Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

Application of a modified z-cosy experiment for the analysis of spectra of oriented molecules - the spectrum of cis,cis-mucanonitrile

NMR spectra of cis,cis-mucanonitrile oriented in a liquid crystal have been analysed using the connectivity information obtained from a modified Z-COSY experiment which provided crucial clues for the starting parameters for the iterative analysis. The proton spectra with and without C-13 satellites and the C-13 spectra have thus been interpreted. The indirect spin-spin couplings required for the analyses have been obtained from the corresponding isotropic spectra. The H-1-H-1 and C-13-H-1 dipolar couplings so obtained have been utilized to determine the relative internuclear distances. The results indicate that the molecule is planar. (C) 1994 Academic Press, Inc.

Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field

We study the bound states of two spin-1/2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters (lambda(x),lambda(y),lambda(z)). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ``BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., lambda(x) = lambda(y) = lambda(z)) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid He-3. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

Signals of additional Z ` boson in e(+)e(-) -> W+W- at the ILC with polarized beams

We consider the possibility of fingerprinting the presence of heavy additional Z' bosons that arise naturally in extensions of the standard model such as E-6 models and left-right symmetric models, through their mixing with the standard model Z boson. By considering a class of observables including total cross sections, energy distributions and angular distributions of decay leptons we find significant deviation from the standard model predictions for these quantities with right-handed electrons and left-handed positrons at root s= 800GeV. The deviations being less pronounced at smaller centre of mass energies as the models are already tightly constrained. Our work suggests that the ILC should have a strong beam polarization physics program particularly with these configurations. On the other hand, a forward backward asymmetry and lepton fraction in the backward direction are more sensitive to new physics with realistic polarization due to interesting interplay with the neutrino t-channel diagram. This process complements the study of fermion pair production processes that have been considered for discrimination between these models.

Study of the reaction between 1,2,3-trihydroxybenzene and 8-hydroxyquinoline in the solid state

1.2,3-Trihydroxybenzene (THB) reacts with 8-hydroxyquinoline (8HQ) in the solid state forming an orange-coloured charge transfer complex THB* (8HQ)(2). When the reaction was carried out in a petri dish, or when the vapours of 8HQ were allowed to react with solid THB (gravimetric study), the reaction product separated out as good quality, shiny single crystals. X-Ray diffraction studies on single crystals showed that they belong to the orthorhombic system with a = 15.408(1), b = 16.276(1), c = 7.825(1) Angstrom, Z = 4, D-x = 1.413 g cm(-3) and space group Pnaa. From the crystallographic evidence it has been found that the proton of the middle OH group of THB is transferred to the N atom of 8HQ. This accounts for the observed colour change. Kinetic studies on the solid state reaction showed that the 8HQ molecules diffuse towards THB, and the lateral diffusion occurs through surface migration, grain boundary diffusion and vapour phase diffusion. Gravimetric studies of the reaction between solid THB and 8HQ vapour showed that the diffusion of 8HQ molecules into the crystal lattice of THB has a higher energy of activation than that observed when the reactants are in contact. The nature of the crystal packing in the reaction product indicates diffusion of 8HQ molecules into the crystal lattice of THB along the c-axis, to occupy the cavities present between the THB molecules in the unit cell.

1,3-Dipolar cycloaddition reaction of ?,?-unsaturated esters and lactones with diazomethane

1,3-Dipolar cycloaddition of diazomethane to the alpha,beta-unsaturated esters and lactones such as 2-4, 6-8, 10 and 13 occurs in a stereoselective manner affording conjugated Delta(2)-pyrazolines. E and Z isomers of D-mannitol lead to identical product which was cyclised to investigate the absolute stereochemistry of the product. The regiospecificities of all the reactions are consistent with FMO coefficients obtained through AM1 calculations.

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

Structure of N-nitroso-r-2,c-7-diphenylhexahydro-1,4-diazepin-5-one

C17H17N3O2, M(r) = 295.34, orthorhombic, P2(1)2(1)2(1), a = 7.659 (1), b = 12.741 (1), c = 15.095 (1) angstrom, V = 1473.19 (2) angstrom 3, Z = 4, D(m) = 1.33, D(x) = 1.32 Mg m-3, lambda(Cu K-alpha) = 1.5418 angstrom, mu = 0.68 mm-1, F(000) = 624, T = 295 K, R = 0.031 for 1549 unique observed reflections with I > 2.5-sigma(I). The seven-membered heterocyclic ring adopts a boat conformation flattened at the nitroso end of the ring. The substituent phenyl rings occupy pseudo-axial positions and the nitroso group is coplanar with the C(2), N(1), C(7) plane of the central ring. The crystal structure is stabilized by intermolecular N-H...O and weak C-H...O hydrogen bonds.

