and {sup 2}S. We then use a direct extension of the Landau-Zener theory to obtain transition probabilities at each avoided crossing, allowing the formation of an HAlCH{sub 3} intermediate that eventually leads to the final pair of products H+AlCH{sub 3} and HAl+CH{sub 3}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Characteristics of level-spacing statistics in chaotic graphene billiards

A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

The automorphism group of separable states in quantum information theory

We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by natural automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. We apply our results to the preservers of the product numerical range.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Balancing single- and multi-reference correlation in the chemiluminescent reaction of dioxetanone using the anti-Hermitian contracted Schroedinger equation

Direct computation of energies and two-electron reduced density matrices (2-RDMs) from the anti-Hermitian contracted Schroedinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)], it is shown, recovers both single- and multi-reference electron correlation in the chemiluminescent reaction of dioxetanone especially in the vicinity of the conical intersection where strong correlation is important. Dioxetanone, the light-producing moiety of firefly luciferin, efficiently converts chemical energy into light by accessing its excited-state surface via a conical intersection. Our previous active-space 2-RDM study of dioxetanone [L. Greenman and D. A. Mazziotti, J. Chem. Phys. 133, 164110 (2010)] concluded that correlating 16 electrons in 13 (active) orbitals is required for realistic surfaces without correlating the remaining (inactive) orbitals. In this paper we pursue two complementary goals: (i) to correlate the inactive orbitals in 2-RDMs along dioxetanone's reaction coordinate and compare these results with those from multireference second-order perturbation theory (MRPT2) and (ii) to assess the size of the active space--the number of correlated electrons and orbitals--required by both MRPT2 and ACSE for accurate energies and surfaces. While MRPT2 recovers very different amounts of correlation with (4,4) and (16,13) active spaces, the ACSE obtains a similar amount of correlation energy with either active space. Nevertheless, subtle differences in excitation energies near the conical intersection suggest that the (16,13) active space is necessary to determine both energetic details and properties. Strong electron correlation is further assessed through several RDM-based metrics including (i) total and relative energies, (ii) the von Neumann entropy based on the 1-electron RDM, as well as the (iii) infinity and (iv) squared Frobenius norms based on the cumulant 2-RDM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2010

Perturbative Aspects of Low-Dimensional Quantum Field Theory

We investigate the low-dimensional applications of Quantum Field Theory (QFT), namely Chern-Simons-Witten Theory (CSWT) and Affine Toda Field Theory (ATFT) in 3- and 2- dimensions. We discuss the perturbative aspects of both theories and compare the results to the exact solutions obtained nonperturbatively. For the three dimensions CSWT case, the perturbative term agree with the nonperturbative polynomial invariants up to third order of the coupling constant 1/k. In the two dimensions ATFT, we investigate the perturbative aspect of S-matrices for A{sub 1}{sup (1)} case in eighth order of the coupling constant {beta}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Entropy distance: New quantum phenomena

We study a curve of Gibbsian families of complex 3 Multiplication-Sign 3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance, and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology, and information geometry. This research is motivated by a theory of infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Fluctuation studies in the infinite interval matrix representations of operator products and their decompositions

In this work a study on finite dimensional matrix approximations to products of quantum mechanical operators is conducted. It is emphasized that the matrix representation of the product of two operators is equal to the product of the matrix representation of each of the operators when all the fluctuation terms are ignored. The calculation of the elements of the matrices corresponding to the matrix representation of various operators, based on three terms recursive relation is defined. Finally it is shown that the approximation quality depends on the choice of higher values of n, namely the dimension of Hilbert space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl{sub -1}(2)

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl{sub -1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from the q{yields}-1 limit of the dual q-Hahn polynomials. The Hopf algebra sl{sub -1}(2) has four generators including an involution, it is also a q{yields}-1 limit of the quantum algebra sl{sub q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of the -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl{sub -1}(2) algebras, so that the Clebsch-Gordan coefficients of sl{sub -1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

An explicit SU(12) family and flavor unification model

An explicit SUSY SU(12) unification model with three light chiral families is presented which avoids any external flavor symmetries. The hierarchy of quark and lepton masses and mixings is explained by higher dimensional Yukawa interactions involving Higgs bosons containing SU(5) singlet fields with VEVs appearing at or below the SUSY GUT scale of 2 Multiplication-Sign 10{sup 16} GeV, approximately 50 times smaller than the SU(12) unification scale. The model has been found to be in good agreement with the observed quark and lepton masses and mixings, with nearly all prefactors of {beta}(1) in the four Dirac and one Majorana fermion mass matrices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

New simple A{sub 4} neutrino model for nonzero {theta}{sub 13} and large {delta}{sub CP}

In a new simple application of the non-Abelian discrete symmetry A{sub 4} to charged-lepton and neutrino mass matrices, we show that for the current experimental central value of sin{sup 2} 2{theta}{sub 13} Asymptotically-Equal-To 0.1, leptonic CP violation is necessarily large, i.e. Double-Vertical-Line tan{delta}{sub CP} Double-Vertical-Line > 1.3. We also consider T{sub 7} model with one parameter to be complex, thus allowing for one Dirac CP phase {delta}{sub CP} and two Majorana CP phases {alpha}{sub 1,2}. We find a slight modification to this correlation as a function of {delta}{sub CP}. For a given set of input values of {Delta}m{sup 2}{sub 21}, {Delta}m{sup 2}{sub 32}, {theta}{sub 12}, and {theta}{sub 13}, we obtain sin{sup 2} 2{theta}{sub 23} and m{sub ee} (the effective Majorana neutrino mass in neutrinoless double beta decay) as functions of tan {delta}{sub CP}. We find that the structure of this model always yields small Double-Vertical-Line tan {delta}{sub CP} Double-Vertical-Line .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