Computing excited states of dipolar Bose--Einstein condensates by constrained gentlest ascent dynamics

@misc{zheng2026computing,
  title = {{Computing excited states of dipolar Bose--Einstein condensates by constrained gentlest ascent dynamics}},
  author = {Fu Zheng and Wei Liu and Xu Qian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27878},
  eprint = {2610.27878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27878},
}

TY  - UNPB
TI  - Computing excited states of dipolar Bose--Einstein condensates by constrained gentlest ascent dynamics
AU  - Fu Zheng
AU  - Wei Liu
AU  - Xu Qian
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27878
UR  - https://arxiv.org/abs/2610.27878
AB  - Dipolar Bose--Einstein condensates (BECs), i.e., BECs with long-range dipole-dipole interactions (DDI), exhibit extraordinarily rich physics and serve as a versatile experimental platform for exploring exotic quantum states of matter. Within the mean-field framework, a dipolar BEC can be described by the Gross--Pitaevskii (GP) model with a DDI term. Its stationary states consist of the ground state, which minimizes the GP energy functional under the normalization constraint, and excited states, which are higher-energy critical points that typically correspond to constrained saddle points. Excited states encode collective excitation modes and play a key role in the dynamical stability and quantum phase transitions of cold-atom systems. However, in contrast to the extensively studied ground state, they remain far less explored numerically, especially in dipolar systems. In this work, we develop a numerical method based on the constrained gentlest ascent dynamics (CGAD) that systematically computes excited states of dipolar BECs by stably targeting constrained saddle points with any prescribed Morse index. Specifically, a semi-implicit sine-pseudospectral discretization with an orthonormalization correction step is adopted, and the nonlocal DDI terms are evaluated efficiently and accurately via the nonuniform fast Fourier transform (NUFFT). The resulting scheme is applied to one-, two-, and three-dimensional dipolar BECs, enabling a detailed numerical investigation of their excited states. Remarkably, our simulations reveal that excited states can persist even in regimes where the ground state of the condensate becomes mean-field unstable. This work provides a computational framework for studying excited states in dipolar quantum gases and offers insights for future theoretical and experimental investigations.
ER  -