Specific propagation directions of acoustic waves for piezoelectric and nonpiezoelectric media

I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss the problem of acoustic axes for piezoelectric media of the symmetry class mm2. The text was submitted by the author in English.     

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.     

Dynamics of the Weyl scale invariant non-BPS <Emphasis Type="Italic">p</Emphasis> = 3 brane

In this paper a Weyl scale-invariant p = 3-brane scenario is introduced, with the brane embedded in a higher-dimensional bulk space with N = 1, 5D Super-Weyl symmetry. Its action, which describes its long wave oscillation modes into the ambient superspace and breaks the target symmetry down to the lower dimensional Weyl W(1, 3) symmetry, is constructed by the approach of coset method.     

Ground states of two-dimensional quasicrystals

Hamiltonians for nonperiodic tilings are considered. It is shown that the quasicrystalline tiling obtained by the cut-and-strip method from aD-dimensional cubic lattice may bs a ground state only if the tiling possesses a high orientational symmetry: the (2,D)-quasicrystal should haveD-fold symmetry ifD is even and 2D-fold symmetry ifD is odd. For interactions of a finite range the restrictions are stronger: only a (2, 5)-quasicrystal (Penrose tiling) may be a stable ground state.     

On long-range curve crossings

The V symmetry coupling coefficients for the icosahedral double group are generated from the behaviour of a minimum number of |JM> ket vectors where the symmetry coupling coefficients are defined as analogues of the Racah V coefficients. The phases are determined from the way the irreducible representations for the specific J values are defined. An investigation of the symmetry properties of the system by a translation of the |JM> ket vectors for integral J values is examined. The handling of the irreducible-tensor method in group notation is discussed briefly.     

New spherically symmetric solutions in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>)-gravity by Noether symmetries

Spherical symmetry for f (R)-gravity is discussed by searching for Noether symmetries. The method consists in selecting conserved quantities in form of currents that reduce dynamics of f (R)-models compatible with symmetries. In this way we get a general method to obtain constants of motion without setting a priori the form of f (R). In this sense, the Noether symmetry results a physical criterium. Relevant cases are discussed.     

The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N -body density correlations. While the original Hamiltonian has an exact Z₂ symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z₂ symmetry is recovered by enforcing Z₂ symmetry as a constraint on N -body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.     

Effect of crystal field on the spin density at the copper nucleus in copper complexes

The role of lower symmetry component of the crystal field in causing a mixing of excited 3d ^x−1 4s with the ground 3d ^x configuration and leading to spin density at the nucleus for iron group ions was suggested by Griffith and Orgel. This mechanism has been examined in detail for the two low-symmetry copper complexes, one square planar (D_4h symmetry) and the other distorted tetrahedron (D_2d symmetry) and the calculation has been performed using the powerful Racah method and tensor operator technique. It is found that for the two types of copper complexes, copper pthalocyanin (square planar, D_4h symmetry) and cesium copper chloride (distorted tetrahedron, D_2d symmetry) the contribution from this mechanism to the spin density at the nucleus vanishes identically.     

旋转对二维正方晶格介质柱内空结构光子晶体禁带的影响

采用平面波展开的方法计算了三种旋转操作下二维正方晶格各向异性材料(Te)介质柱内空结构光子晶体TE,TM模式能带.讨论了三种旋转操作对TE,TM模式带隙及完全光子禁带的影响.发现TM模式高频带隙与结构的旋转对称性有着密切的关系.而TE模式的带隙不仅受到晶体旋转对称性的影响同时也受到介质在x-y平面分布情况的影响.     

Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential

Based upon the tight-binding formalism a model of a high-T_c superconductor with isotropic and anisotropic attractive interactions is considered analytically. Symmetry facets of the group C_4v are included within a method of successive transformations of the reciprocal space. Complete sets of basis functions of C_4v irreducible representations are given. Plausible spin-singlet and spin-triplet superconducting states are classified with regard to the chosen basis functions. It is displayed that pairing interaction coefficients and the dispersion relation, which can be characterized by the parameter η= 2t₁/t₀, have a diverse and mutually competing influence on the value of the transition temperature. It is also shown that in the case of a nearly half-filled conduction band and an anisotropic pairing interaction the spin-singlet d-wave symmetry superconducting state is realized for small values of the parameter η, whereas in the opposite limit, for sufficiently large values, the spin-triplet p-wave symmetry superconducting state has to be formed. This result cannot be obtained within the Van Hove scenario or BCS-type approaches, where the p-wave symmetry superconducting state absolutely dominates. The specific heat jump and the isotope shift as functions of the parameter η are assessed and discussed for the d-wave symmetry singlet and the p-wave symmetry triplet states.     

