TIME-DEPENDENT SOLUTION OF THE LIOUVILLE-VONNEUMANN EQUATION - NONDISSIPATIVE EVOLUTION
TIME-DEPENDENT SOLUTION OF THE LIOUVILLE-VONNEUMANN EQUATION - NONDISSIPATIVE EVOLUTION
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DOI：
10.1016/0010-4655(91)90233-b
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发表时间：
1991-02-01
影响因子：
6.3
通讯作者：
KOSLOFF, R
中科院分区：
文献类型：
--
作者：
BERMAN, M;KOSLOFF, R
给出了求解Liouville-von Neumann方程的一种方法。算子的作用在坐标和/或动量表示中局部计算。快速傅立叶变换（FFT）用于在坐标和动量表示之间来回传递，这种变换保留了所有精确的通信关系。时间传播是通过时间演化算子的切比雪夫展开计算的。该方法的精度和收敛性进行了研究，并与一个精确可解的模型问题进行了比较。精确的收敛结果得到使用相空间边界略超过最小理论值。通过算法提供的自然矢量化选项来实现效率。一个典型的非平凡的应用，即分裂的概率密度的非纯态到传输和反射的分支，由于散射的势垒。
A method for solving the Liouville-von Neumann equation is presented. The action of operators is calculated locally in coordinate and/or momentum representation. The Fast Fourier Transform (FFT) is used to pass back and forth between coordinate and momentum representations, this transformation preserving all exact communication relations. The time propagation is calculated by a Chebychev expansion of the time evolution operator. The accuracy and convergence properties of the method are investigated and compared with an exactly solvable model problem. Accurate converged results are obtained using a phase space boundary slightly exceeding the minimum theoretical value. Efficiency is attained by the natural vectorization options provided by the algorithm. A typical non-trivial application is presented, namely, the splitting up of the probability density of a non-pure state into transmitted and reflected branches due to scattering off a potential barrier.