Tri-bimaximal mixing from twisted Friedberg–Lee symmetry

We investigate the Friedberg–Lee (FL) symmetry and its promotion to include the μ–τ symmetry, and call this the twisted FL symmetry. Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing. In the first scheme, we suggest the semi-uniform translation of the FL symmetry. The second one is based on the S ₃ permutation family symmetry. The breaking terms, which are twisted FL symmetric, are introduced. Some viable models in each scheme are also presented.     

SU4群与基本粒子的对称性

从李羣的一般理论,具体地讨论了SU₄的数学处理,给出了羣的代数结构、不可约表示维数的公式、三个基本表示的明显形式及表示直积分解的主要结果。根据SU₄对称,下列基本粒子的对称模型被构成:(1)Bacry和Van Hove模型,(2)Schwinger模型,(3)正反粒子对称的坂田模型,(4)正反粒子对称的八度法模型。在这些模型中,一些与实验一致的新的结果被得到。     

The su q(2) algebra in the off-diagonal basis and applications to quantum optics

We consider a new exactly solvable nonlinear quantum model as a Hamiltonian defined in terms of the generators of the su _q(2) algebra. The corresponding matrix elements of finite rotations (the q-deformed Wigner d functions) are introduced. It is shown that the quantum optical model of the three-wave interaction has an approximate su _q(2) dynamical symmetry given by this Hamiltonian. Such q symmetry allows us to investigate the spectral and dynamical properties of the three wave model through new perturbation techniques.     

Metastability and Spinodal Points for a Random Walker on a Triangle

We investigate time-dependent properties of a single-particle model in which a random walker moves on a triangle and is subjected to nonfocal boundary conditions. This model exhibits spontaneous breaking of a Z ₂ symmetry. The reduced size of the configuration space (compared to related many-particle models that also show spontaneous symmetry breaking) allows us to study the spectrum of the time evolution operator. We break the symmetry explicitly and find a stable phase, and a metastable phase which vanishes at a spinodal point. At this point, the spectrum of the time evolution operator has a gapless and universal band of excitations with a dynamical critical exponent z=1. Surprisingly, the imaginary parts of the eigenvalues E _j(L) are equally spaced, following the rule . Away from the spinodal point, we find two time scales in the spectrum. These results are related to scaling functions for the mean path of the random walker and to first passage times. For the spinodal point, we find universal scaling behavior. A simplified version of the model which can be handled analytically is also presented.     

Normal Coordinates Analysis for The M(NH3)2+ 4 Complex Ions in D4h and Td Symmetries. Simplified Molecular Models

A normal coordinates analysis for the M(NH₃)²⁺ ₄ complex ions in T_d symmetry (M = Zn, Cd, Co) and in D_4h symmetry (M = Cu, Pd, Pt) has been undertaken on the basis of a General Valence Force Field (GVFF), using simplified molecular models. Throughout the course of the present work, we have relaxed the point mass approximation for the NH₃-ligands in order to investigate, on a quantitative basis, some relevant ligand - framework coupling vibrations. The simplest molecular model able to accomplish this purpose is to treat the ammino group, in a linear ligator approximation. We show that these model calculations provide a satisfactory set of vibrational frequencies as well as consistent sets of force constants.     

用重整化群流方程方法求解t-J模型元激发能谱

t-J模型是研究电子强关联作用和高T_c超导理论的重要模型之一.将重整化群方法应用于t-J模型，得出相应的流方程，再由流方程求解t-J模型的元激发能谱，并利用函数的对称性，解出t-J模型在零温条件下能谱的具体表达式，最后与常规的格林函数方法所得的结果作了比较. 关键词： 重整化群 t-J模型 流方程     

The Flavor Physics in Unified Gauge Theory from an S3 × P Discrete Symmetry

We investigate the phenomenological implication of the discrete symmetry S₃ × P on flavor physics in SO(10) unified theory. We construct a minimal renormalizable model which reproduce all the masses and mixing angle of both quarks and leptons. As usually the SO(10) symmetry gives up to relations between the down sector and the charged lepton masses. The underlining discrete symmetry gives a contribution (from the charged lepton sector) to the PMNS mixing matrix which is bimaximal. This gives a strong correlation between the down quark and charged lepton masses, and the lepton mixing angles. We obtain that the small entries V _ub, V _cb, V _td, and V _ts in the CKM matrix are related to the small value of the ratio δ m² _solΔ m² _atm: they come from both the S₃×P structure of our model and the small ratio of the other quark masses with respect to m _t. Wonderfully, with our model, we fit 17 experimental data %with only 13 free relevant combinations of vevs.     

Hubbard model,conserved quantities,and computer algebra

The constants of motion of the half-filled four-point Hubbard model with cyclic boundary conditions are given in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C_4v symmetry and in Bloch representation we have the total momentum operator which is conserved. The anticommutation relations for Fermi operators with spin are implemented using computer algebra. Using computer algebra, all the constants of motion are given. The one-dimensional Hubbard model admits a Lax representation. From the Lax pair we find a new constant of motion.     

