Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices

Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. (c) 2007 Elsevier B.V. All rights reserved.

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

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

Low dimensional behavior in three-dimensional coupled map lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gap solitons in a model of a superfluid fermion gas in optical lattices

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

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Generalized neighbor-interaction models induced by nonlinear lattices

It is shown that the tight-binding approximation of the nonlinear Schrodinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrodinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

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

Cation-oxygen interaction and oxygen stability in CaCu3Ti4O12 and CdCu3Ti4O12 lattices

The cubic perovskite related material CaCu3Ti4O12 has attracted a great deal of attention due to the high values of the static dielectric constant, of order 104, approximately constant in the temperature range 100-600 K. The substitution of Ca by Cd results in a similar temperature dependence but a static dielectric constant more than one order of magnitude lower. A theoretical electronic structure study is performed on CaCu3Ti4O12 (CCTO) and CdCu3Ti4O12 (CdCTO) using a tight binding with overlap method. Although the calculations are performed in a paramagnetic configuration, excellent agreement with experiment was found for the calculated band gap of CCTO. In spite of the fact that the band structures of both systems look practically the same, a significant difference is found in the calculated bond strength of Ca-O and Cd-O pairs, driven by the presence of Ti, with Ca-O interaction in CCTO loosened with respect to Cd-O interaction in the cadmium compound. It is suggested that O vacancies are more easily formed in CCTO, this being related to the lower electronegativity of Ca as compared to Cd. The formation of oxygen vacancies could be the origin of the difference in the static dielectric constant of the two compounds.

Rural-urban migration in D-dimensional lattices

The rural-urban migration phenomenon is analyzed by using an agent-based computational model. Agents are placed on lattices which dimensions varying from d = 2 up to d = 7. The localization of the agents in the lattice defines that their social neighborhood (rural or urban) is not related to their spatial distribution. The effect of the dimension of lattice is studied by analyzing the variation of the main parameters that characterizes the migratory process. The dynamics displays strong effects even for around one million of sites, in higher dimensions (d = 6, 7).

Band edge states of the < n >=0 gap of Fibonacci photonic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Special subsets and optimum codes based on lattices and cosets

This paper introduces the concept of special subsets when applied to generator matrices based on lattices and cosets as presented by Calder-bank and Sloane. By using the special subsets we propose a non exhaustive code search for optimum codes. Although non exhaustive, the search always results in optimum codes for given (k1, V, Λ/Λ′). Tables with binary and ternary optimum codes to partitions of lattices with 8, 9 e 16 cosets, were obtained.

On the Optimality of Finite Constellations from Algebraic Lattices

A construction technique of finite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to find constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and four. © 2001.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.