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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
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DOE OSTI2010

Spectral properties of embedded Gaussian unitary ensemble of random matrices with Wigner's SU(4) symmetry

For m fermions in {Omega} number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of random matrices generated by random two-body interactions that are SU(4) scalar [EGUE(2)-SU(4)]. Here the SU(4) algebra corresponds to the Wigner's supermultiplet SU(4) symmetry in nuclei. Embedding algebra for the EGUE(2)-SU(4) ensemble is U(4{Omega}) contains U({Omega}) x SU(4). Exploiting the Wigner-Racah algebra of the embedding algebra, analytical expression for the ensemble average of the product of any two m particle Hamiltonian matrix elements is derived. Using this, formulas for a special class of U({Omega}) irreducible representations (irreps) {l_brace}4{sup r}, p{r_brace}, p = 0, 1, 2, 3 are derived for the ensemble averaged spectral variances and also for the covariances in energy centroids and spectral variances. On the other hand, simplifying the tabulations of Hecht for SU({Omega}) Racah coefficients, numerical calculations are carried out for general U({Omega}) irreps. Spectral variances clearly show, by applying Jacquod and Stone prescription, that the EGUE(2)-SU(4) ensemble generates ground state structure just as the quadratic Casimir invariant (C{sub 2}) of SU(4). This is further corroborated by the calculation of the expectation values of C{sub 2}[SU(4)] and the four periodicity in the ground state energies. Secondly, it is found that the covariances in energy centroids and spectral variances increase in magnitude considerably as we go from EGUE(2) for spinless fermions to EGUE(2) for fermions with spin to EGUE(2)-SU(4) implying that the differences in ensemble and spectral averages grow with increasing symmetry. Also for EGUE(2)-SU(4) there are, unlike for GUE, non-zero cross-correlations in energy centroids and spectral variances defined over spaces with different particle numbers and/or U({Omega}) [equivalently SU(4)] irreps. In the dilute limit defined by {Omega} {yields} {infinity}, r >> 1 and r/{Omega} {yields} 0, for the {l_brace}4{sup r}, p{r_brace} irreps, we have derived analytical results for these correlations. All correlations are non-zero for finite {Omega} and they tend to zero as {Omega} {yields} {infinity}.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Nonlinear Bogolyubov-Valatin transformations: Two modes

Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary SU(2{sup n}=4) transformations, is isomorphic to SO(6;R)/Z{sub 2}. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin-1/2 and single-spin-3/2 systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin-1/2 and single-spin-3/2 Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of SU(4) and SO(6;R) matrices (of respective sizes 4x4 and 6x6) and their mutual relation. - Highlights: > Reveals the structure of nonlinear canonical transformations for two fermionic modes. > Studies nonlinear basis transformations in a Clifford algebra. > Focuses on methodological and structural aspects. > Presents a new approach to the diagonalization of 4x4 matrix Hamiltonians. > Presents the relation between explicit parametrizations of SU(4) and SO(6;R) matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

SU(2s+1) symmetry and nonlinear dynamics of high spin magnets

The article is devoted to the description of dynamics of magnets with arbitrary spin on the basis of the Hamiltonian formalism. The relationship of quantum states and magnetic degrees of freedom has been considered. Subalgebras of Poisson bracket of magnetic values for spin s=1/2; 1; 3/2 have been established. We have obtained non-linear dynamic equations for the normal and degenerate non-equilibrium states of high-spin magnets with the SO(3), SU(4), SU(2)×SU(2), SU(3), SO(4), SO(5) symmetries of exchange interaction. The connection between models of magnetic exchange energy and the Casimir invariants has been discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A compact 341 model at TeV scale

We build a gauge model based on the SU(3){sub c}⊗SU(4){sub L}⊗U(1){sub X} symmetry where the scalar spectrum needed to generate gauge boson and fermion masses has a smaller scalar content than usually assumed in literature. We compute the running of its abelian gauge coupling and show that a Landau pole shows up at the TeV scale, a fact that we use to consistently implement those fermion masses that are not generated by Yukawa interactions, including neutrino masses. This is appropriately achieved by non renormalizable effective operators, suppressed by the Landau pole scale. Also, SU(3){sub c}⊗SU(3){sub L}⊗U(1){sub N} models embedded in this gauge structure are bound to be strongly coupled at this same energy scale, contrary to what is generally believed, and neutrino mass generation is rather explained through the same effective operators used in the larger gauge group. Besides, their nice features, as the existence of cold dark matter candidates and the ability to reproduce the observed standard model Higgs-like phenomenology, are automatically inherited by our model. Finally, our results imply that this model is constrained to be observed or discarded soon, since it must be realized at the currently probed energy scale in LHC. - Highlights: • We build a SU(4){sub L}⊗U(1){sub N} electroweak model with a reduced scalar spectrum. • The existence of a Landau pole at TeV scale is investigated. • Fermion masses in this model, including neutrinos, emerge from effective operators. • Imposition of an extra Z{sub 2} symmetry avoids fast proton decay.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Effective interactions and long distance symmetries in the Nucleon-Nucleon system

