Theoretical Nuclear Physics

PI和他的合作者已经证明了将算子exp[-dt(T+V)]分解为纯正系数的四阶的方法，它产生了求解经典动力学问题的优越辛积分器，也产生了求解时变薛定谔方程，Fokker-Plank方程，Kramers方程和虚时间薛定谔方程的优秀数值算法。后者产生了一些新的四阶扩散蒙特卡罗算法。这些新算法需要知道势和势的梯度。这些新算法的四阶误差系数比现有的分裂算子（二阶）方法小几个数量级，并且可以使用10-50倍的时间步长产生收敛结果。这种算子分解方法为解决核物理、凝聚态物理和原子物理中的各种量子多体和动力学问题提供了一类新的更有效的算法。本提案旨在开发进一步的四阶算法，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。

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.