The Experts below are selected from a list of 17559 Experts worldwide ranked by ideXlab platform
Romain Duboscq - One of the best experts on this subject based on the ideXlab platform.
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GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: dynamics and stochastic simulations
Computer Physics Communications, 2015Co-Authors: Xavier Antoine, Romain DuboscqAbstract:GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross–Pitaevskii equations that arise in the physics of Bose–Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross–Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.
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Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation
2013Co-Authors: Romain DuboscqAbstract:Dans cette thèse, nous étudions différents aspects mathématiques et numériques des équations de Gross-Pitaevskii et de Schrödinger non linéaire. Nous commençons (chapitre 1) par introduire différents modèles à partir des systèmes physiques que sont les condensats de Bose-Einstein et les impulsions lumineuses dans les fibres optiques. Cette modélisation conduit aux équations aux dérivées partielles stochastiques suivantes : l'équation de Gross-Pitaevskii stochastique et l'équation de Schrödinger non linéaire avec dispersion aléatoire. Ensuite, dans le second chapitre, nous nous intéressons au problème de l'existence et l'unicité d'une solution de ces équations. On montre notamment que le problème de Cauchy a une solution pour l'équation de Gross-Pitaevskii stochastique avec rotation grâce à la construction de la solution associée au problème. Nous abordons ensuite dans le troisième chapitre le problème du calcul des états stationnaires pour l'équation de Gross-Pitaevskii. Nous développons une méthode pseudo-spectrale de discrétisation du Continuous Normalized Gradient Flow, associée à une résolution itérative préconditionnée des sous-espaces de Krylov. Le quatrième chapitre concerne l'étude de schémas pseudo-spectraux pour la dynamique de l'équation de Gross-Pitaevskii et de Schrödinger non linéaire. On procède à une étude numérique de ces schémas (schéma de splitting de Lie et de Strang, ainsi qu'un schéma de relaxation). De plus, on analyse le schéma de Lie dans le cadre de l'équation de Schrödinger non linéaire avec dispersion aléatoire. Finalement, nous présentons, dans le cinquième chapitre, une boîte à outils Matlab (GPELab) développée dans le but de fournir les méthodes numériques que nous avons étudiées
J. Alberto Montero - One of the best experts on this subject based on the ideXlab platform.
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Vortices for a Rotating Toroidal Bose–Einstein Condensate
Archive for Rational Mechanics and Analysis, 2008Co-Authors: Stan Alama, Lia Bronsard, J. Alberto MonteroAbstract:We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid torus of revolution in $${\mathbb{R}}^3$$ with starshaped cross-section. We show that for angular speeds ω_ε = O (|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε . These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the torus.
Klaus Ziegler - One of the best experts on this subject based on the ideXlab platform.
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A renormalized Gross-Pitaevskii Theory and vortices in a strongly interacting Bose gas
Journal of Physics B: Atomic Molecular and Optical Physics, 2007Co-Authors: Ch. Moseley, Klaus ZieglerAbstract:We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.
Didier Smets - One of the best experts on this subject based on the ideXlab platform.
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ON THE LINEAR WAVE REGIME OF THE GROSS-Pitaevskii EQUATION
Journal d'analyse mathématique, 2010Co-Authors: Fabrice Bethuel, Raphaël Danchin, Didier SmetsAbstract:We study long-wavelength asymptotics for the Gross-Pitaevskii equation corresponding to perturbations of a constant state of modulus one. We exhibit lower bounds on the first occurrence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.
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On the Korteweg-de Vries long-wave approximation of the Gross-Pitaevskii equation II
Communications in Partial Differential Equations, 2010Co-Authors: Fabrice Bethuel, Philippe Gravejat, Jean-claude Saut, Didier SmetsAbstract:In this paper, we proceed along our analysis of the Korteweg-de Vries approximation of the Gross-Pitaevskii equation initiated in a previous paper. At the long-wave limit, we establish that solutions of small amplitude to the one-dimensional Gross-Pitaevskii equation split into two waves with opposite constant speeds $\pm \sqrt{2}$, each of which are solutions to a Korteweg-de Vries equation. We also compute an estimate of the error term which is somewhat optimal as long as travelling waves are considered. At the cost of higher regularity of the initial data, this improves our previous estimate.
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Les équations d'Euler, des ondes et de Korteweg-de Vries comme limites asymptotiques de l'équation de Gross-Pitaevskii
2008Co-Authors: Raphaël Danchin, Fabrice Bethuel, Philippe Gravejat, Jean-claude Saut, Didier SmetsAbstract:Dans cet exposé, on expose plusieurs résultats récents concernant la dynamique onde longue pour l'équation de Gross-Pitaevskii
Jimena Royo-letelier - One of the best experts on this subject based on the ideXlab platform.
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Non existence of vortices in the small density region of a condensate
Journal of Functional Analysis, 2011Co-Authors: Amandine Aftalion, Robert L Jerrard, Jimena Royo-letelierAbstract:In this paper, we answer a question raised by Len Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose Einstein condensate at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted jacobian estimates.
