A Statistical Mechanical Approximation for the Calculation of Time Auto-Correlation Functions

Details A Statistical Mechanical Approximation for the Calculation of Time Auto-Correlation Functions A Statistical Mechanical Approximation for the Calculation of Time Auto-Correlation Functions

1997-12-18

arxiv.org/abs/cond-mat/9712222v1

Physics

Condensed Matter

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This paper considers the problem of estimating the time auto-correlation function for a quantity that is defined in configuration space, given a knowledge of the mean-square displacement as function of time in configuration space. The problem is particularly relevant for viscous liquids, where the interesting time-scales are often beyond those reachable by computer simulation. An approximate formula is derived which reduces the calculation of the time auto- correlation function to a "double canonical" average. In this approximation, in the case of Langevin dynamics the mean-square displacement itself may be evaluated from the "double partition function" . The scheme developed is illustrated by computer simulations of a simple one-dimensional system at different temperatures, showing good agreement between the exact time auto-correlation functions and those found by the approximation.

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