Within the framework of Feynman–Kleinert variational theory, simple equations for correlation functions of arbitrary nonlinear operators are derived. These correlation functions, meaningful only for short times, are extended to longer times by a well established ansatz. The approach is tested against exact results for the quantum force correlation function in a two-dimensional Helium cluster problem and is found to perform very well. The theory is also applied to calculate quantum force correlation functions for a diatomic in a larger Neon bath. The results indicate that the method is effective for vibrational energy relaxation processes in simple liquids when quantum effects are significant.

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