A Continued-Fraction Representation of the Time-Correlation Functions

Abstract

A continued-fraction expansion of the Laplace transform of the time-correlation functions is obtained, which enables us to express the generalized susceptibilities and the transport coefficients in terms of the static correlation functions of a set of quantities. This expansion has a different feature from the moment and cumulant expansions, and has a convenient form to introduce the long-time approximation as well as the short-time approximation. Its application to the anomalous relaxation and transport phenomena near the second-order phase transition points is discussed.