当前位置：
X-MOL 学术
›
SIAM J. Sci. Comput.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
Ground States of Spin-$F$ Bose--Einstein Condensates
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-07-30 , DOI: 10.1137/19m1271117 Tonghua Tian , Yongyong Cai , Xinming Wu , Zaiwen Wen
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-07-30 , DOI: 10.1137/19m1271117 Tonghua Tian , Yongyong Cai , Xinming Wu , Zaiwen Wen
SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B983-B1013, January 2020.
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. 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 interesting physical phenomena.
中文翻译：
自旋-$ F $玻色-爱因斯坦凝聚物的基态
SIAM科学计算杂志，第42卷，第4期，第B983-B1013页，2020年1月。
自旋$ F $玻色-爱因斯坦凝聚物（BEC）的基态的计算可以公式化为具有两个二次约束的能量最小化问题。我们使用傅立叶拟谱方案离散化能量函数和约束，并将离散化问题视为流形上的优化问题。设计了到歧管的三种不同类型的缩回。它们使我们能够在流形上应用各种优化方法来解决问题。具体来说，自适应正则化牛顿法与级联多网格技术一起使用可加快收敛速度。我们的方法是第一个适用于具有任意整数自旋的BEC（包括复杂的spin-3 BEC）的算法。关于spin-1，spin-2，
更新日期：2020-07-30
The computation of the ground states of spin-$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. 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 interesting physical phenomena.
中文翻译：
自旋-$ F $玻色-爱因斯坦凝聚物的基态
SIAM科学计算杂志，第42卷，第4期，第B983-B1013页，2020年1月。
自旋$ F $玻色-爱因斯坦凝聚物（BEC）的基态的计算可以公式化为具有两个二次约束的能量最小化问题。我们使用傅立叶拟谱方案离散化能量函数和约束，并将离散化问题视为流形上的优化问题。设计了到歧管的三种不同类型的缩回。它们使我们能够在流形上应用各种优化方法来解决问题。具体来说，自适应正则化牛顿法与级联多网格技术一起使用可加快收敛速度。我们的方法是第一个适用于具有任意整数自旋的BEC（包括复杂的spin-3 BEC）的算法。关于spin-1，spin-2，
京公网安备 11010802027423号