Symmetry-breaking scenarios of Wilson-loop broken E6

In superstring theories formulated on a multiply-connected manifold, E₆ gauge symmetry can be broken at the Planck scale to an extended standard model via an effective Higgs adjoint. It is possible to arrange for the coloured components of a Higgs 27 to gain a large mass via this Wilson-Loop breaking while leaving some colour singlet components massless. The remaining light Higgs representations can then be applied to break the extended electroweak symmetry at a lower scale. We investigate some of the symmetry-breaking scenarios for a rank-six extended group. We find that the Higgs multiplets left light after Wilson-loop breaking are not sufficient to break the extended electroweak symmetry to U₁^em     

Local symmetry in some quasicrystalline AlTFe alloys

Mössbauer spectra of AlTFe-alloys with T=Cr or Mn, show a quadrupole splitting QS≈0.4 mm/s. This shows that the iron atom is not in an icosahedral site. In order to investigate the local symmetry further, we applied an external magnetic field H_ext≈5T, so that the asymmetry parameter ν can be obtained. Using a one site approximation the results are: ν=0.7 for decagonal Al₇(Mn_0.7Fe_0.3)₂ and ν=0.8 for icosahedral Al₆Cr_0.7Fe_0.3. This means that the iron atoms are in sites with a symmetry lower than axially symmetric. Most of the vertices in a Penrose lattice show such a symmetry.     

Thermal expansion and magnetostriction of GdAg2, and relations to the magnetoelastic paradox

The antiferromagnet GdAg₂ has been shown to be a good model system for the magnetoelastic paradox (MEP), because it exhibits large symmetry conserving magnetoelastic strains and the antiferromagnetic propagation vector breaks the tetragonal lattice symmetry (therefore a large symmetry breaking magnetoelastic strain can be expected in a single magnetic structure). As in many similar Gd based compounds no symmetry breaking strain has been found in the experiment. In order to investigate this MEP further, we have measured magnetostriction and magnetization on a textured polycrystal. The behaviour closely resembles that of GdNi₂B₂C, the prototype system for the magnetoelastic paradox (MEP). Our forced magnetostriction data indicate that the crystal distorts in applied magnetic field and gives further evidence that the MEP is a low field effect. The observed phase transitions are in agreement with available specific heat and neutron diffraction data. Moreover, the saturation magnetic field was measured in high pulsed magnetic fields and agrees well with the value calculated from the Standard Model of Rare Earth Magnetism (SMREM).     

Traffic flow models with ‘slow-to-start’ rules

We investigate two models for traffic flow with modified acceleration (‘slow-to-start’) rules. Even in the simplest case v_max = 1 these rules break the ‘particle-hole’ symmetry of the model. We determine the fundamental diagram (flow-density relationship) using the so-called car-oriented mean-field approach (COMF) which yields the exact solution of the basic model with v_max = 1. Here we find that this is no longer true for the models with modified acceleration rules, but the results are still in good agreement with simulations. We also compare the effects of the two different slow-to-start rules and discuss their relevance for real traffic. In addition, in one of these models we find a new phase transition to a completely jammed state.     

Testing Theories of Chiral Symmetry

We investigate various physical consequences of theories of chiral symmetry. Predictions of the symmetry are given for the meson electroproduction process at an on-shell kinematical point where unknown contributions are minimized. Sum rules are derived for the corrections. Then we present a sum rule for the ∑ term in meson-baryon scattering from the assumptions of Bjorken limit, precocious asymptopia, and finite-mass dispersion relations. We use the commutation relations of the gluon model as input for a numerical evaluation. Next the explicit canonical structure of the light-cone restriction of the commutator of the weak current with its divergence is considered in the interacting quark-gluon model quantized in the infinite–momentum frame. The implications on neutrino scattering are analyzed. W₄ and W₅ are predicted to scale nontrivially as v⁻²F₄(ω) and v⁻²F₅(ω), which provides a simple test of light-cone current algebra feasible in the near future. The ∑ term for weak currents is deduced from a causal representation near the light-cone, and a correction is also made in the W₅ – sum rule obtained by naive infinite momentum techniques. As a by-product we obtain improved derivations of the Adler neutrino sum rules.     

