LATTICE-DYNAMICS OF ALKALI-METALS IN A 3-BODY INTERACTION

The original model of Das et al. is modified in extending the electron-ion interaction on a three-body forces and including the crystal equilibrium condition to reduce one independent parameter. We studied the phonon dispersion relations along the three principal symmetry directions i.e. [xi, 0, 0], [xi, xi, 0] and [xi, xi, xi] and theta-T curves of alkali metals, Na, K, Rb, Cs and Li. There is close agreement between the computed results and the experimental observations.

Bethe ansatz solutions for Temperley-Lieb quantum spin chains

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups U-q(X-n) for X-n = A(1), B-n, C-n and D-n. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, bleak quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

Toda and Volterra lattice equations from discrete symmetries of KP hierarchies

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.

Lattice dynamics of noble metals on effective three-body interaction

Quite recently we modified the original model of Sarkar et al. for cubic metals in extending the ion-ion interaction, ion-electron interaction and the introduction of crystal equilibrium condition. We applied our scheme to alkali metals. We studied here the lattice dynamics of noble metals on our approach by calculating phonon dispersion relations along the three principal symmetry directions, [ξ00], [ξξ00] and [ξξξ] and the (θ-T) curves of three noble metals: copper, silver and gold. We obtained reasonable agreement with the experimental findings.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

Vortex lattice and matching fields for a long superconducting wire

We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner states, with boundary conditions appropriate for this geometry. Using the Monte Carlo simulated annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed states provides expressions for the matching fields. We find that, as in the case of samples of different geometry, the finite-size effect provokes a delay on the vortex penetration and a vortex accumulation in the center of the sample. The vortex patterns obtained are in good agreement with experimental results.

Lattice dynamics of metallic glass Ca70Mg30 on the model of Bhatia and Singh

The lattice dynamical studies of the metallic glass Ca70Mg30 by Bhatia and Singh on their model contained two shortcomings, firstly the electron-ion interaction matrix was wrong and secondly, the numerical value of the bulk modulus of the electron gas was accepted arbitrarily. By modifying the electron-ion dynamical matrix and determining all the model parameters from the experimental data, we made a fresh study of the lattice dynamics of Ca70Mg30 and compared it to the earlier studies of Bhatia and Singh and also with experimental phonons.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Effect of barium titanate seed particles on the sintering and lattice parameters in PbMg1/3Nb2/3O3 ceramics

PbMg1/3Nb2/3O3 (PMN) powder was prepared by citrate organic solution, and barium titanate (BT) seed particles were added to encourage the perovskite phase formation. Sintering was followed using the constant heating rate mode of a dilatometer, and it was observed that the seed concentration affected the PMN shrinkage rate and crystal structure. The study of the lattice parameters of the samples after the sintering process indicates that the diffusion of the titanium and of the barium inside perovskite and pyrochlore PMN phases occurs. Moreover, this substitution provoked a decrease of the lattice parameters as showed by the Rietveld refinement.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

A new number field construction of the lattice E8

Known number theoretical constructions of the lattice E8 use the cyclotomic fields Q(ζ15), Q(ζ20), and Q(ζ24). In this work, an infinite family of Abelian number fields yielding rotated versions of the lattice E 8 is exhibited. © 2012 The Managing Editors.

Visualization of Protein Folding Funnels in Lattice Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)