Effective interactions, when defined in a coarse grained sense, such as V{sub lowk} at the scale {Lambda} = 450 MeV, display a remarkable symmetry pattern. Serber symmetry works with high accuracy for spin triplet states. Wigner SU(4) spin-isospin symmetry with nucleons in the fundamental representation works only for even partial waves exactly as predicted by large N{sub c} limit of QCD with accuracy O(1/N{sub c}{sup 2}). This suggests tailoring the very definition of effective interactions to provide a best possible fulfillment of long distance symmetries. With the V{sub lowk} definition Wigner symmetry requires that chiral potentials have low cut-offs {Lambda}{sub {chi}{approx}4}50 MeV. Perturbative saturation of exchanged heavy mesonic resonances does not faithfully display the Serber symmetry pattern.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Graphene, Lattice Field Theory and Symmetries

Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

SU(6) superset of SU(3) x SU(2) and SU(8) superset of SU(4) x SU(2) Clebsch-Gordan coefficients

Tables of scalar factors are presented for 63 x 63 and 120 x 63 in SU(8) superset of SU(4) x SU(2), and for 35 x 35 and 56 x 35 in SU(6) superset of SU(3) x SU(2). Related tables for SU(4) superset of SU(3) x U(1) and SU(3) superset of SU(2) x U(1) are also provided so that the Clebsch-Gordan coefficients can be completely reconstructed. These are suitable to study meson-meson and baryon-meson interactions within a spin-flavor symmetric scheme.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

New look at the [70,1{sup -}] nonstrange and strange baryons in the 1/N{sub c} expansion

The masses of excited nonstrange and strange baryons belonging to the multiplet [70,1{sup -}] are calculated in the 1/N{sub c} expansion to order 1/N{sub c} with a new method which allows to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Spin(7)-structures on complex linear bundles and explicit Riemannian metrics with holonomy group SU(4)

A system of differential equations with 5 unknowns is fully investigated; this system is equivalent to the existence of a parallel Spin(7)-structure on a cone over a 3-Sasakian manifold. A continuous one-parameter family of solutions to this system is explicitly constructed; it corresponds to metrics with a special holonomy group, SU(4), which generalize Calabi's metrics. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Reduced-complexity numerical method for optimal gate synthesis

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate-design problem is equivalent to the solution of an associated optimal-control problem; the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality-free techniques) that determine the optimal control, thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control-set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, which is used in previous research. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on SU(4) - a problem that is computationally intractable by grid-based approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Origin of a sensitive dependence of calculated {beta}{beta}-decay amplitudes on the particle-particle residual interaction

In the present work the sensitivity of calculated {beta}{beta}-decay amplitudes to a realistic residual interaction is analyzed in the framework of the approach of O. A. Rumyantsev and M. H. Urin, Phys. Lett. B 443, 51 (1998). and V. A. Rodin, M. H. Urin, and A. Faessler, Nucl. Phys. A 747, 297 (2005). Both the Gamow-Teller (GT) and Fermi (F) matrix elements M{sup 2}{nu} for two-neutrino {beta}{beta} decay (2{nu}{beta}{beta} decay), along with the monopole transition contributions to the total matrix elements M{sup 0{nu}} of neutrinoless {beta}{beta} decay (0{nu}{beta}{beta} decay), are calculated within the quasiparticle random-phase approximation (QRPA). In the aforementioned approach decompositions of M{sup 2{nu}} and M{sup 0{nu}} can be obtained in terms of the corresponding energy-weighted sum rules S. It is shown that in most of the cases almost the whole dependence of M{sup 2{nu}} and M{sup 0{nu}} on the particle-particle (p-p) renormalization parameter g{sub pp} is accounted for by the g{sub pp} dependence of the corresponding sum rules S. General expressions relating S to a realistic residual particle-particle interaction are derived, which show a pronounced sensitivity of S to the singlet-channel interaction in the case of F transitions and to the triplet-channel interaction in the case of GT transitions. Thus, the sensitivity of M{sup 2{nu}} and M{sup 0{nu}} to the SU(4)-symmetry-breaking part of the p-p residual interaction is dictated by the generic structure of the {beta}{beta}-decay amplitudes. Therefore, a choice of this part in a particular calculation needs a special caution. Finally, a better isospin-consistent way of renormalization of a realistic residual p-p interaction to use in QRPA calculations is suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2010

