虚时间步长法的狄拉克海难

On Avoidance of the Tsunami of the Dirac Sea by ITS

通过用虚时间步长法(ITS)演化由Dirac方程导出的Schrdinger-like方程得到了Fermi海和Dirac海中12C分离的单粒子能谱,避免了出现狄拉克海难。将ITS方法直接用于求解Dirac方程,会导致单粒子能谱只能演化到狄拉克海中。研究发现,通过将Dirac方程转化为等效的Schrdinger-like方程,从正无穷延伸到负无穷的单粒子能谱可以分别在Fermi海或Dirac海中通过ITS演化而获得。利用ITS方法演化等效的Schrdinger-like方程得到了与常规Shooting方法相同的结果,此事实证明了该算法的可行性、实用性及可靠性,同时消除了能否将ITS方法应用于描述相对论系统的质疑。

The discrete single-particle spectra of 12C in both the Fermi and Dirac sea have been calculated by the imaginary time step（ITS）method for the Schr dinger-like equation after avoiding the ＂tsunami＂ of the Dirac sea,i.e.,the diving behavior of the single-particle level into the Dirac sea in the direct application of the ITS method for the Dirac equation.It is found that by the transform from the Dirac equation to the Schr dinger-like equation,the single-particle spectra,which extend from the positive to the negative infinity,can be separately obtained by the ITS evolution in either the Fermi sea or the Dirac sea.Identical results with those in the conventional shooting method have been obtained via the ITS evolution for the equivalent Schr dinger-like equation,which demonstrates the feasibility,practicality and reliability of the present algorithm and dispels the doubts on the ITS method in the relativistic system.