Numerical solution of the stationary multicomponent nonlinear Schrödinger equation with a constraint on the angular momentum

Abstract

We formulate a damped oscillating particle method to solve the stationary nonlinear Schrödinger 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.

References in corpus (3)

• Persistent currents in spinor condensates
• Numerical solution of the non-linear Schrodinger equation using smoothed-particle hydrodynamics
• Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures

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• Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions
• Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length
• Stationary states of Bose-Einstein condensed atoms rotating in an asymmetric ring potential
• A numerical damped oscillator approach to constrained Schrödinger equations
• On the second order asymptotical regularization of linear ill-posed inverse problems
• Damped second order flow applied to image denoising
• Yrast states of quantum droplets confined in a ring potential