The algebra and geometry ofSU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular groupSU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real linear vector space, are developed in anSU(3) covariant manner. Thef andd symbols ofSU(3) lead to two ways of ‘multiplying’ two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization ofSU(3) is developed as a generalization of that forSU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.     

Spinless Excitons Implicit in SO(5) Theory

A pair of up-down operators are constructed explicitly for S.C.Zhang‘s SO(5) theory of high Tc superconductivity.From them two good quantum numbers are derived.The up-down operators are related to the spin-independent excitons which are not considered before.``     

O(n) tricriticality in two dimensions

We present exact results for several universal parameters of the tricritical O(n) model in two dimensions. The results apply to the range −2⩽n⩽3/2, and include the central charge and three scaling dimensions, associated with temperature, magnetic field and the introduction of an interface. Since these results are based on an extrapolation of known relations between the O(n) and the Potts model, they cannot be considered as rigorous. For this reason, we perform an accurate numerical analysis of the central charge and the critical exponents. This analysis, which is based on transfer-matrix calculations on the honeycomb lattice, is in a full and precise agreement with the theoretical predictions.      

Characters of Finite-Dimensional Irreducible q(n) -Modules

The solution of the Kac character problem for thequeer series of Lie superalgebras q(n) is announced. An explicit algorithm which computes the character of an arbitrary finite-dimensional irreducible q(n)-module is presented. As an illustration, the correction terms to the generic character formula of Penkov (Monatsh. Math.118 (1994), 419) are written down for all finite-dimensional irreducible representations of q(n), for n4, with nongeneric character.     

利用SU（2）_（q，s）量子代数的两参数变形振子实现讨论SU（2）_（q，s）相干态

利用ＳＵ（２）ｑ，ｓ量子代数的两参数变形振子实现构造出与Ｐｅｒｅｌｏｍｏｖ相干态形式不同的ＳＵ（２）ｑ，ｓ相干态．证明了ＳＵ（２）ｑ，ｓ，量子代数的表示基是正交的，并讨论了它的相干态的归一性和完备性．指出ＳＵ（２）ｑ，ｓ相干态的相干性受参数ｑ，ｓ的影响，它比单参数变形ＳＵ（２）ｑ相干态更具一般性．     

Form-preserving Transformations for the Time-dependent Schrödinger Equation in (n + 1) Dimensions

We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schrödinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is shown to be invertible and to preserve L ²-normalizability. We give a class of time-dependent TDSEs that can be mapped onto stationary Schrödinger equations by our form-preserving transformation. As an example, we generate a solvable, time-dependent potential of Coulombic ring-shaped type together with the corresponding exact solution of the TDSE in (3+1) dimensions. We further consider TDSEs with position-dependent (effective) masses and show that there is no form-preserving transformation between them and the conventional TDSEs, if the spatial dimension of the system is higher than one.     

Migdal-Kadanoff renormalization group for theO(n) model

We perform a Migdal-Kadanoff renormalization group calculation on anO(n) symmetric model on ad-dimensional hypercubic lattice,d=2, 3. We find that in two dimensions the critical fixed point disappears asn=n _KT1.96, which is in good agreement with the exact valuen _KT=2. In three dimensions the fixed point persists much longer, albeit not all the way up to infinity. Surface critical phenomena in a semiinfiniteO(n) model are also considered.     

Properties of 2 × 2 h-Deformed Quantum (Super)Matrices

We investigate the h-deformed quantum (super)group of 2 × 2 matrices and use a kind of contraction procedure to prove that the n-th power of this deformed quantum (super)matrix is quantum (super)matrix with the deformation parameter nh.     

51(p,n)51Cr reaction from E p 1.9 to 4.5 MeV

The total cross-section for the reaction⁵¹V(p, n)⁵¹Cr has been measured fromE _p 1.9 to 4.5 MeV by using two different techniques: (i) by detecting the neutron using the 4π neutron counter and (ii) by measuring the activity of the residual nucleus⁵¹Cr. The two measurements are consistent with each other and together they are in good agreement with the data of Zyskindet al. The thermonuclear reaction rates have also been extracted starting from these cross-sections.     

Nuclear Algebraic Geometry and SO(10)

In this contribution nuclear representations of the Dirac ring, developed over many years, are shown to be a particular case of a theorem in algebraic geometry which at the same time associates them with a Hodge decomposition of a Kaehler manifold. This yields a shape that in some cases is independent of any appeal to a symmetry group. However, because the nuclear representations are in the infinitesimal ring of SO(4) and the internal space of each representation is in a Kaehler (even Calabi-Yau) manifold K; the group SO(10) = SO(4) × K can give additional information. This paper develops the very fruitful symbiosis between algebra and irreducible representations of SO(10) and covers some aspects of string theory.     

