论文标题
限制了最温和的上升动力学及其在寻找Bose-Einstein凝结激发态的应用
A constrained gentlest ascent dynamics and its applications to finding excited states of Bose-Einstein condensates
论文作者
论文摘要
在本文中，[W. E和X. Zhou，非线性，24（2011），第1831---1842页]扩展到受约束的最绅士上升动力学（CGAD），以找到具有任何指定的Morse指数的约束鞍点。事实证明，所提出的CGAD的线性稳定稳态恰好是具有相应Morse指数的非排定约束鞍点。同时，还验证了带有相应指数的非排定约束鞍点附近理想化的CGAD的局部指数融合。然后，将CGAD应用于在归一化约束下，通过计算相应的毛 - 皮塔夫斯基能量功能的计算约束的鞍点，以其摩尔斯的指数的顺序找到单组玻色凝结物（BEC）的激发态。另外，在线性/非线性情况下，BEC激发态的特性是数学/数值研究的。据报道，广泛的数值结果显示了我们方法的有效性和鲁棒性，并证明了一些有趣的物理学。
In this paper, the gentlest ascent dynamics (GAD) developed in [W. E and X. Zhou, Nonlinearity, 24 (2011), pp. 1831--1842] is extended to a constrained gentlest ascent dynamics (CGAD) to find constrained saddle points with any specified Morse indices. It is proved that the linearly stable steady state of the proposed CGAD is exactly a nondegenerate constrained saddle point with a corresponding Morse index. Meanwhile, the locally exponential convergence of an idealized CGAD near nondegenerate constrained saddle points with corresponding indices is also verified. The CGAD is then applied to find excited states of single-component Bose--Einstein condensates (BECs) in the order of their Morse indices via computing constrained saddle points of the corresponding Gross--Pitaevskii energy functional under the normalization constraint. In addition, properties of the excited states of BECs in the linear/nonlinear cases are mathematically/numerically studied. Extensive numerical results are reported to show the effectiveness and robustness of our method and demonstrate some interesting physics.
