In this work, we discuss a general protocol for analyzing the quality of approximate quantum time correlation functions of non-trivial systems in many dimensions. This approach is based on the generalized deconvolution of the Kubo transformed quantum time correlation function onto an alternative quantum correlation function, at a given point in imaginary time, which leads to a series of sum rules linking derivatives of different order in the corresponding pair of convoluted correlation functions. We focus on a particular case for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibit a polynomial divergence and show that thermally symmetrized static averages, are ideally suited to investigate the quality of approximate quantum time correlation functions at successively larger, and up to arbitrarily long, times. This overall strategy is illustrated analytically for a harmonic system, and numerically for a multidimensional double-well potential and a Lennard-Jones fluid representing liquid neon at 30 K.

Assesing the quality of approximate quantum dynamics in condensed phase via sum rules

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