Self-Bound vortex states in nonlinear Schrödinger equations with LHY correction

2021/12/16 by Anudeep K. Arora, Arora, Anudeep K., Christof Sparber +1
Mathematics · Physics and Astronomy · #35A01 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35A01 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.2112.09213

19 pages

arxiv created 2021/12/16 · arxiv updated 2021/12/20

Abstract

We study the cubic-quartic nonlinear Schrödinger equation (NLS) in two and three spatial dimension. This equation arises in the mean-field description of Bose-Einstein condensates with Lee-Huang-Yang correction. We first prove global existence of solutions in natural energy spaces which allow for the description of self-bound quantum droplets with vorticity. Existence of such droplets, described as central vortex states in 2D and 3D, is then proved using an approach via constrained energy minimizers. A natural connection to the NLS with repulsive inverse-square potential in 2D arises, leading to an orbital stability result under the corresponding flow.

Related

• A new form of liquid matter: quantum droplets
• Axially confined binary quantum droplets: ground states and central vortices
• Multidimensional self-trapping in linear and nonlinear potentials
• Uniqueness and orbital stability of standing waves for the nonlinear Schrodinger equation with a partial confinement
• Multidimensional Soliton Systems