Fabcic Tomaz, Main Jörg, Wunner Günter
Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany.
J Chem Phys. 2008 Jan 28;128(4):044116. doi: 10.1063/1.2821751.
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be calculated from a set of ordinary differential equations. Unfortunately, the set of equations is ill behaved in most practical applications, depending on the number of propagated Gaussian wave packets, and methods for regularization are needed. We present a general method for regularization based on applying adequate nonholonomic inequality constraints to the evolution of the parameters, keeping the equations of motion well behaved. The power of the method is demonstrated for a nonintegrable system with two degrees of freedom.
量子系统的动力学可以通过高斯波包的时间传播来近似。应用含时变分原理，耦合高斯波包参数的时间演化可以从一组常微分方程中计算出来。不幸的是，在大多数实际应用中，这组方程表现不佳，这取决于传播的高斯波包数量，因此需要正则化方法。我们提出了一种基于对参数演化应用适当的非完整不等式约束的正则化通用方法，以使运动方程表现良好。该方法的有效性在一个具有两个自由度的不可积系统中得到了证明。
