Symmetry Limit Research Articles

繰り返し水平載荷を受ける立体骨組の対称限界および構面内挙動限界解析法

A finite element analysis method is proposed for finding the symmetry limit and the in-plane limit of space frames subjected to cyclic horizontal displacement. Analyses are performed for two types of one-story space frames based on the proposed method. As a result of the analyses, displacement amplitudes and bifurcation modes of the in-plane limit and the symmetry limit are obtained, respectively. Accuracy of those limits is verified by hysteretic response analyses for the frames.

Interrelation between the isoscalar octupole phonon and the proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei

The interrelation between the octupole phonon and the low-lying proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei is investigated. The one-phonon states decay by collective E3 and E2 transitions to the ground state and by relatively strong E1 and M1 transitions to the isoscalar 2 + 1 state. We apply the proton–neutron version of the interacting boson model including quadrupole and octupole bosons ( sdf -IBM-2). Two F -spin symmetric dynamical symmetry limits of the model, namely the vibrational and the γ -unstable ones, are considered. We derive analytical formulae for excitation energies as well as B( E1) , B( M1) , B( E2) and B( E3) values for a number of transitions between low-lying states.

Group theoretical properties and band structure of the Lamé Hamiltonian

We study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits.

Symmetry limit properties ofa priori mixing amplitudes fornon-leptonic and weak radiative decays ofhyperons

We show that, even if a priori mixings of positive-parity butflavour-violating eigenstates are allowed in physical hadrons, in the strongflavour symmetry limit the mixing angle will drop out of the matrixelements of the Yukawa and electromagnetic Hamiltonians that lead tonon-leptonic and weak radiative decays of hyperons in this scheme.We compare this result with related theorems for the same W-mediateddecays and give a concrete example of this behaviour by considering theU-spin symmetry of baryons and the U-doublet formed by p andΣ+.

Symmetry limit theory for elastic-perfectly plastic continua in the shakedown region

The symmetry limit theory, originally developed for beam-columns with uni-axial constitutive relations, is extended to elastic-perfectly plastic continua in the shakedown region. In the symmetry limit theory, we trace the steady-state path, or the variation of a steady-state cyclic response under an idealized cyclic loading program with continuously increasing amplitude. A steady-state response is represented by a set of the equilibrium configurations at load reversals. Key extension in the present theory is the derivation of the multi-axial constitutive relations for tracing the steady-state path. Noting that plastic strains are constant throughout a steady cycle in shakedown elements, we derive the constitutive relations in which stress rates and strain rates at load reversals may be coupled. With these constitutive relations, the symmetry limit can be found as the first branching point of the steady-state path. The present theory is verified through numerical examples.

Regular and chaotic motions in nuclear dynamics

A careful quantum statistical analysis of regular and chaotic dynamical behaviours in shape-transitional regions within the framework of IBM-2 has been performed, thus providing striking evidence that regular patterns extend far away from dynamical symmetry limits, mainly in the case of transitions from deformed (axially symmetric and triaxial) to spherical shapes.

One-pion transitions between heavy baryons in the constituent quark model

Single pion transitions of S wave to S wave, P wave to S wave and P wave to P wave heavy baryons are analyzed in the framework of the Heavy Quark Symmetry limit (HQS). We use a constituent quark model picture for the light diquark system with an underlying SU(2N_{f}) X O(3) symmetry to reduce the number of the HQS coupling factors required to describe these transitions. We also use the quantum theory of angular momentum to rewrite the one-pion transitions constituent quark model results in a more general form using the 6j- and 9j-symbols. We finally estimate the decay rates of some single pion transitions between charm baryon states.

On different criteria for confinement

We compare two approaches in supersymmetric confinement, the Seiberg formulation and the superconvergence rule. For the latter, the critical point is γ 00=0 in the Landau gauge. We find 4 γ 00= β 0 is the critical point for most of confining theories without a tree-level superpotential in the Seiberg formulation, in particular, in the large N c and N f limit. We show how confining theories with a discrete symmetry and a tree-level superpotential connect these two critical points: the large and small discrete symmetry limits correspond to the critical points 4 γ 00= β 0 and γ 00=0, respectively.

