虚时间步长法对Dirac方程演化的优化

Optimization of the Imaginary Time Step Evolution for the Dirac Equation

本文利用虚时间步长法(ITS)演化由Dirac方程导出的Schr dinger-like方程和电荷共轭Schr dinger-like方程,得到在Fermi和Dirac海中的12C的单粒子能级,并讨论演化的时间步长、空间大小和格点间距对ITS演化收敛性的影响。为了保证ITS演化收敛到"精确"解,对于给定的单粒子能级,演化的时间步长必须小于"临界"时间步长Δtc.相对于单粒子能级的能量,"临介"时间步长Δtc对量子数|κ|更加敏感。对于弱束缚状态,收敛结果要与"精确"解一致,需要相对较大的空间大小。无论是深束缚或弱束缚状态,对于不同的格点间距,ITS演化的收敛结果变化不大。在以后的自洽计算中,可以应用这些结论来优化演化过程。

The convergence for the Imaginary Time Step（ITS） evolution with time step,box size,and mesh size are investigated by performing the ITS evolution for the Schrdinger-like or charge-conjugate Schrdinger-like equation deduced from Dirac equation for the single-particle levels of 12C in both the Fermi and Dirac seas.For the guaranteed convergence of the ITS evolution to the ＂exact＂ results,the time step should be smaller than a ＂critical＂ time step Δtc for a given single-particle level.The ＂critical＂ time step Δtc is more sensitive to the quantum numbers ｜κ｜ than to the energy of the single-particle level.For the weakly bound states,in order to reproduce the exact single-particle energies,relatively large box size is required.While for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.The conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.