A positive-conservative Fourier optimization method for ground states of Bose--Einstein condensates with higher-order interactions
Abstract
We develop a positive-conservative Fourier optimization (PCFO) method for computing ground states of Bose--Einstein condensates with higher-order interactions. The ground-state problem admits a convex density formulation, but the singular behavior near zero density poses difficulties for high-accuracy computation. We introduce convex regularizations of the density energy and establish their Γ-convergence on the computational domain as the regularization parameters vanish. The regularized problem is discretized by a Fourier pseudospectral method with mass conservation and nodal positivity. For the resulting constrained optimization problem, we use an accelerated first-order method for the main energy reduction, followed by a Newton refinement to reduce the remaining optimality residual. Numerical experiments show spectral-type convergence for regularized problems, quantify the effects of the regularization parameters on accuracy and spatial resolution, and demonstrate the effectiveness of the two-stage optimization method.
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BibTeX
@misc{lin2026positiveconservative,
title = {{A positive-conservative Fourier optimization method for ground states of Bose--Einstein condensates with higher-order interactions}},
author = {Bo Lin and Xinran Ruan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38965},
eprint = {2609.38965},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38965},
}
RIS
TY - UNPB
TI - A positive-conservative Fourier optimization method for ground states of Bose--Einstein condensates with higher-order interactions
AU - Bo Lin
AU - Xinran Ruan
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38965
UR - https://arxiv.org/abs/2609.38965
AB - We develop a positive-conservative Fourier optimization (PCFO) method for computing ground states of Bose--Einstein condensates with higher-order interactions. The ground-state problem admits a convex density formulation, but the singular behavior near zero density poses difficulties for high-accuracy computation. We introduce convex regularizations of the density energy and establish their Γ-convergence on the computational domain as the regularization parameters vanish. The regularized problem is discretized by a Fourier pseudospectral method with mass conservation and nodal positivity. For the resulting constrained optimization problem, we use an accelerated first-order method for the main energy reduction, followed by a Newton refinement to reduce the remaining optimality residual. Numerical experiments show spectral-type convergence for regularized problems, quantify the effects of the regularization parameters on accuracy and spatial resolution, and demonstrate the effectiveness of the two-stage optimization method.
ER -