2022/05/12 by Amandine Aftalion, Aftalion, Amandine, Étienne Sandier +1 · 1 citation
Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Physics of Superconductivity and Magnetism
paper · doi:10.48550/arxiv.2205.06031
openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the ground state of the Gross Pitaveskii energy in a strip, with a phase imprinting condition, motivated by recent experiments on matter waves solitons. We prove that when the width of the strip is small, the ground state is a one dimensional soliton. On the other hand, when the width is large, the ground state is a solitonic vortex. We provide an explicit expression for the limiting phase of the solitonic vortex as the size of the strip is large: it has the same behaviour as the soliton in the infinite direction and decays exponentially due to the geometry of the strip, instead of algebraically as vortices in the whole space.