Vibrational Study of the Complexes Pentamethyl Cyclopenta-Dienyldicarbonyl Rhenium Phosphine and Phosphite : (n5-C5Me5)Re(CO)2(PR3) R= Me,OMe, OPh

Abstract

A complete vibrationalassignment of the title compounds is performed from their IR and Raman Spectra. A normal coordinate treatment of these molecules based on a simplified model allow us to confirm most of the experimental assignments.

A comparison of some structural aspects of these complexes with Cp?Re(CO)₃ are also discussed. Additionally, the preparation and characterization of the trimethylphosphite derivative is reported.     

Quantum Gates and Quantum Algorithms with Clifford Algebra Technique

We use the Clifford algebra technique (J. Math. Phys. 43:5782, 2002; J. Math. Phys. 44:4817, 2003), that is nilpotents and projectors which are binomials of the Clifford algebra objects γ ^a with the property {γ ^a ,γ ^b }₊=2η ^ab , for representing quantum gates and quantum algorithms needed in quantum computers in a simple and an elegant way. We identify n-qubits with the spinor representations of the group SO(1,3) for a system of n spinors. Representations are expressed in terms of products of projectors and nilpotents; we pay attention also on the nonrelativistic limit. An algorithm for extracting a particular information out of a general superposition of 2 ⁿ qubit states is presented. It reproduces for a particular choice of the initial state the Grover’s algorithm (Proc. 28th Annual ACM Symp. Theory Comput. 212, 1996).     

Comment on ‘Supersymmetry, PT-symmetry and spectral bifurcation’

We demonstrate that the recent paper by Abhinav and Panigrahi entitled ‘Supersymmetry, PT-symmetry and spectral bifurcation’ [K. Abhinav, P.K. Panigrahi, Ann. Phys. 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex sl(2) potential algebra.     

Quasi-two-dimensional magnetism in (CnH2n+1NH3)2CuCl4 studied by electron paramagnetic resonance

The quasi-two-dimensional magnetism in the layered transition metal compound (C_nH_2n+1NH₃)₂CuCl₄ (n=10, 14) was investigated by means of electron paramagnetic resonance (EPR) and superconducting quantum interference device measurements. As a result, the high temperature magnetic phase transitions were reflected in the EPR parameters in a sensitive manner.     

双参数变形多模玻色算符的代数结构及其应用(Ⅱ)

给出了双参数变形量子代数ＳＵ（２）ｑ，ｓ和ＳＵ（１，１）ｑ，ｓ的多模Ｊｏｒｄａｎ－Ｓｃｈｗｉｎｇｅｒ实现。     

Cross-sections for the formation of isomeric pair Ge through (n, 2n), (n, p) and (n, α) reactions measured over 13.73 MeV to 14.77 MeV and calculated from near threshold to 20 MeV neutron energies

The cross-sections for formation of isomeric pair, ⁷⁵Ge^m(σ_m) and ⁷⁵Ge^g(σ_g), through ⁷⁶Ge(n, 2n), ⁷⁵As(n, p) and ⁷⁸Se(n, α) reactions were measured at 13.73 MeV, 14.42 MeV and 14.77 MeV neutrons and also estimated using EMPIRE-II and TALYS codes over neutron energies from near threshold to 20 MeV. For each (n, 2n), (n, p) and (n, α) reaction, the cross-section initially increases with neutron energy, but starts decreasing as the neutron energy exceeds the respective threshold of (n, 3n), (n, pn) and (n, αn) reactions. The higher values of σ_m relative to σ_g reveal that the transitions of the excited ⁷⁵Ge from higher energy levels to metastable state (7⁺/2) are favored as compared to unstable ground state (1⁻/2). The present values of cross sections for formation of ⁷⁵Ge^m,g through (n, 2n) and (n, α) reactions are lower, and that of (n, p) reaction are higher compared to most of the corresponding literature cross-sections.     

Measurement of beam quality factor (M) by slit-scanning method

Beam quality factor (M²) and far-field scattering angle of LD end-pump Nd : YVO₄ laser were measured by slit-scanning method. The experimental results showed that the laser operated on a multi-mode state. The corresponding analytical treatments for slit-scanning method and M² factor measurement also were presented in this paper.