A New Iterative Approach for the Exact Solution of the Standard Pairing Model
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摘要: 建立了一种求解标准对力模型的新迭代方法。该方法基于标准对力模型的多项式方案，为球形和形变系统提供了方便的初始值预测。特别是对于大尺寸系统，该方法将求解k对多项式的系统方程式简化为分步求解1对多项式系统的迭代过程，并通过快速Newton-Raphson以及Monte Carlo采样算法逐步提供初始值预测。通过扩展，本算法还可用于解决Gaudin型量子多体问题，例如考虑超过100条轨道、50对的大尺寸系统，以及超形变核、核裂变的研究中。
A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.Abstract: A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.-
Keywords:
- standard pairing problem /
- iterative approach /
- super-heavy nuclei /
- nuclear fission
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