Organometallic Chemistry of Diphosphazanes. 11. Reactions of fac-[Mo(CO)3(MeCN){.eta.2-Ph2PN(Pri)PPh(DMP)}] (DMP = 3,5-Dimethyl-1-Pyrazolyl) with Diphosphazanes and Diphosphinoalkanes and Oxidative Addition with Iodine

The use of fac-[Mo(CO)(3)(MeCN)(eta(2)-L(1))] (1a) {L(1) = Ph(2)PN(Pr-i)PPh(DMP)}(2) as a precursor to metalloligands and bimetallic, heterotrimetallic, and heptacoordinated complexes is reported. The reaction of 1a with diphosphazane, dppa, or a diphosphinoalkane such as dppm or dppe yields the fac-eta(1)-diphosphine substituted metalloligands, fac-[Mo(CO)(3)(eta(2)-L(1))(eta(1)-PXP)] {PXP = dppa (2), dppm (3), and dppe (4)}. These undergo isomerization to yield the corresponding mer-diphosphine complexes (5-7). Oxidation of the uncoordinated phosphorus atom of the mer-eta(1)-dppm-substituted complex eventually provides mer-[Mo(CO)(3)-(eta(2)-L(1)){eta(1)-Ph(2)PCH(2)P(O)Ph(2)}](8). The structure of the latter complex has been confirmed by single crystal X-ray diffraction {triclinic system, P ($) over bar 1; a = 11.994(3), b = 14.807(2), c = 15.855(3) Angstrom; alpha = 114.24(1), beta = 91.35(2), and gamma = 98.95(1)degrees; Z = 2, 4014 data (F-0 > 5 sigma(F-0)), R = 0.066, R(W) = 0.069}. Treatment of the dppe metalloligand 7 with [PtCl2(COD)] yields the heterotrimetallic complex cis-[PtCl2{mer-[Mo(CO)(3)(eta(2)-L(1))(eta(1)-dppe]}(2)] (9). Attempts to prepare a related trimetallic complex with the dppm-containing metalloligand were unsuccessful; only the tetracarbonyl complex cis-[Mo(CO)(4)(eta(2)-L(1))] (1b) and cis-[PtCl2(eta(2)-dppm)] were obtained. Reaction of la with dppe in the ratio 2:1 yields the mer-mer dinuclear complex [{mer-[Mo(CO)(3)(eta(2)-L(1))]}(2)(mu-dppe)] (10) bridged by dppe. Oxidation of 1a with iodine yields the Mo(II) heptacoordinated complex [MoI2(CO)(2)(eta(3)-L(1))] (11) with tridentate PPN coordination. The same Mo(II) complex 11 is also obtained by the direct oxidation of the tetracarbonyl complex cis-[Mo(CO)(4)(eta(2)-L(1))] (1b) with iodine. The structure of 11 has been confirmed by X-ray diffraction studies {monoclinic system, Cc; a = 10.471(2), b = 19.305(3), c = 17.325(3) Angstrom; beta = 95.47(2)degrees; Z = 4, 3153 data (F-0 > 5 sigma(F-0)), R = 0.049, R(W) = 0.051}. This complex exhibits an unusual capped-trigonal prismatic geometry around the metal. A similar heptacoordinated complex 12 with a chiral diphosphazane ligand {L(3) = (S,R)-P(h)2PN-(*CHMePh)*PPh(DMP)} has also been synthesized.

Magneto-structural correlation in (mu-alkoxo/hydroxo)(mu-carboxylato)dicopper(II) systems: Synthesis, X-ray structure and magnetic properties of aquo(mu-hydroxo) (mu-arylcarboxylato)bis(N,N,N ',N '-tetramethylethane-1,2-diamine)dicopper(II) diperchlorate

