An efficient preconditioned conjugate-gradient solver for a two-component dipolar Bose-Einstein condensate

• URL: http://arxiv.org/abs/2510.24543v1
• Date: Tue, 28 Oct 2025 15:44:47 GMT
• Title: An efficient preconditioned conjugate-gradient solver for a two-component dipolar Bose-Einstein condensate
• Authors: Weijing Bao, Zhenhao Wang, Jia-Rui Luo, Kui-Tian Xi,
• Abstract summary: We develop a preconditioned nonlinear conjugate-gradient solver for ground states of binary dipolar Bose-Einstein condensates.<n>We reproduce representative textures and droplet-stability windows reported for dipolar mixtures.
• Score: 1.3037017215576174
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a preconditioned nonlinear conjugate-gradient solver for ground states of binary dipolar Bose-Einstein condensates within the extended Gross-Pitaevskii equation including Lee-Huang-Yang corrections. The optimization is carried out on the product-of-spheres normalization manifold and combines a manifold-preserving analytic line search, derived from a second-order energy expansion and validated along the exact normalized path, with complementary Fourier-space kinetic and real-space diagonal (Hessian-inspired) preconditioners. The method enforces monotonic energy descent and exhibits robust convergence across droplet, stripe, and supersolid regimes while retaining spectrally accurate discretizations and FFT-based evaluation of the dipolar term. In head-to-head benchmarks against imaginary-time evolution on matched grids and tolerances, the solver reduces iteration counts by one to two orders of magnitude and overall time-to-solution, and it typically attains slightly lower energies, indicating improved resilience to metastability. We reproduce representative textures and droplet-stability windows reported for dipolar mixtures. These results establish a reliable and efficient tool for large-scale parameter scans and phase-boundary mapping, and for quantitatively linking numerically obtained metastable branches to experimentally accessible states.

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