Department of Chemistry, University of California, Berkeley, California 94720-1460, USA.
J Chem Phys. 2011 Mar 14;134(10):104102. doi: 10.1063/1.3555274.
We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.
我们在量子力学的相空间表述中展示了量子力学时间相关函数的确切表达式。然后，使用在论文 I 中提出的基于轨迹的保持量子正则分布的动力学（ELD）来近似评估精确表达式。它给出了在经典、高温和调和极限下的精确热相关函数（甚至是非线性算子的，即位置或动量算子的非线性函数）。已经提出了各种方法来实现 ELD。已经在谐振子和两个强非谐模型问题的维格纳或赫希米相位空间中对 ELD 方法进行了数值测试，对于每个势自相关函数，已经计算了线性和非线性算子的。这表明 ELD 可能是描述凝聚相复杂系统量子效应的一种有用方法。
