An efficient preconditioned conjugate-gradient solver for a two-component dipolar Bose-Einstein condensate
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| Format: | Preprint |
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2025
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| _version_ | 1866914118806536192 |
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| author | Bao, Weijing Wang, Zhenhao Luo, Jia-Rui Xi, Kui-Tian |
| author_facet | Bao, Weijing Wang, Zhenhao Luo, Jia-Rui Xi, Kui-Tian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_24543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An efficient preconditioned conjugate-gradient solver for a two-component dipolar Bose-Einstein condensate Bao, Weijing Wang, Zhenhao Luo, Jia-Rui Xi, Kui-Tian Quantum Gases Computational Physics Quantum Physics 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. |
| title | An efficient preconditioned conjugate-gradient solver for a two-component dipolar Bose-Einstein condensate |
| topic | Quantum Gases Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.24543 |