Symmetry classification of states in high temperature superconductors

The symmetry classification of possible singlet and also triplet states in the case of the 2-dim square lattice, and 3-dim tetragonal and orthorhombic lattices is examined. If particle-hole symmetry is present then an additional symmetry classification is possible. However in the lower symmetry crystal structures that actually occur, no distinction on symmetry grounds can be drawn between usuals-wave, extendeds-wave and some of thed-wave states.     

旋转对二维正方晶格介质柱内空结构光子晶体禁带的影响

采用平面波展开的方法计算了三种旋转操作下二维正方晶格各向异性材料(Te)介质柱内空结构光子晶体TE,TM模式能带.讨论了三种旋转操作对TE,TM模式带隙及完全光子禁带的影响.发现TM模式高频带隙与结构的旋转对称性有着密切的关系.而TE模式的带隙不仅受到晶体旋转对称性的影响同时也受到介质在x-y平面分布情况的影响. 关键词： 二维光子晶体 内空结构 旋转操作 光子带隙     

Noncommutative geometry in string and twisted Hopf algebra of diffeomorphism

We discuss the Hopf algebra structure in string theory and present the twist quantization as a unified formulation of the world sheet quantization of the string and the symmetry of the target spacetime. Applying it to the case with a nonzero B-field background, we explain a method to decompose the twist into two successive twists. There are two different possibilities of decomposition: The first is a natural decomposition from the viewpoint of the twist quantization, leading to a new type of twisted Poincaré symmetry. The second decomposition reveals the relation of our formulation to the twisted Poincaré symmetry on the Moyal type noncommutative space.     

Approximate <Emphasis Type="Italic">κ</Emphasis>-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C _s from the valence energy spectrum of particle and also for pseudospin symmetry constant C _ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

Equivalent rotations associated with the permutation inversion group revisited: symmetry projection of the rovibrational functions of methane

In this work the analysis of the equivalent rotations from the permutation inversion group formalism is revisited. We emphasize that explicit knowledge of changes in the Euler angles are not required in order to determine the transformation that a given symmetry operation causes to the rotational functions when dealing with the permutation inversion group formalism. Indeed, matrix elements of the equivalent rotations are provided by a single Wigner's D ^(j)(R) function. Taking advantage of this, we propose a symmetry projection approach to build the rovibrational functions of methane. This approach focuses on the relevance of the isomorphism between permutations and equivalent rotations. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigner's D functions and vibrational matrix representations provided by a local scheme. The proposed approach is general and permits us to obtain in a systematic fashion an orthonormal set of symmetry-projected functions, with good total angular momentum, and carrying the irreducible representations of the molecular symmetry group.     

Magnetoelastic excitations and structural phase transitions in tetragonal paramagnets

The systematic discussion of the elastic and structural properties of the tetragonal paramagnetic model with the maximum value of the total angular momentumJ=1 in an external magnetic field along thez orx direction is given. The sound velocities of all the symmetry modes are calculated by using the standard perturbation theory and Green's function method. It is shown that only in the presence of the external field directed along thez-axis, for some values of this field and temperature one of the symmetry elastic constantsc ₄₄ orc _B becomes zero and the phase transition to monoclinic (triclinic) or volume change transition can occur.     

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.     

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.     

Method of group foliation and non-invariant solutions of partial differential equations

Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By studying the integrability conditions of this automorphic system, i.e. the resolving equations, one can provide an explicit foliation of the entire solution manifold into separate orbits. The new important feature of the method is the extensive use of the operators of invariant differentiation for the derivation of the resolving equations and for obtaining their particular solutions. Applying this method we obtain exact analytical solutions of the heavenly equation, non-invariant under any subgroup of the symmetry group of the equation. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: sheftel@gursey.gov.tr