Apoptosis of moving nonorthogonal basis functions in many-particle quantum dynamics
Apoptosis of moving nonorthogonal basis functions in many-particle quantum dynamics
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DOI：
10.1103/physrevb.101.174315
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发表时间：
2019-08
影响因子：
3.7
通讯作者：
Michael Werther;F. Grossmann
中科院分区：
文献类型：
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作者：
Michael Werther;F. Grossmann
由于动基函数的数值作用力随着自由度的增加而呈指数增长，因此在量子动力学中有着悠久的历史。此外，新基函数的产生也是例行公事。在这里，我们主张相反的过程：程序化地去除选定的基函数的运动自由度。这对于关于非正交基的大小的收敛的数值结果是必要的，因为通常两个或更多个状态在早期过于接近彼此，使得使运动方程显式所需的矩阵求逆不稳定。对亚欧姆自旋玻色子模型和荷斯坦分子晶体模型中极化子动力学的应用证明了所提出的方法的有效性。
Due to the exponential increase of the numerical effort with the number of degrees of freedom, moving basis functions have a long history in quantum dynamics. In addition, spawning of new basis functions is routinely applied. Here we advocate the opposite process: the programmed removal of motional freedom of selected basis functions. This is a necessity for converged numerical results with respect to the size of a non-orthogonal basis, because generically two or more states approach each other too closely early on, rendering unstable the matrix inversion, required to make the equations of motion explicit. Applications to the sub-Ohmic spin-boson model as well as to polaron dynamics in a Holstein molecular crystal model demonstrate the power of the proposed methodology.