A constrained gentlest ascent dynamics and its applications to finding excited states of Bose-Einstein condensates

Bibliographic Details
Title:	A constrained gentlest ascent dynamics and its applications to finding excited states of Bose-Einstein condensates
Authors:	Liu, Wei, Xie, Ziqing, Yuan, Yongjun
Source:	Journal of Computational Physics, Vol. 473 (2023), 111719
Publication Year:	2022
Collection:	Computer Science Mathematics Condensed Matter Quantum Physics
Subject Terms:	Mathematics - Numerical Analysis, Condensed Matter - Quantum Gases, Quantum Physics, 35B38, 35Q55, 49K20, 65M12, 81-08
More Details:	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. Comment: 28 pages, 7 figures; Submitted to Journal of Computational Physics on January 30, 2021
Document Type:	Working Paper
DOI:	10.1016/j.jcp.2022.111719
Access URL:	http://arxiv.org/abs/2209.04684
Accession Number:	edsarx.2209.04684
Database:	arXiv

More Details
DOI:	10.1016/j.jcp.2022.111719