Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions

Abstract

We present new approaches for solving constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose stationary solution is the solution to the time-independent nonlinear Schrödinger equation. Constraints are often considered by projection onto the constraint set, here we include them explicitly into the dynamical system. We show the applicability and efficiency of the methods on examples of relevance in modern physics applications.

arXiv commentNote that Eq. (74) here corrects Eq. (74) in the published version

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• Second-order flows for computing the ground states of rotating Bose-Einstein condensates
• Rotating quantum droplets confined in a harmonic potential
• Stationary states of Bose-Einstein condensed atoms rotating in an asymmetric ring potential
• Rotating quantum droplets confined in an anharmonic potential
• Rapidly-rotating quantum droplets confined in a harmonic potential
• Yrast states of quantum droplets confined in a ring potential