Topology of multiple log transforms of 4-manifolds

Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, from that we deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of E(1) # 5(-CP^2) differs from the original one by a codimension zero simply connected Stein submanifold M_{p,q}, which are therefore examples of infinitely many Stein manifolds that are exotic copies of each other (rel boundaries). Furthermore, by a similar method we produce infinitely many simply connected Stein submanifolds Z_{p} of E(1)_{p,2} # 2(-CP^2)$ with the same boundary and the second Betti number 2, which are (absolutely) exotic copies of each other; this provides an alternative proof of a recent theorem of the author and Yasui [AY4]. Also, by using the description of S^2 x S^2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that multiple log transforms along the tori in these cusps do not change smooth structure of S^2 x S^2.Comment: Updated, with 17 pages 21 figure

Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu2_2O3_3 and CaV2_2O5_5

We study the spin-1/2 trellis lattice Heisenberg model, a coupled spin ladder system, both by perturbation around the dimer limit and by quantum Monte Carlo simulations. We discuss the influence of the inter-ladder coupling on the spin gap and the dispersion, and present results for the temperature dependence of the uniform susceptibility. The latter was found to be parameterized well by a mean-field type scaling ansatz. Finally we discuss fits of experimental measurements on SrCu$_2$O$_3$ and CaV$_2$O$_5$ to our results.Comment: 7 pages, 8 figure

Production of Sodium Borohydride by Using Dynamic Behaviors of Protide at the Extreme Surface of Magnesium Particles

Abstract An advanced process for the production of sodium borohydride (NaBH 4 ) as a hydrogen storage material was developed, which applied the dynamic hydriding and dehydriding behaviors of protide (H − ) in Mg-H system under transitional temperature conditions. An abundant natural resource named borax (Na 2 B 4 O 7 ·10H 2 O) and the anhydrous sodium metaborate (NaBO 2 ) recovered from the "spent fuel" as NaBO 2 ·4H 2 O were used as the starting material in the present process. Powder-state Mg played an important role in the transitional hydriding and dehydriding process where the gaseous hydrogen was converted to protide at the extreme surface of Mg to form NaBH 4 in exchange with the simultaneous transition of oxygen in NaBO 2 to form MgO. In the present process, the protide as the most reactive state among the four states of hydrogen is applied for the synthesis of NaBH 4 , which can exist in metal-hydrogen complexes, such as NaAlH 4 and NaBH 4 . The NaBH 4 yield was reached higher than 90% by a single batch process but was found to be largely dependent on the rate of temperature change and the particle size, i.e., the specific surface area of Mg particles

Infrared and Raman spectra of LiV2O5 single crystals

The phonon dynamics of LiV2O5 single crystals is studied using infrared and Raman spectroscopy techniques. The infrared-active phonon frequencies and dielectric constants are obtained by oscillator fitting procedure of the reflectivity data measured at room temperature. The Raman scattering spectra are measured at room temperature and at T=10 K in all nonequivalent polarized configurations. The assignment of the phonons is done by comparing the infrared and Raman spectra of LiV2O5 and NaV2O5. The factor-group-analysis of the LiV2O5 crystal symmetry and of its constituent layers is performed to explain the symmetry properties of the observed modes. We concluded that layer symmetry dominates in the vibrational properties of this compound.Comment: 10 pages, 5 figure

Diffuse Neutron Scattering Study of a Disordered Complex Perovskite Pb(Zn1/3Nb2/3)O3 Crystal

Diffuse scattering around the (110) reciprocal lattice point has been investigated by elastic neutron scattering in the paraelectric and the relaxor phases of the disordered complex perovskite crystal-Pb(Zn1/3Nb2/3)O3(PZN). The appearance of a diffuse intensity peak indicates the formation of polar nanoregions at temperature T*, approximately 40K above Tc=413K. The analysis of this diffuse scattering indicates that these regions are in the shape of ellipsoids, more extended in the direction than in the direction. The quantitative analysis provides an estimate of the correlation length, \xi, or size of the regions and shows that \xi ~1.2\xi , consistent with the primary or dominant displacement of Pb leading to the low temperature rhombohedral phase. Both the appearance of the polar regions at T*and the structural transition at Tc are marked by kinks in the \xi curve but not in the \xi one, also indicating that the primary changes take place in a direction at both temperatures.Comment: REVTeX file. 4 pages, 3 figures embedded, New version after referee cond-mat/010605

Electronic structure and exchange interactions of the ladder vanadates CaV2O5 and MgV2O5

We have performed ab-initio calculations of the electronic structure and exchange couplings in the layered vanadates CaV2O5 and MgV2O5. Based on our results we provide a possible explanation of the unusual magnetic properties of these materials, in particular the large difference in the spin gap between CaV2O5 and MgV2O5

Universal Static and Dynamic Properties of the Structural Transition in Pb(Zn1/3Nb2/3)O3

The relaxors Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PZN) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) have very similar properties based on the dielectric response around the critical temperature $T_{c}$ (defined by the structural transition under the application of an electric field). It has been widely believed that these materials are quite different below $T_{c}$ with the unit cell of PMN remaining cubic while in PZN the low temperature unit cell is rhombohedral in shape. However, this has been clarified by recent high-energy x-ray studies which have shown that PZN is rhombohedral only in the skin while the shape of the unit cell in the bulk is nearly cubic. In this study we have performed both neutron elastic and inelastic scattering to show that the temperature dependence of both the diffuse and phonon scattering in PZN and PMN is very similar. Both compounds show a nearly identical recovery of the soft optic mode and a broadening of the acoustic mode below $T_{c}$. The diffuse scattering in PZN is suggestive of an onset at the high temperature Burns temperature similar to that in PMN. In contrast to PMN, we observe a broadening of the Bragg peaks in both the longitudinal and transverse directions below $T_{c}$. We reconcile this additional broadening, not observed in PMN, in terms of structural inhomogeneity in PZN. Based on the strong similarities between PMN and PZN, we suggest that both materials belong to the same universality class and discuss the relaxor transition in terms of the three-dimensional Heisenberg model with cubic anisotropy in a random field.Comment: 11 pages, 10 figures. Updated version after helpful referee comment

Identification of Nuclear Relaxation Processes in a Gapped Quantum Magnet: Proton NMR in the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4

The proton hyperfine shift K and NMR relaxation rate $1/T_1$ have been measured as a function of temperature in the S=1/2 Heisenberg antiferromagnetic ladder Cu2(C5H12N2)2Cl4. The presence of a spin gap $\Delta \simeq J_\perp-J_\parallel$ in this strongly coupled ladder ($J_\parallel < J_\perp$) is supported by the K and $1/T_1$ results. By comparing $1/T_1$ at two different proton sites, we infer the evolution of the spectral functions $S_z(q,\omega_n)$ and $S_\perp(q,\omega_n)$. When the gap is significantly reduced by the magnetic field, two different channels of nuclear relaxation, specific to gapped antiferromagnets, are identified and are in agreement with theoretical predictions.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Letter

Single-hole dynamics in dimerized and frustrated spin-chains

We present a unified account for the coupled single-hole- and spin-dynamics in the spin-gap phase of dimerized and frustrated spin-chains and two-leg spin ladders. Based on the strong dimer-limit of a one-dimensional $t_123$-$J_123$-model a diagrammatic approach is presented which employs a mapping of the spin-Hamiltonian onto a pseudo-fermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasi-particle weight is observed and studied for a variety of system parameters. A comparison with existing exact diagonalization data is performed and good agreement is found.Comment: 10 pages, 12 figure