Weak decays ΞQ→ ΛQπ

The weak decays Ξ b→Λ b π and Ξ c→Λ c π , in which the heavy quark is not destroyed, are discussed. The branching fractions for these decays, corresponding to an absolute rate of order 0.01 ps −1 , should be at a one percent level for the b hyperons and at a (few) per mill level for Ξ c , possibly making feasible their experimental study in future. It is shown, through an application of the heavy quark limit, the flavor SU(3) symmetry, and PCAC, that the ΔI=1/2 rule should hold very well in these decays, and also that the Ξ b decays are purely S wave in the symmetry limit, while the difference between the S wave amplitudes of the Ξ c decays and those for the Ξ b is related, in terms of the heavy quark expansion, to the difference of the total decay rates within the ( Ξ c, Λ c ) triplet of charmed hyperons. We also comment on the amplitudes of the semileptonic transitions Ξ Q→Λ Q ℓ ν and on the weak radiative decays Ξ Q→Λ Q γ .

O(36) Symmetry Limit of IBM-4 with Good s, d, and sd Boson Spin–Isospin Wigner's SU(4)∼O(6) Symmetries for N≈Z Odd–Odd Nuclei

Led by the current interest in nuclear structure experiments at the N=Z line and the problem of competing isospin T=0 and T=1 pairing modes in such nuclei, it has become important to investigate the properties of the spin–isospin invariant interacting boson model (IBM-4) of Elliott and White. Following this, in the present work the IBM-4 OsdST(36)⊃OSsTs(6)⊕OdST(30)⊃OL(3)⊕OST(6) symmetry limit with not only good sd boson spin–isospin O(6) symmetry but also good s and d boson space O(6) symmetries (i.e., Wigner's spin–isospin SU(4)'s) is identified and analyzed. This symmetry limit is expected to carry signatures typical of some heavy (proton-rich) N≈Z odd–odd nuclei. For this symmetry limit group chain, irrep labels, group generators, quadratic Casimir operators, and energy formula are given. Both in the symmetry limit and allowing for mixing, the number of T=0 pairs in the ground states as a function of boson number and isospin is studied for N=Z nuclei and the results are consistent with known shell model predictions. For N=Z odd–odd nuclei, in the symmetry limit analytical formulas are derived for B(E2)'s in low-lying levels (with O(36) quantum number ω=N, where N is boson number) and also for the yrast band with (ST)=(01) (say as in 74Rb). It is seen that the pattern of B(E2)'s in low-lying levels depend sensitively on the structure of the E2 operator with respect to OST(6) and the symmetry limit generates a isospin dictated ΔJ=4 staggering in (ST)=(01) yrast B(E2)'s. Finally, it is shown that two-nucleon transfer strengths from even–even to odd–odd N=Z nuclei give information about high-lying states with O(36) quantum number ω=N−2.

Quadrupole shape invariants in the interacting boson model

In terms of the Interacting Boson Model, shape invariants for the ground state, formed by quadrupole moments up to sixth order, are studied in the dynamical symmetry limits and, for the first time, over the whole structural range of the IBM-1. The results are related to the effective deformation parameters and their fluctuations in the geometrical model. New signatures that can distinguish vibrator and gamma-soft rotor structures, and one that is related to shape coexistence, are identified.

Local mirror symmetry and type IIA monodromy of Calabi–Yau manifolds

We propose a monodromy invariant pairing Khol(X) H3(X _ ;Z) ! Q for a mirror pair of Calabi-Yau manifolds, (X; X _ ). This pairing is utilized implicitly in the previous calculations of the prepotentials for Gromov-Witten invariants. After identifying the pairing explicitly we interpret some hypergeometric series from the viewpoint of homo- logical mirror symmetry due to Kontsevich. Also we consider the local mirror symmetry limit to del Pezzo surfaces in Calabi-Yau 3-folds.

Hexagonal theory of flavor

We construct a supersymmetric theory of flavor based on the discrete gauge group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one to distinguish the third from the lighter two generations of matter fields, so that in the symmetry limit only the top quark Yukawa coupling is allowed and scalar superpartners of the first two generations are degenerate. Light fermion Yukawa couplings arise from a sequential breaking of the flavor symmetry, and supersymmetric flavor-changing processes remain adequately suppressed. We contrast our model with others based on non-Abelian discrete gauge symmetries described in the literature, and discuss the challenges in constructing more minimal flavor models based on this approach.

