A projection operator technique for determining selection rules

Second-order spectral line shift comparisons

Changes in the structural and electronic properties of zinc oxide (ZnO) due to the O vacancy and F-centre were studied using a semi-empirical quantum-chemical approach based on Hartree–Fock theory. A periodic supercell of 128 atoms was exploited throughout the study. The semi-empirical parameters for the Zn atom are obtained by reproducing the main properties of the ZnO crystal as well as the first three ionization potentials of the Zn atom. The perturbation imposed by the defect leads to atomic relaxation, which is computed and discussed in detail. It is found that electron density redistribution in the vicinity of defects plays an important role in the determination of atomic movements. The introduction of an oxygen vacancy generates a local one-electron energy level placed below the conduction band while the presence of an F-centre produces a local energy level just above the upper valence band of the material. The deep situation of the local energy level corresponding to the F-centre implies that the F-centre cannot serve as a source of unintentional n-type electrical conductivity in ZnO. Changes in the chemical bonding are observed, showing that it becomes slightly more covalent because of oxygen-vacancy-type defects.

Let R be a quantum solvable algebra. It is proved that every prime ideal I of R which is stable with respect to the quantum adjoint action is completely prime, and Fract(R/I) is isomorphic to the skew field of fractions of an algebra of twisted polynomials. We study the correspondence between symplectic leaves and irreducible representations. A conjecture of De Concini-Kac--Procesi on the dimension of irreducible representations is proved for sufficiently large 1.

Let M M be a cusped hyperbolic 3 3 -manifold, e.g. a knot complement. Thurston showed that the space of deformations of its fundamental group in P G L ( 2 , C ) \mathrm {PGL}(2,\mathbf {C}) (up to conjugation) is of complex dimension the number ν \nu of cusps near the hyperbolic representation. It seems natural to ask whether some representations remain discrete after deformation. The answer is generically not. A simple reason for it lies inside the cusps: the degeneracy of the peripheral representation (i.e. representations of fundamental groups of the ν \nu peripheral tori). They indeed generically become non-discrete, except for a countable set. This last set corresponds to hyperbolic Dehn surgeries on M M , for which the peripheral representation is no more faithful. We work here in the framework of P G L ( n , C ) \mathrm {PGL}(n,\mathbf {C}) . The hyperbolic structure lifts, via the n n -dimensional irreducible representation, to a representation ρ g e o m \rho _{\mathrm {geom}} . We know from the work of Menal-Ferrer and Porti that the space of deformations of ρ geom \rho _{\textrm {geom}} has complex dimension ( n − 1 ) ν (n-1)\nu . We prove here that, unlike the P G L ( 2 ) \mathrm {PGL}(2) -case, the generic behaviour becomes the discreteness (and faithfulness) of the peripheral representation: in a neighbourhood of the geometric representation, the non-discrete peripheral representations are contained in a real analytic subvariety of codimension ≥ 1 \geq 1 .

Generalized projection operator method to derive the pulse parameters equations for the nonlinear Schrödinger equation

In !.heir fundamental paper IBH I j, J. Bruning and E. Heintze studied elliptic operators and their eigenvalues by means of the action of a compact Lie group of isometries conunuting with the operator. For a fixed irreducible representation of the group, they single out those eigenvalues in whose eigenspaces this representation occurs, and prO\'e general theorems, inter alia, on the asymptotic distribution of such eigenvalues. The aim of the present paper is to use this approach in a very ronrrete situation, namely for the eigenfunctions and eigenvalues of the Laplacian on dosed surfaces of revolution. Such surfaces are homeomorphic to the sphere or to the torus; their isomt'try group cont i\in~ 0(2). The reprt'sentation ohhis group on C2(M) induces a representation on each eigenspace E~ . We determine the form of the eigenfunctions belonging to irredudble components of this representation, and the of their nodal domains. The main reswts are estimates (most l.V under convexity ronditions) of the fust eigenvalue in whose eigenspace a fued irreducible representation of 0(2) occurs, and estimates of the dimensions of a rbitrary eigenspaces. The irreducible representations of 0(2), much in the same \I'av as !host' of 50(2), are of dimension one or two, S~ 2.1. Each irreducible representation of dimension two is characterized by the winding number k E IN of the corresponding representation of 50(2); we denote it by pl<. By po we denote the trivial representation of dimension one. The eigenfunctions in an irreducible component or EA will be proved to have the following particwarly simplt' form:

It has been well established by Roy, Fox, Yu and Zhu that in the growth of dye-laser radiation the multiplicative colored noise leads to an increase of the variance and skewness of first-passage time distribution (FPTD) as the laser intensity approaches steady state. In this paper, we develop an analytic method for the approximate treatment of the colored noise effects in the FPTD problem based on the Hanggi ansatz. The mean, variance, and skewness of the FPTD with multiplicative colored noise are obtained by means of the projection operator technique used by the authors to develop a theory of nonlinear external noises. The theoretical results are compared with those obtained from numerical simulations.

