核密度泛函理论框架下线性响应的约化基方法
Reduced-basis method for linear response within nuclear density functional theory
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中文总结 AI 辅助
该研究针对核密度泛函理论中QRPA计算成本高的问题，构建基于RBM的FAM模拟器，可高精度复现相关模式并降低一个数量级以上的计算成本，有望应用于核物理相关研究。
中文摘要 AI 辅助
背景：核密度泛函理论框架内的准粒子随机相位近似（QRPA）是描述集体激发的有力工具。尽管有限振幅方法（FAM）可高效求解QRPA问题，但针对不同外场参数的重复计算仍存在计算量大的问题。目的：我们构建了一种基于约化基方法（RBM）的FAM模拟器，将外场的复能量视为模型参数，以高效复现FAM振幅和QRPA本征模式。方法：在复能量平面的少量训练点上执行高保真FAM计算，得到的FAM振幅构成非正交约化基；通过变分方程得到模拟器，无需额外的完整FAM计算即可预测任意复能量下的响应及QRPA本征解。结果：当训练集覆盖相关能量域时，RBM模拟器可精确复现巨共振区和低能区的FAM强度分布，还能复现与HFB态形状不稳定性相关的虚QRPA模式。将其应用于真实模型空间中稀土Dy同位素的K^π=0^+模式时，模拟器复现强度分布和最低0^+集体态的精度与完整FAM计算相当，计算成本降低一个数量级以上。结论：RBM是一种高效且精确的FAM模拟器，其能以大幅降低的计算成本复现巨共振、低能及虚能模式，有望用于密度泛函优化、集体惯性计算及核集体激发的大规模研究。
英文摘要
Background: The quasiparticle random-phase approximation (QRPA) within nuclear density functional theory provides a powerful framework for describing collective excitations. Although the finite-amplitude method (FAM) efficiently solves the QRPA problem, repeated calculations for different external-field parameters remain computationally demanding. Purpose: We construct a reduced basis method (RBM)-based emulator for the FAM that treats the complex energy of the external field as a model parameter to efficiently reproduce FAM amplitudes and QRPA eigenmodes. Methods: High-fidelity FAM calculations are performed at a small set of training points in the complex-energy plane. The resulting FAM amplitudes form a non-orthogonal reduced basis. A variational equation yields an emulator that can predict the response at arbitrary complex energies and QRPA eigensolutions without additional full FAM calculations. Results: The RBM emulator accurately reproduces FAM strength distributions in both giant-resonance and low-energy regions when the relevant energy domain is covered by the training set. It also reproduces imaginary QRPA modes associated with shape instabilities of the HFB state. Applied to the $K^π=0^+$ mode of rare-earth Dy isotopes in a realistic model space, the emulator reproduces strength distributions and the lowest $0^+$ collective states with precision comparable to full FAM calculations, reducing the computational cost by more than an order of magnitude. Conclusions: The RBM provides an efficient and accurate FAM emulator. Its ability to reproduce giant-resonance, low-energy, and imaginary-energy modes at drastically reduced computational cost makes it promising for density-functional optimization, calculations of collective inertia, and large-scale surveys of nuclear collective excitations.
发表机构
- Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）
- Faculty of Pure and Applied Sciences, University of Tsukuba（筑波大学理学院）
- Department of Physics and Astronomy, University of North Carolina（北卡罗来纳大学物理与天文学系）
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