Asymmetrically dibridged dicopper(II) complexes, [Cu-2(OH)(O2CC6H4-p-Me)(tmen)(2)(H2O)](ClO4)(2) (1) and [Cu-2(OH)(O2CC6H4-p-OMe)(tmen)(2)(H2O)](ClO4)(2) (2) (tmen = N,N,N',N'-tetramethylethane-1,2-diamine), were prepared and structurally characterized. Complex 1 crystallizes in the monoclinic space group P2(1)/a with a = 17.718(2), b = 9.869(1), c = 19.677(2) Angstrom, beta = 115.16(1)degrees, V = 3114.3(6) Angstrom(3) and Z = 4. The structure was refined to R(wR(2)) = 0.067(0.178). Complex 2 crystallizes in the monoclinic space group P2(1)/a with a = 17.695(3), b = 9.574(4), c = 20.104(2) Angstrom, beta = 114.18(1)degrees, V = 3107(1) Angstrom(3) and Z = 4. The final residuals are R(wR(2)) = 0.067(0.182). The complexes have a [Cu-2(mu-OH)(mu-OH)(mu-O2CAr)](2+) core with tmen Ligands occupying the terminal sites of the core. In addition, one copper is axially bound to a water molecule. The Cu ... Cu distances and the Cu-OH Cu angles in the core are 3.394(1) Angstrom, 124.4(2)degrees for 1 and 3.374(1) Angstrom, 123.3(3)degrees for 2. The complexes show axial X-band EPR spectral features in methanol glass at 77 K giving g(perpendicular to) = 2.02, g(parallel to) = 2.3 (A(parallel to) = 165 x 10(-4) cm(-1)) and a visible band near similar to 630 nm in methanol. The complexes are weakly antiferromagnetic. A theoretical fit of the magnetic susceptibility data in the temperature range 40-295 K gives -J = 10 cm(-1), g = 2.05 for 1 and -J = 10 cm(-1), g = 2.0 for 2. Plots of -2J versus the Cu-OH-Cu angle (phi) in this class of asymmetrically dibridged dicopper(II) complexes having d(x2-y2)-d(x2-y2) magnetic orbitals show a linear magneto-structural correlation: -2J(cm(-1)) = 11.48 phi(deg) - 1373.

(4aR, 8aS, 9aR, 10aS)-8a, 9a-Difluoro-1,4,4a, 5,8,8a, 9,9a, 10,10a-decahydroanthracene-4a, 10a-diol hemihydrate

The title compound, C(14)H(18)F(2)O(2)center dot 0.5H(2)O, a hemihydrate of a C(s)-symmetric unsaturated difluorodiol, crystallizes in the centrosymmetric space group P2/m (Z = 4). The asymmetric unit contains two crystallographically independent difluorodiol half-molecules, occupying the mirror planes at (x, 0, z) and (x, 1/2, z), and half a molecule of water, lying on the twofold axis at (0, y, 0). Four difluorodiol molecules self-assemble around each solvent water molecule via O-H center dot center dot center dot O hydrogen bonds in a near tetrahedral symmetry to generate a cylindrical column-like architecture.

Additions to the z transform table

The ztransform method is a widely used tool for the analysis and synthesis of discrete systems. In this note a table of ztransform pairs when F(z) is an irrational function of z is given. The table is also useful for obtaining closed-form sums for some infinite series.

Isolating CP-violating gamma ZZ coupling in e(+)e(-) -> gamma Z with transverse beam polarizations

We revisit the process e(+)e(-) -> gamma Z at the ILC with transverse beam polarization in the presence of anomalous CP- violating gamma ZZ coupling lambda(1) and gamma gamma Z coupling lambda(2). We point out that if the final- state spins are resolved, then it becomes possible to fingerprint the anomalous coupling Re lambda(1). 90% confidence level limit on Re lambda(1) achievable at ILC with center- of- mass energy of 500 GeVor 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of 10(-2) when the helicity of Z is used and 10(-3) when the helicity of gamma is used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. The benefits of such polarization programmes at the ILC are compared and contrasted for the process at hand. We also discuss possible methods by which one can isolate events with a definite helicity for one of the final- state particles.

Robust Approach for Identification of Bad Data in State Estimation Using SLP Technique

This paper proposes a new approach for solving the state estimation problem. The approach is aimed at producing a robust estimator that rejects bad data, even if they are associated with leverage-point measurements. This is achieved by solving a sequence of Linear Programming (LP) problems. Optimization is carried via a new algorithm which is a combination of “upper bound optimization technique" and “an improved algorithm for discrete linear approximation". In this formulation of the LP problem, in addition to the constraints corresponding to the measurement set, constraints corresponding to bounds of state variables are also involved, which enables the LP problem more efficient in rejecting bad data, even if they are associated with leverage-point measurements. Results of the proposed estimator on IEEE 39-bus system and a 24-bus EHV equivalent system of the southern Indian grid are presented for illustrative purpose.