Boundaries, Cusps and Caustics in the Multimagnon Continua of 1D Quantum Spin Systems

The multimagnon continua of 1D quantum spin systems possess several interesting singular features that may soon be accessible experimentally through inelastic neutron scattering. These include cusps and composition discontinuities in the boundary envelopes of two-magnon continuum states and discontinuities in the density of states, "caustics", on and within the continuum, which will appear as discontinuities in scattering intensity. In this note we discuss the general origins of these continuum features, and illustrate our results using the alternating Heisenberg antiferromagnetic chain and two-leg ladder as examples.Comment: 18 pages, 10 figure

Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension

In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a contour integral representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a $d$-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.Comment: 26 Pages, 1 Figur

Perturbative Expansion around the Gaussian Effective Action: The Background Field Method

We develop a systematic method of the perturbative expansion around the Gaussian effective action based on the background field method. We show, by applying the method to the quantum mechanical anharmonic oscillator problem, that even the first non-trivial correction terms greatly improve the Gaussian approximation.Comment: 16 pages, 3 eps figures, uses RevTeX and epsf. Errors in Table 1 are corrected and new references are adde

Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As the inter-chain coupling decreases we observe a transition in the anisotropic XY case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases are found to be qualitatively the same, however, in the regime of weak inter-chain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.Comment: to appear in Physical Review

A Study of the Roper Resonance as a Hybrid State from J/ψJ/\psi Decays

The structure of the Roper resonance as a hybrid baryon is investigated through studying the transitional amplitudes in J/psi-> p\barN*, N*\barN* decays. We begin with perturbative QCD to describe the dynamical process for the J/psi-> 3\bar q+3q decay to the lowest order of \alpha_s, and by extending the modified quark creation model to the J/psi energy region to describe the J/psi-> 3\bar q+3q +g process. The non-perturbative effects are incorporated by a simple quark model of baryons to evaluate the angular distribution parameters and decay widths for the processes J/psi-> pbar N*,N*bar N*. From fitting the decay width of J/psi->gamma p pbar to the experimental data, we extract the quark-pair creation strength g_I=15.40 GeV. Our numerical results for J/psi->pbar N*,N* bar N* decays show that the branching ratios for these decays are quite different if the Roper resonance is assumed to be a common $3q$ state or a pure hybrid state. For testing its mixing properties, we present a scheme to construct the Roper wave function by mixing |qqqg> state with a normal |qqq,2s> state. Under this picture, the ratios of the decay widths to that of the J/psi->p pbar decay are re-evaluated versus the mixing parameter. A test of the hybrid nature of the Roper resonance in J/psi decays is discussed.Comment: 18 pages,3 figures, To appear in Nuclear Physics

Spectral properties of the dimerized and frustrated S=1/2S=1/2 chain

Spectral densities are calculated for the dimerized and frustrated S=1/2 chain using the method of continuous unitary transformations (CUTs). The transformation to an effective triplon model is realized in a perturbative fashion up to high orders about the limit of isolated dimers. An efficient description in terms of triplons (elementary triplets) is possible: a detailed analysis of the spectral densities is provided for strong and intermediate dimerization including the influence of frustration. Precise predictions are made for inelastic neutron scattering experiments probing the S=1 sector and for optical experiments (Raman scattering, infrared absorption) probing the S=0 sector. Bound states and resonances influence the important continua strongly. The comparison with the field theoretic results reveals that the sine-Gordon model describes the low-energy features for strong to intermediate dimerization only at critical frustration.Comment: 21 page

Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent omega governing the approach to the strong-coupling, or scaling limit. Otherwise the procedure either does not converge at all or to the wrong limit. This invalidates all papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/34

Elementary Excitations in Dimerized and Frustrated Heisenberg Chains

We present a detailed numerical analysis of the low energy excitation spectrum of a frustrated and dimerized spin $S=1/2$ Heisenberg chain. In particular, we show that in the commensurate spin--Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory . We discuss the relevance of our data in connection with recent experiments on $CuGeO_{3}$, $NaV_2O_5$, and $(VO)_2P_2O_7$.Comment: Corrections to the text + 1 new figure, will appear in PRB (august 98

The Λ\Lambda(1600): A Strange Hybrid Baryon

We use the method of QCD sum rules to investigate a possible hybrid baryon with the quantum numbers of the $\Lambda$. Using a current composed of uds quarks in a color octet and a gluon, a strange hybrid, the $\Lambda_H$ is found about 500 MeV above the $\Lambda$, and we identify it as the $\Lambda(1600)$. Using our sigma/glueball model we predict a large branching fraction for the $\Lambda_H \to \Lambda + \sigma(\pi\pi$ resonance), and the experimental search for this decay mode could provide a test of the hybrid nature of the $/Lambda(1600)$.Comment: Revtex file, 3 Figure

Influence of Yb:YAG laser beam parameters on Haynes 188 weld fusion zone microstructure and mechanical properties

The weldability of 1.2 mm thick Haynes 188 alloy sheets by a disk Yb:YAG laser welding was examined. Butt joints were made, and the influence of parameters such as power, size, and shape of the spot, welding speed, and gas flow has been investigated. Based on an iconographic correlation approach, optimum process parameters were determined. Depending on the distribution of the power density (circular or annular), acceptable welds were obtained. Powers greater than 1700 W, welding speeds higher than 3.8 m mm1, and spot sizes between 160 and 320 lm were needed in the circular (small fiber) configuration. By comparison, the annular (large fiber) configuration required a power as high as 2500 W, and a welding speed less than 3.8 m min�1. The mechanical properties of the welds depended on their shape and microstructure, which in turn depended on the welding conditions. The content of carbides, the proportion of areas consisting of cellular and dendritic substructures, and the size of these substructures were used to explain the welded joint mechanical properties