SU(4){sub L}xU(1){sub X} models with little Higgs mechanism

We study the aspects of the fermion and gauge boson sectors in SU(4){sub L}xU(1){sub X} models with a little Higgs mechanism. We introduce a new setup of fermions, which ensures the cancellation of gauge anomaly and the cancellation of one-loop quadratic divergence to the Higgs mass for all fermion multiplets and gauge bosons. We explicitly present the interactions between the standard model fermions and the heavy gauge bosons to discuss the phenomenological implications of extra Z{sup '} and Z{sup ''} gauge bosons based on recent experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Dual instantons in antimembranes theory

We introduce two ansatzs for the 3-form potential of Euclidean 11d supergravity on skew-whiffed AdS{sub 4}xS{sup 7} background which results in two scalar modes with m{sup 2}=-2 on AdS{sub 4}. Being conformally coupled with a quartic interaction, it is possible to find the exact solutions of the scalar equation on this background. These modes turn out to be invariant under the SU(4) subgroup of the SO(8) isometry group, whereas there are no corresponding SU(4) singlet Bogomol'nyi-Prasad-Sommerfeld operators of dimensions one or two on the boundary theory constructed by Aharony, Bergman, Jafferis, and Maldacena. Noticing the interchange of 8{sub s} and 8{sub c} representations under skew-whiffing in the bulk, we propose the theory of antimembranes should similarly be obtained from Aharony, Bergman, Jafferis, and Maldacena's theory by swapping these representations. In particular, this enables us to identify the dual boundary operators of the two scalar modes. We deform the boundary theory by the dual operators and examine the fermionic field equations, and compare the solutions of the deformed theory with those of the bulk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Baryogenesis via leptogenesis from quark-lepton symmetry and a compact heavy N{sub R} spectrum

By demanding a compact spectrum for the right-handed neutrinos and an approximate quark-lepton symmetry inspired from SO(10) gauge unification (assuming a Dirac neutrino mass matrix close to the up quark mass matrix), we construct a fine-tuning scenario for baryogenesis via leptogenesis. We find two solutions with a normal hierarchy, with the lightest neutrino mass m{sub 1} different from zero, providing an absolute scale for the spectrum. In the approximations of the model, there are three independent CP phases: {delta}{sub L} (that we take of the order of the quark Kobayashi-Maskawa phase) and the two light neutrino Majorana phases {alpha} and {beta}. A main conclusion is that, although this general scheme is rather flexible, in some regions of parameter space we find that the necessary baryogenesis with its sign is given in terms of the {delta}{sub L} phase alone. The light Majorana phases can also be computed, and they turn out to be close to {pi}/2 or very small. Moreover, SO(10) breaks down to the Pati-Salam group SU(4)xSU(2)xSU(2) at the expected natural intermediate scale of about 10{sup 10}-10{sup 11} GeV. A prediction is made for the effective mass in ({beta}{beta}){sub 0{nu}} decay, the {nu}{sub e} mass, and the sum of all light neutrino masses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Symmetry breaking phase transitions in the Aharony-Bergman-Jafferis-Maldacena theory with a finite U(1) chemical potential

We consider the U(1) charged sector of ABJM theory at finite temperature, which corresponds to the Reissner-Nordstrom AdS black hole in the dual type IIA supergravity description. Including back-reaction to the bulk geometry, we show that phase transitions occur to a broken phase where SU(4) R-symmetry of the field theory is broken spontaneously by the condensation of dimension one or two operators. We construct the composite operators out of fields in ABJM theory and describe the phase transition with the dual gravity solutions. We show numerically and analytically that the relevant critical exponents for the dimension one operator agree precisely with those of mean field theory in the strongly coupled regime of the large N planar limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Giant Gamow-Teller resonance in neutron-rich nuclei

The giant Gamow-Teller resonance and other branches of collective nuclear excitations are described on the basis of the theory of finite Fermi systems. A connection between the Gamow-Teller resonance and Wigner SU(4) symmetry is proven. The beta-decay strength function and processes accompanying the {beta}{sup -} decay of neutron-rich nuclei are described. The effect of the satellites of the Gamow-Teller resonance on the decay properties of neutron-rich nuclei is analyzed.

74 ATOMIC AND MOLECULAR PHYSICS↗