Numerical solution of the stationary multicomponent nonlinear Schr\"{o}dinger equation with a constraint on the angular momentum

TL;DR

This paper introduces a damped oscillating particle method for solving the stationary nonlinear Schrödinger equation, effectively handling multiple components and angular momentum constraints, with demonstrated accuracy and adaptability.

Contribution

A novel damped oscillating particle approach for stationary NLSE that efficiently incorporates angular momentum constraints and extends to multi-component systems.

Findings

Successfully reproduces the yrast curve for single-component NLSE.

First to produce an analogous curve for two-component NLSE.

Demonstrates accuracy through comparison with analytic solutions.

Abstract

We formulate a damped oscillating particle method to solve the stationary nonlinear Schr\"{o}dinger equation (NLSE). The ground state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.