On action ground states of defocusing nonlinear Schrödinger equations

Abstract

We investigate the action ground states of the defocusing nonlinear Schrödinger equation with and without rotation. Our primary focus is on characterizing the relationship between the action ground states and the energy ground states. Theoretically, we prove a complete equivalence of the two in the non-rotating case and a conditional equivalence in the rotating case. Our theoretical results are supported by extensive numerical experiments. Notably, in the rotating case, we provide numerical examples of non-equivalence showing that non-equivalence typically occurs at the transition points where the number of vortices in the action ground state is increasing. Additionally, we study the asymptotic behaviour of the action ground states and the associated physical quantities in certain limiting parameter regimes, with numerical results validating and complementing our analysis. Furthermore, we explore the formation and change of the vortex pattern in the action ground states numerically.

arXiv comment28 pages, 12 figures

References in corpus (9)

• Mathematical theory and numerical methods for Bose-Einstein condensation
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Gross-Pitaevskii Theory of the Rotating Bose Gas
• On global minimizers for a mass constrained problem
• The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications
• Stability and instability properties of rotating Bose-Einstein condensates
• Second-order flows for computing the ground states of rotating Bose-Einstein condensates
• Computing the least action ground state of the nonlinear Schrödinger equation by a normalized gradient flow
• Computing the action ground state for the rotating nonlinear Schrödinger equation