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for selected values. Full lines are the AIMD results. Dashed lines are the fits to an exponential function for long times (in the inset of the upper left panel, the short time behavior is enhanced to appreciate the initial slopes). Dotted lines: Gaussian approximation. The results from the cumulant expansion are indistinguishable from the AIMD ones. The insets in the right panels show 1000 times the difference between the AIMD data and the Gaussian approximation (dotted lines) or the cumulant expansion (dashed-dotted lines).
Coefficients of the long time fit of to an exponential function for several values. The circles are the data. Dashed line: fit of the data to functions linear in . Full line: fit of the data to the expressions provided by the cumulant expansion.
Functions , defined in the text, for several wavevectors. When increases the function becomes smaller. Liquid Hg: , 0.68, 0.84, 0.96, 1.08, and . Liquid Mg: , 0.29, 0.41, 0.53, 0.67, and . Liquid Si: , 0.33, 0.47, 0.60, 0.76, and . The insets show an expanded view of the short time behavior.
Coefficients of linear fits of for .
Coefficients of the fits of and to the expressions provided by the cumulant expansion.
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