The Interacting Boson Model with SU(3) Charge Symmetry and Its Application to Even–Even N≈Z Nuclei

The isospin-invariant interacting boson model IBM-3 is analyzed in situations where SUT (3) charge symmetry (or, equivalently, UL(6)sd symmetry) is conserved. Analytic expressions for energies, electromagnetic transitions, two-nucleon transfer probabilities, and boson-number expectation values are obtained for the three possible dynamical symmetry limits, U(5), SU(3), and O(6). Results found in IBM-3 are related to corresponding ones in IBM-1 and IBM-2. Numerical calculations are presented for f7/2-shell nuclei and some features that distinguish IBM-3 from its predecessors IBM-1 and IBM-2 are pointed out.

Quantum XY Spin Glass Model with Longitudinal Ferromagnetic Coupling

The quantum XY spin glass model with longitudinal ferromagnetic coupling is investigated in static replica symmetry limit. Several thermodynamic quantities are calculated numerically. We find that the ferromagnetic coupling enhances the stability of replica symmetric solution. A 2-dimensional Ising model like transition is found, which demonstrates that the ferromagnetic coupling increases the order of spin glass model. Affected by the ferromagnetic coupling, transverse component of the susceptibility has two cusps corresponding to transverse-longitudinal spin-glass phase transition and longitudinal spin glass-paramagnetic transition separately.

Where does flavour mixing come from?

We argue that flavour mixing, both in the quark and charged lepton sector, is basically determined by the lightest family mass generation mechanism. So, in the chiral symmetry limit when the up and down quark masses vanish, all the quark mixing angles vanish. This mechanism is not dependent on the number of quark-lepton families nor on any “vertical” symmetry structure, unifying quarks and leptons inside a family as in Grand Unified Theories. Together with a hypothesis of maximal CP violation, the model leads to a completely predictive ansatz for all the CKM matrix elements in terms of the quark masses. Some implications for neutrino masses and oscillations are briefly discussed.

SU(3) coupling schemes for odd-odd nuclei in the interacting boson – fermion – fermion model with both odd proton and odd neutron in natural parity orbits

The SUBFF(3) dynamical symmetry limits of interacting boson – fermion – fermion model are identified and they are appropriate for heavy deformed odd – odd nuclei for configurations with both the odd proton and odd neutron occupying all the natural parity orbits in the corresponding valence shells. There are three symmetry limits and their correspondence with two quasi-particle (proton-neutron) Nilsson configurations is established; one of the limits mixes both Nilsson nz's and Λ's and other two limits mix only Nilsson Λ's. The 191Ir (d,t) 190Ir single nucleon transfer spectroscopic strengths are well described by one of the symmetry limits that mixes only Nilsson Λ's.

SU(3)symmetry breaking in hyperon semileptonic decays

Flavor $\mathrm{SU}(3)$ symmetry breaking in hyperon semileptonic decay form factors is analyzed using the ${1/N}_{c}$ expansion. A detailed comparison with experimental data shows that corrections to ${f}_{1}$ are approximately 10%, which agrees with theoretical expectations. Corrections to ${g}_{1}$ are compatible with first-order symmetry breaking. A fit to the experimental data allows one to predict the ${g}_{1}$ form factor for ${\ensuremath{\Xi}}^{0}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{+}$ decay. The proton matrix element of the ${T}^{8}$ component of the axial vector current [which is equal to $3F\ensuremath{-}D$ in the $\mathrm{SU}(3)$ symmetry limit] is found to be $\ensuremath{\approx}0.34--0.46.$

Symmetry schemes for spectroscopy of drip line nuclei

The , and O(36) symmetry limits of IBM-4 contain group chains with good s and d boson spins and isospins and they provide, just as IBM-3 symmetry limits with good s and d boson isospins, symmetry schemes for near-proton drip line nuclei. Using an group chain with good s and d boson spins and isospins, the observed ground T = 1 and excited T = 0 bands in are described.

Parameter symmetry of the interacting boson model

We discuss the symmetry of the parameter space of the interacting boson model (IBM). It is shown that for any set of the IBM Hamiltonian parameters (with the only exception of the U(5) dynamical symmetry limit) one can always find another set that generates the equivalent spectrum. We discuss the origin of the symmetry and its relevance for physical applications.