Shao Jiushu, Pollak Eli
Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovot, Israel.
J Chem Phys. 2006 Oct 7;125(13):133502. doi: 10.1063/1.2207142.
Frantsuzov and Mandelshtam [J. Chem. Phys. 121, 9247 (2004)] have recently demonstrated that a time evolving Gaussian approximation (TEGA) to the imaginary time propagator exp(-betaH) is useful for numerical computations of anharmonically coupled systems with many degrees of freedom. In this paper we derive a new exact series representation for the imaginary time propagator whose leading order term is the TEGA. One can thus use the TEGA not only as an approximation but also to obtain the exact imaginary time propagator. We also show how the TEGA may be generalized to provide a family of TEGA's. Finally, we find that the equations of motion governing the evolution of the center and width of the Gaussian may be thought of as introducing a quantum friction term to the classical evolution equations.
弗兰苏佐夫和曼德尔斯塔姆[《化学物理杂志》121, 9247 (2004)]最近证明，对虚时传播子exp(-βH)的时间演化高斯近似(TEGA)对于多自由度非谐耦合系统的数值计算很有用。在本文中，我们推导了虚时传播子的一个新的精确级数表示，其首项是TEGA。因此，人们不仅可以将TEGA用作近似，还可以用它来获得精确的虚时传播子。我们还展示了如何推广TEGA以提供一族TEGA。最后，我们发现，控制高斯中心和宽度演化的运动方程可以被认为是在经典演化方程中引入了一个量子摩擦项。