We examine the propagation of ultra-short optical light pulses in dispersion-managed birefringent fiber transmission systems, in which the pulse dynamics is governed by the coupled higher-order nonlinear Schrodinger equations with higher-order linear and nonlinear optical effects. We derive the equations of motion in terms of pulse parameters such as amplitude, temporal position, width, chirp, frequency and phase, using a projection operator method, and we obtain the spatial dynamical behavior of picosecond and femtosecond pulse parameters. From our detailed analysis, we show that the stimulated Raman scattering has a strong impact on the pulse dynamics.

The coupled magnon—Phonon modes in magnetic crystals with shubnikov symmetry

In the wireless sensor network (WSN), selecting cluster head (CH) is important issue to increase the network lifetime and selection time of CH is critical. We propose improved CH selection method that the election time of CH does not be increased as the local energy level is decreased. The proposed method, Distributed Cluster Head Election Algorithm using Local Energy Estimation (DCHEA), uses energy levels of neighboring sensor nodes as well as local energy level to prevent the decrease of the CH probability of the sensor node. The simulation result shows that the life time of the WSN using the proposed scheme is extended.

The direct l-type resonance spectrum of CF 3CCH in the vibrational state v10=3: Extension of the theory of reduction to H 6 n terms

In an earlier work [M. Havlı́ček et al., J. Math. Phys. 40, 2135 (1999)] we defined for any finite dimension five nonequivalent irreducible representations of the nonstandard deformation Uq′(so3) of the Lie algebra so3 where q is not a root of unity [for each dimension only one of them (called classical) admits limit q→1]. In the first part of this paper we show that any finite-dimensional irreducible representation is equivalent to some of these representations. In the case qn=1 we derive new Casimir elements of Uq′(so3) and show that a dimension of any irreducible representation is not higher than n. These elements are Casimir elements of Uq′(som) for all m and even of Uq′(isom+1) due to Inönu–Wigner contraction. According to the spectrum of one of the generators, the representations are found to belong to two main disjoint sets. We give full classification and explicit formulas for all representations from the first set (we call them nonsingular representations). If n is odd, we have full classification also for the remaining singular case with the exception of a finite number of representations.

Let [Formula: see text] be a [Formula: see text]th root of unity where [Formula: see text] is odd. Let [Formula: see text] denote the quantum group with large center corresponding to the Lie algebra [Formula: see text] with generators [Formula: see text], and [Formula: see text]. A semicyclic representation of [Formula: see text] is an [Formula: see text]-dimensional irreducible representation [Formula: see text], so that [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. We construct a tangle functor for framed homogeneous tangles colored with semicyclic representations, and prove that for [Formula: see text]-tangles coming from knots, the invariant defined by the tangle functor coincides with Kashaev’s invariant.

Flavour symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups of some discrete symmetry group $G_f$. $G_f$ can be a subgroup of SU(3) if the third neutrino is massive and we derive general results on the mixing angle predictions for various discrete subgroups of SU(3). The main results are: (a) All the SU(3) subgroups of type C fail in simultaneously giving correct $\theta_{13}$ and $\theta_{23}$. (b) All the groups of type D can predict a relation $\cos^2\theta_{13} \sin^2\theta_{23}=\frac{1}{3}$ among the mixing angles which appears to be a good zeroth order approximation. Among these, various $\Delta(6n^2)$ groups with $n\geq 8$ can simultaneously lead also to $\sin^2 \theta_{13}$ in agreement with global fit at 3$\sigma$. (c) The group $\Sigma(168)\cong PSL(2,7)$ predicts near to the best fit value for $\theta_{13}$ and $\theta_{23}$ within the 1$\sigma$ range. All discrete subgroups of U(3) with order $<512$ and having three dimensional irreducible representation are considered as possible $G_f$ when the third neutrino is massless. Only seven of them are shown to be viable and three of these can correctly predict $\theta_{13}$ and/or $\theta_{23}$. The solar angle remains undetermined at the leading order in all the cases due to degeneracy in the masses. A class of general perturbations which can correctly reproduce all the observables are discussed in the context of several groups which offer good leading order predictions.

The charge conjugation C and the parity P are assumed to generate a finite group without assuming any apriori commutation or anti-commutation relation. The group then generated is the di-hedral group D/sub n/ (n being even) which has two dimensional irreducible representations. This implies that we could have in principle, elementary particles with parity and charge-conjugation doublet structure.