Ground states and their characterization of spin-\(F\) Bose-Einstein condensates

The computation of the ground states of spin-\(F\) Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier pseudospectral schemes and view the discretized problem as an...

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Published in:arXiv.org 2019-07
Main Authors: Tian, Tonghua, Cai, Yongyong, Wu, Xinming, Wen, Zaiwen
Format: Article
Language:English
Subjects:
Algorithms
Bose-Einstein condensates
Energy conservation
Ground state
Manifolds
Newton methods
Optical lattices
Optimization
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description The computation of the ground states of spin-\(F\) Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier pseudospectral schemes and view the discretized problem as an optimization problem on manifold. Three different types of retractions to the manifold are designed. They enable us to apply various optimization methods on manifold to solve the problem. Specifically, an adaptive regularized Newton method is used together with a cascadic multigrid technique to accelerate the convergence. According to our limited knowledege, our method is the first applicable algorithm for BECs with an arbitrary integer spin, including the complicated spin-3 BECs. Extensive numerical results on ground states of spin-1, spin-2 and spin-3 BECs with diverse interaction and optical lattice potential in one/two/three dimensions are reported to show the efficiency of our method and to demonstrate some interesting physical phenomena.
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subjects Algorithms
Bose-Einstein condensates
Energy conservation
Ground state
Manifolds
Newton methods
Optical lattices
Optimization
title Ground states and their characterization of spin-\(F\) Bose-Einstein condensates
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