Toda lattice realization of integrable hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudo-differential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld-Sokolov realization.

MESON PROPERTIES FROM A BAG MODEL COMPARED TO LATTICE THEORY AND HEAVY-ION EXPERIMENTS

A bag at temperature (T) with pressure B(T) = B(0)[1 - (T/T(c))4] is shown to be consistent with recent lattice data on the pi and the rho mesons. The limiting temperature, T(l), of the pion bag from the Bekenstein entropy bound is lower than that of other mesons. This agrees with the thermal distribution of pi, K and the rho in heavy ion collisions, which (unlike proton-nucleus or pp data) show a marked difference in T of pion and other mesons in the mid-rapidity region.

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.

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.

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

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.

Renormalization of the one-pion-exchange interaction

A renormalization scheme for the nucleon-nucleon (NN) interaction based on a subtracted T-matrix equation is proposed and applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. With only one scaling parameter (μ), the results show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. The agreement is qualitative in the 1 S0 channel. Between the low-energy NN observables we have examined, the mixing parameter of the 3S1-3D1 states is the most sensitive to the scale. The scheme is renormalization group invariant for μ → ∞. © 1999 Elsevier Science B.V. All rights reserved.

Optimized delta expansion for relativistic nuclear models: Renormalization of vacuum fluctuations

We use the optimized linear δ expansion and functional methods to study vacuum contributions in nuclear matter up to the lowest non-trivial order which includes exchange terms. We show that well known results (MFT, RHA and HF) can be easily reproduced when appropriate limits are taken. Neglecting vacuum contributions we explicitly show that the δ expansion goes beyond the traditional loop approximation previously used to study two loop vacuum contributions in nuclear matter. We then evaluate and renormalize vacuum exchange contributions showing that they are numerically very large, as predicted by the ordinary loop approximation.

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.