用虚时间步长方法避免狄拉克海海啸
Avoid the Tsunami of the Dirac sea in the Imaginary Time Step method
摘要：
在避开狄拉克海的“海啸”后，用类薛定谔方程的虚时间步方法计算了费米海和狄拉克海中的离散单粒子能谱，在直接应用ITS方法求解Dirac方程时，研究了单粒子能级进入Dirac海的行为。通过将Dirac方程转化为Schrödinger-like方程，我们发现无论是在Fermi海还是在Dirac海，单粒子谱都可以通过ITS演化分别得到从正无穷远到负无穷远的谱.对等效的类薛定谔方程进行了ITS演化，得到了与传统打靶法完全一致的结果，证明了该算法的可行性、实用性和可靠性，消除了相对论系统中ITS方法的疑虑.
英文摘要：
The discrete single-particle spectra in both the Fermi and Dirac sea have been calculated by the imaginary time step (ITS) method for the Schrödinger-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 Schrödinger-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 Schrödinger-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.
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