2009/11/16 by Ionut Danaila, Danaila, Ionut, Parimah Kazemi +1 · 9 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Quantum Gases (cond-mat.quant-gas) #Quantum and electron transport phenomena #Strong Light-Matter Interactions
paper · doi:10.48550/arxiv.0911.3129
openalex publication_date 2009/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we improve traditional steepest descent methods for the direct minimization of the Gross-Pitaevskii (GP) energy with rotation at two levels. We first define a new inner product to equip the Sobolev space H1 and derive the corresponding gradient. Secondly, for the treatment of the mass conservation constraint, we use a projection method that avoids more complicated approaches based on modified energy functionals or traditional normalization methods. The descent method with these two new ingredients is studied theoretically in a Hilbert space setting and we give a proof of the global existence and convergence in the asymptotic limit to a minimizer of the GP energy. The new method is implemented in both finite difference and finite element two-dimensional settings and used to compute various complex configurations with vortices of rotating Bose-Einstein condensates. The new Sobolev gradient method shows better numerical performances compared to classical L2 or H1 gradient methods, especially when high rotation rates are considered.