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Results for “SU-4 GROUPS”

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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE 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 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 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 OSTI2012

Spontaneous SU(2) symmetry violation in the SU(2){sub L} Multiplication-Sign SU(2){sub R} Multiplication-Sign SU(4) electroweak model

A new approach to electroweak (EW) composite scalars is developed starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure SU(2){sub L} Multiplication-Sign SU(2){sub R} Multiplication-Sign SU(4), where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Wave fluctuations in the system with some Yang-Mills condensates

Self-consistent dynamics of non-homogeneous fluctuations and homogeneous and isotropic condensate of Yang–Mills fields was investigated in zero, linear and quasilinear approximations over the wave modes in the framework of N = 4 supersymmetric model in Hamilton gauge in quasiclassical theory. The models with SU(2), SU(3) and SU(4) gauge groups were considered. Particle production effect and effect of generation of longitudinal oscillations were obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

SU(4) based classification of four-level systems and their semiclassical solution

We present a systematic method to classify the four-level system using SU(4) symmetry as the basis group. It is shown that this symmetry allows three dipole transitions which eventually leads to six possible configurations of the four-level system. Using a dressed atom approach, the semi-classical version of each configuration is exactly solved under rotating wave approximation and the symmetry among the Rabi oscillation among various models is studied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

On a microscopic representation of space–time IV

We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact “counterpart” SU*(4) being the complex embedding of SL(2,H). So after having related the 16-dim Dirac algebra to SU*(4), on the one hand we have access to real, complex, and quaternionic Lie group chains and their respective algebras, on the other hand it is of course possible to relate physical descriptions to the respective representations. With emphasis on the common maximal compact subgroup USp(4), we are led to projective geometry of the real 3-space and various transfer principles which we use to extend the previous work on the rank 3-algebras above. On real spaces, such considerations are governed by the groups SO(n,m) with n + m = 6. The central thread, however, focuses here on line and Complex geometry which finds its well-known counterparts in descriptions of electromagnetism and special relativity as well as—using transfer principles—in Dirac, gauge, and quantum field theory. We discuss a simple picture where Complexe of second grade play the major and dominant rôle to unify (real) projective geometry, complex representation theory and line/Complex representations in order to proceed to dynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Neutrino masses in SU(4){sub L}⊗U(1){sub X} gauge models

Neutrino masses are obtained within SU(4){sub L}⊗U(1){sub X} electroweak gauge models with spontaneous symmetry breaking by simply exploiting the tree level realization of certain dimension-five effective operators. The scalar sector needs not to be enlarged, since these operators are constructed as direct products among scalar multiplets already existing in the model. There is a unique generic matrix for Yukawa couplings in the neutrino sector, while the charged leptons are already in their diagonal basis. The experimentally observed phenomenology in the neutrino sector is obtained as a natural consequence of this particular approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Tunnel magnetoresistance and linear conductance of double quantum dots strongly coupled to ferromagnetic leads

We analyze the spin-dependent linear-response transport properties of double quantum dots strongly coupled to external ferromagnetic leads. By using the numerical renormalization group method, we determine the dependence of the linear conductance and tunnel magnetoresistance on the degree of spin polarization of the leads and the position of the double dot levels. We focus on the transport regime where the system exhibits the SU(4) Kondo effect. It is shown that the presence of ferromagnets generally leads the suppression of the linear conductance due to the presence of an exchange field. Moreover, the exchange field gives rise to a transition from the SU(4) to the orbital SU(2) Kondo effect. We also analyze the dependence of the tunnel magnetoresistance on the double dot levels' positions and show that it exhibits a very nontrivial behavior.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2011

Entanglement and separability of two-qubit states on Minkowski space with compact support

The entanglement properties of a two-qubit system are analyzed from the point of view of Lie algebras and geometry. We deal with 4x4 matrices belonging to a particular class having seven free parameters, constructed from the imposed symmetries on two-qubit states expanded in terms of a basis whose elements belong to a subalgebra of su(4). The entanglement or separability character of the state is determined and measured by analyzing the eigenvalues of an auxiliary matrix obtained from the original state after performing on it a nonunitary operation. In terms of its eigenvalues, we define two squared distances having a Minkowski metric, s{sup 2}=t{sup 2}-V(vector sign){sup 2}, which become a measure of the entanglement. The Minkowski metric is a signature of that class of two-qubit states (matrices) and also of the auxiliary matrices to be constructed. The squared distance is invariant by any unitary transformation on the two-qubit state. We illustrate the theory with examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Evaluation of the degree of restoration of broken Wigner's SU(4) spin-isospin symmetry in nuclei

The Franzini-Radicati factor R was calculated on the basis of experimental data on the masses of nuclei in the mass-number range of 5 {<=} A {<=} 257. The values calculated for this factor made it possible to evaluate the degree of fulfillment of Wigner's SU(4) spin-isospin symmetry in nuclei. An expression for the factor R was obtained on the basis of Wigner's mass formula. This expression is isospin-dependent and takes into account odd-even variations in the mass. The formula for the factor R describes the separation of nuclei into threeWigner-type groups. The values calculated for the factor R were analyzed by the method of Student's t criterion, and it was inferred from the results of this analysis that only for nuclei having odd values of the mass number A and an isospin in the range of T{sub z} {>=} 53/2 is broken Wigner's SU(4) spin-isospin symmetry restored, the confidence level being {alpha} = 0.01.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Some special features of Wigner’s mass formula for nuclei

Experimental data on anomalous values of the empirical function b(A) in Wigner’s mass formula are presented, the application of Student’s t criterion in experimentally proving the restoration of Wigner’s SU(4) symmetry in nuclei is validated, and a physical interpretation of the basic parameter of the empirical function a(A) in Wigner’s mass formula is given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Charge-exchange resonances and restoration of Wigner’s supersymmetry in heavy and superheavy nuclei

Various facets of the question of whether Wigner’s supersymmetry [SU(4) symmetry] may be restored in heavy and superheavy nuclei are analyzed on the basis of a comparison of the results of calculations with experimental data. The energy difference between the giant Gamow–Teller resonance and the analog resonance (the difference of E{sub G} and E{sub A}) according to calculations based on the theory of finite Fermi systems is presented for the case of 33 nuclei for which experimental data are available. The calculated difference ΔE{sub G–A} of E{sub G} and E{sub A} tends to zero in heavier nuclei, showing evidence of the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring isobaric nuclei is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of A = 5–244. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of SU(4) symmetry is compatible with the possible existence of the stability island in the region of superheavy nuclei.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