Linear and Nonlinear Bullets of the Bogoliubov-de Gennes Excitations

We report on the focalization of Bogoliubov–de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov–de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear “bullets”). These traveling Bogoliubov–de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.Peer ReviewedPostprint (published version

Transformation Optics in Coupled Waveguides

Treball final de màster oficial fet en col·laboració amb Universitat Autònoma de Barcelona (UAB), Universitat de Barcelona (UB) i Institut de Ciències Fotòniques (ICFO)English: The technique of transformation optics is applied to a system of three coupled waveguides undergoing adiabatic passage of a light beam. We show that it is possible, by applying different transformations to different parts of the system, to modify at wish the geometry of the waveguides, keeping the efficiency of the process. The performance of this technique is demonstrated through 2D numerical simulations. All the analysis is performed for non-magnetic optical materials and for electromagnetic waves in the microwave region.Castellano: La técnica de óptica transformacional es aplicada a un sistema de tres guías de onda acopladas sometidas a un pasaje adiabático de un haz de luz. Mostramos que es posible, mediante la aplicación de diferentes transformaciones en diferentes partes del sistema, modificar a voluntad la geometría de las guíes de onda, manteniendo la eficiencia del proceso. Demostramos el rendimiento de esta técnica a través de simulaciones numéricas en 2D. Todos los análisis se realizan para materiales ópticos no magnéticos y para ondas electromagnéticas en la región de las microondas.Català: La tècnica d'òptica transformacional és aplicada a un sistema de tres guies d'ona acoblades sotmès a un passatge adiabàtic d'un feix de llum. Mostrem que és possible, mitjançant l'aplicació de diferents transformacions a diferents parts del sistema, modificar a voluntat la geometria de les guies d'ona, mantenint l'eficiència del procés. Demostrem el rendiment d'aquesta tècnica a través de simulacions numèriques en 2D. Totes les anàlisis es realitzen per a materials òptics no magnètics i per a ones electromagnètiques a la regió de les micrones

Perturbations in higher derivative gravity beyond maximally symmetric spacetimes

We study (covariant) scalar-vector-tensor (SVT) perturbations of infinite derivative gravity (IDG), at the quadratic level of the action, around conformally-flat, covariantly constant curvature backgrounds which are not maximally symmetric spacetimes (MSS). This extends a previous analysis of perturbations done around MSS, which were shown to be ghost-free. We motivate our choice of backgrounds which arise as solutions of IDG in the UV, avoiding big bang and black hole singularities. Contrary to MSS, in this paper we show that, generically, all SVT modes are coupled to each other at the quadratic level of the action. We consider simple examples of the full IDG action, and illustrate this mixing and also a case where the action can be diagonalized and ghost-free solutions constructed. Our study is widely applicable for both non-singular cosmology and black hole physics where backgrounds depart from MSS. In appendices, we provide SVT perturbations around conformally-flat and arbitrary backgrounds which can serve as a compendium of useful results when studying SVT perturbations of various higher derivative gravity models.Comment: 36 pages, 1 figur

The Unique Solvability Conditions for the Generalized Absolute Value Equations

This paper investigates the conditions that guarantee unique solvability and unsolvability for the generalized absolute value equations (GAVE) given by $Ax - B \vert x \vert = b$. Further, these conditions are also valid to determine the unique solution of the generalized absolute value matrix equations (GAVME) $AX - B \vert X \vert =F$. Finally, certain aspects related to the solvability and unsolvability of the absolute value equations (AVE) have been deliberated upon

A Note on the Paper "The unique solution of the absolute value equations"

In this note, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195-200, 2018)