Theoretical Nuclear Physics

理论核物理

• 批准号: 0100839
• 负责人: Siu Chin
• 金额: $ 5万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100839&HistoricalAwards=false
• 关键词: Theoretical; Nuclear; Physics

The PI and his collaborators have shown that the method of factorizing the operator exp[-dt(T+V)] to fourth order with purely positive coefficients, which has produced superior symplectic integrators for solving classical dynamical problems, has also yielded excellent numerical algorithms for solving the time-dependent Schroedinger equation, the Fokker-Plank equation, the Kramers equation, and the imaginary time Schroedinger equation. The latter has resulted in a number of new fourth order Diffusion Monte Carlo algorithms. These new algorithms require knowing the potential and the gradient of the potential. The fourth order error coefficients of these new algorithms are orders of magnitude smaller then those of the existing split operator (second-order) method and can produce converged results using time steps 10-50 times as large. This operator factorization approach suggests a new class of more efficient algorithms for solving diverse quantum many-body and dynamical problems in nuclear, condensed matter and atomic physics. This proposal seeks to develop further fourth order algorithms for solving large scale, grid based, Hartree-Fock, Kohn-Sham and Gross-Pitaevskii equations in arbitrary three-dimensional geometry.

PI和他的合作者已经证明，将算子exp[-dt（T+V）]分解为四阶纯正系数的方法，产生了用于解决经典动力学问题的上级辛积分器，也产生了用于求解时间相关的薛定谔方程、福克-普朗克方程、克拉默斯方程和虚时薛定谔方程的优秀数值算法。后者导致了一些新的四阶扩散蒙特卡罗算法。这些新的算法需要知道的潜力和梯度的潜力。这些新算法的四阶误差系数比现有的分裂算子（二阶）方法的误差系数小几个数量级，并且可以使用10-50倍大的时间步长产生收敛结果。这种算子因式分解方法提出了一类新的更有效的算法，用于解决核物理、凝聚态物理和原子物理中的各种量子多体和动力学问题。该建议旨在进一步发展四阶算法，用于求解任意三维几何中的大规模、基于网格的Hartree-Fock、Kohn-Sham和Gross-Pitaevskii方程。