Study of localized solutions of the nonlinear discrete model for dipolar Bose-Einstein condensate in an optical lattice by the homoclinic orbit method

It is well known that the dynamics of the Bose Einstein condensate (BEC) trapped in an optical lattice can be described in tight-binding approximation by the discrete Nonlinear Schrödinger Equation (DNLSE) [1,2]. This model opens the way to study different aspects of the BEC dynamics in an optical lattice, such as discrete solitons and nonlinear localized modes and their stability and dynamics, modulational instability, superfluid-insulator transition, etc

Modulational instability in salerno model

We investigate the properties of modulational instability in the Salerno equation in quasione dimension in Bose-Einstein condensate (BEC). We analyze the regions of modulational instability of nonlinear plane waves and determine the conditions of its existence in BEC

Closure properties of Watson-Crick grammars

In this paper, we define Watson-Crick context-free grammars, as an extension of Watson-Crick regular grammars and Watson-Crick linear grammars with context-free grammar rules. We show the relation of Watson-Crick (regular and linear) grammars to the sticker systems, and study some of the important closure properties of the Watson-Crick grammars. We establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations, while the differences between other Watson-Crick grammars with their corresponding Chomsky grammars depend on the computational power of the Watson-Crick grammars which still need to be studied

Detecting eve in communication with continuous-variable Einstein-Podolsky-Rosen correlations

We study the validity of the entanglement parameter introduced in a recent publication by Guangqiang et al. Phys. Rev. A 73 012314 (2006)] for detecting Eve, the eavesdropper. We have found that Eve can be detected using this parameter only if Alice establishes a quantum correlation between the Einstein-Podolsky-Rosen (EPR) pair. This quantum correlation is related to the possibility of an apparent violation of the Heisenberg inequality for the quadrature components of the EPR pair

Trigonometric functions and Linear Transformations

This is an introduction to Trigonometric functions and Linear Transformations for undergraduate students

Study of localized solutions of the nonlinear discrete model for dipolar BEC in an optical lattice by the homoclinic orbit method

We use homoclinic orbits to find solutions of a dynamical system of the dipolar Bose Einstein Condensate (BEC) in a deep optical lattice. The equation of motion is transformed to a two-dimensional map and its homoclinic orbits are computed numerically. Each homoclinic orbit leads to a different solution. These different solutions lead to different types of solitons. We also analyse the stability of the solutions