Deflation-based identification of nonlinear excitations of the three-dimensional Gross-Pitaevskii equation

2020/04/30 by Nicolas Boullé, N. Boullé, E. G. Charalampidis +3 · 22 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Bent molecular geometry #Bose–Einstein condensate #Chemistry #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Deflation #Excited state #Gross–Pitaevskii equation #Mechanics #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum mechanics #Strong Light-Matter Interactions #Vortex #Vorticity #cs.NA #math.DS #math.NA #nlin.PS #physics.comp-ph

paper · pdf · doi:10.1103/physreva.102.053307

published in Physical Review A 102(5) (American Physical Society) · 9 pages, 11 figures

arxiv created 2020/09/30 · openalex publication_date 2020/11/09 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We present a number of solutions to the three-dimensional Gross--Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The coherent structures exhibit striking topological features, involving combinations of vortex rings and multiple, possibly bent vortex lines. Although unstable, many of them persist for long times in dynamical simulations. These solutions were identified by a state-of-the-art numerical technique called deflation, which is expected to be applicable to many problems from other areas of physics.

Citations

• Monopole Core Instability and Alice Rings in Spinor Bose-Einstein Condensates
• Chladni Solitons and the Onset of the Snaking Instability for Dark Solitons in Confined Superfluids
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates
• SLEPc
• Firedrake
• Dark spherical shell solitons in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics