Liu Jian, Miller William H
Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA.
J Chem Phys. 2008 Sep 28;129(12):124111. doi: 10.1063/1.2981065.
The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. LSC-IVR provides a very effective "prior" for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T=25 K, but the MEAC procedure produces a significant correction at the lower temperature (T=14 K). Comparisons are also made as to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.
最大熵解析延拓（MEAC）方法用于扩展线性化半经典初值表示（LSC-IVR）/经典维格纳近似在实时关联函数方面的精度范围。LSC-IVR为MEAC过程提供了一种非常有效的“先验”，因为它在短时间内表现出色，对于谐振子势在所有时间和温度下都是精确的（甚至对于非线性算符的关联函数也是如此），并且在经典高温极限下变得精确。这里将这种MEAC + LSC/IVR组合方法应用于两个高度非线性动力学系统，一个是一维纯四次势，另一个是在两个热态点（接近零外压下的25 K和14 K）的液态对氢。前一个例子表明，MEAC过程对于线性和非线性算符的关联函数而言是对LSC-IVR的非常显著的增强，特别是在半经典近似最不准确的低温情况下。对于液态对氢，在T = 25 K时LSC-IVR已经表现出色，但MEAC过程在较低温度（T = 14 K）下产生了显著的修正。还比较了MEAC过程在用作先验时如何能够为其他基于轨迹的动力学近似提供修正。