双成分模型及YBCO/Pb结沿c轴的Josephson效应

根据巡游载流子与具有负U关联的近局域载流子相杂化的双成分模型研究了YBCO/Pb结沿c轴的Josephson效应．在此模型中巡游载流子具有s波对称性，能隙较小．近局域载流子具有d波超导电性，其临界温度决定体系的转变温度，沿c轴的Josephson电流I_c主要由s波贡献．由计算得到的s波能隙大小及其相应的临界温度较好地解释了实验观测到的零温隧穿电流与结电阻之积I_c（O）R_N以及I_c随温度的变化．此外，该模型还能解释在施加 关键词：     

Microscopic model of NaNO2 in the paraelectric phase

Starting from a sterical hindrance potential for the motion of the NO₂-molecular group in the deformable cage of neighbouring Na-ions, we derive a microscopic model for the NaNO₂ crystal in the paraelectric phase. The dynamical variables are the translational displacements of both the NO₂-groups and the Na-ions, and the reorientations of the NO₂-groups. Reorientations are described by means of symmetry adapted functions. From a numerical study of the model, we conclude that reorientations of the NO₂-groups take place essentially through rotations about the crystallographicc-axis. The model explains why optical experiments have led to the incorrect conclusion of reorientations about thea-axis. By studying the symmetry properties of the bilinear coupling of translations and rotations, we separate optical and acoustical displacements. Only the former couple to the order parameter in the long wavelength limit. Therefore there is no acoustical soft mode at the ferroelectric phase transitions. The bilinear coupling leads to an effective lattice mediated interaction among reorienting NO₂-groups.     

Gauge symmetry breaking in compact multiply connected manifolds

In a multiply connected manifold, M₄⊗S₃/Z², we compute at one-loop level the gauge symmetry breaking due to Wilson loops. For an SU(3) model without matter fields a non-trivial vacuum, which breaks the gauge symmetry has lower energy.     

Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators

We study the bifurcation and dynamical behaviour of the system of N globally coupled identical phase oscillators introduced by Hansel, Mato and Meunier, in the cases N=3 and N=4. This model has been found to exhibit robust ‘slow switching’ oscillations that are caused by the presence of robust heteroclinic attractors. This paper presents a bifurcation analysis of the system in an attempt to better understand the creation of such attractors. We consider bifurcations that occur in a system of identical oscillators on varying the parameters in the coupling function. These bifurcations preserve the permutation symmetry of the system. We then investigate the implications of these bifurcations for the sensitivity to detuning (i.e. the size of the smallest perturbations that give rise to loss of frequency locking).For N=3 we find three types of heteroclinic bifurcation that are codimension-one with symmetry. On varying two parameters in the coupling function we find three curves giving (a) an S₃-transcritical homoclinic bifurcation, (b) a saddle-node/heteroclinic bifurcation and (c) a Z₃-heteroclinic bifurcation. We also identify several global bifurcations with symmetry that organize the bifurcation diagram; these are codimension-two with symmetry.For N=4 oscillators we determine many (but not all) codimension-one bifurcations with symmetry, including those that lead to a robust heteroclinic cycle. A robust heteroclinic cycle is stable in an open region of parameter space and unstable in another open region. Furthermore, we verify that there is a subregion where the heteroclinic cycle is the only attractor of the system, while for other parts of the phase plane it can coexist with stable limit cycles. We finish with a discussion of bifurcations that appear for this coupling function and general N, as well as for more general coupling functions.     

Higgs and neutrino sector,EDM and ε<Subscript>K</Subscript> in a spontaneously CP and R-parity breaking supersymmetric model

We construct an extension of the supersymmetric standard model where both CP symmetry and R-parity are spontaneously broken. We study the electroweak symmetry breaking sector of the model and find minima consistent with the experimental bounds on Higgs boson masses. Neutrino masses and mixing angles are generated through both seesaw and bilinear R-parity violation. We show that the hierarchical mass pattern is obtained, and mixings are consistent with measured values. Due to the spontaneous CP and R-parity violation, the neutrino sector is CP violating, and we calculate the corresponding phase. We further restrict the parameter space to agree with the limits on the electric dipole moment of the neutron. Finally, we study the CP violation parameter ε_K in the kaon system and show that we obtain results consistent with the experimental value.     

The sphericalp-spin interaction spin glass model: the statics

The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step replica symmetry breaking. The transition from the replica symmetric solution to the replica replica symmetry broken one is either continuous or discontinuous inq ₁–q₀ depending on the strength of the external magnetic field. The model can be solved explicitly for anyp at any temperature and magnetic field. Below the transition we find an infinite number of metastable states.     

Is U(1)H a good family symmetry?

We analyze U(1)_H as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3)_c ? SU(2)_L ? U(1)_Y ? U(1)_H nonsuper-symmetric, are able to fit the experimental result m_b«m_t. identity, but it is a common prejudice to assume that the appropriate family symmetry may explain this fact as a consequence of (i) and (ii). In what follows we will enlarge the SM gauge group with an extra U(1)_H horizontal local gauge symmetry (the simplest multi-family continuous symmetry we can think of). We then show that the structure SU(3)_c ? SU(2)_L ? U(1)_Y ? U(1)_H by itself is able to explain (ii), and that the simplest supersymmetric (SUSY) extension of this model without a μ-term can not cope with (ii).