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首页> 外文期刊>The Journal of Chemical Physics >Quantal cumulant dynamics: General theory
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Quantal cumulant dynamics: General theory

机译：量子累积动力学：一般理论

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The authors have derived coupled equations of motion of cumulants that consist of a symmetric-ordered product of the position and momentum fluctuation operators in one dimension. The key point is the utilization of a position shift operator acting on a potential operator, where the expectation value of the shift operator is evaluated using the cumulant expansion technique. In particular, the equations of motion of the second-order cumulant and the expectation values of the position and momentum operators are given. The resultant equations are expressed by those variables and a quantal potential that consists of an exponential function of the differential operators and the original potential. This procedure enables us to perform quantal (semiclassical) dynamics in one dimension. In contrast to a second-order quantized Hamilton dynamics by Prezhdo and Pereverzev which conserves the total energy only with an odd-order Taylor expansion of the potential [J. Chem. Phys. 116, 4450 (2002); 117, 2995 (2002)], the present quantal cumulant dynamics method exactly conserves the energy, even if a second-order approximation of the cumulants is adopted, because the present scheme does not truncate the given potential. The authors propose three schemes, (i) a truncation, (ii) a summation of derivatives, and (iii) a convolution method, for evaluating the quantal potentials for several types of potentials. The numerical results show that although the truncation method preserves the energy to some degree, the trajectory obtained gradually deviates from that of the summation scheme after 2000 steps. The phase space structure obtained by the truncation scheme is also different from that of the summation scheme in a strongly anharmonic region. (c) 2006 American Institute of Physics.
机译：作者得出了累积量运动的耦合方程，该方程由一维位置和动量波动算子的对称有序积组成。关键是利用作用于潜在运算符上的位置移位运算符，其中使用累积量扩展技术评估移位运算符的期望值。特别是，给出了二阶累积量的运动方程以及位置和动量算符的期望值。结果方程由这些变量和由微分算子的指数函数和原始电势组成的量子电势表示。此过程使我们能够在一维中执行量化（半经典）动力学。与Prezhdo和Pereverzev的二阶量化汉密尔顿动力学相反，后者仅以势的奇数泰勒展开来保存总能量[J.化学物理116，4450（2002）; 117，2995（2002）]，即使采用了累积量的二阶近似，本发明的量子累积量动力学方法也精确地节省了能量，因为本方案并未截断给定的电势。作者提出了三种方案，（i）截断，（ii）导数的求和，（iii）卷积方法，用于评估几种类型势能的量子势能。数值结果表明，尽管截断法在一定程度上保留了能量，但是在经过2000步后，获得的轨迹逐渐偏离求和方案的轨迹。在强非调和区域中，通过截断方案获得的相空间结构也不同于求和方案。 （c）2006年美国物理研究所。

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