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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

A finite element toolbox for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates

Résumé

We present a finite element toolbox for the computation of Bogoliubovde Gennes modes used to assess the linear stability of stationary solutions of the Gross-Pitaevskii (GP) equation. Applications concern one (single GP equation) or two-component (a system of coupled GP equations) Bose-Einstein condensates in one, two and three dimensions of space. An implementation using the free software FreeFem++ is distributed with this paper. For the computation of the GP stationary (complex or real) solutions we use a Newton algorithm coupled with a continuation method exploring the parameter space (the chemical potential or the interaction constant). Bogoliubov-de Gennes equations are then solved using dedicated libraries for the associated eigenvalue
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Dates et versions

hal-04255543 , version 1 (09-03-2023)
hal-04255543 , version 2 (24-10-2023)

Identifiants

  • HAL Id : hal-04255543 , version 1

Citer

Georges Sadaka, Victor Kalt, Ionut Danaila, Frédéric Hecht. A finite element toolbox for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates. 2023. ⟨hal-04255543v1⟩
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