A New Continued-Fraction Representation of the Time-Correlation Functions of Transport Fluxes

By means of Mori’s memory-function formalism of generalized Brownian motions is obtained a new type of continued-fraction representation of the Laplace transform of current-autocorrelation functions whose time evolution is governed by the usual Liouville operator. In this representation, the memory function consists of two parts. One represents the effect of macroscopic processes and another that of microscopic processes. This is a generalization of the continued-fraction representation previously found by Mori. The relationship between these two representations is discussed. The present method is also applied to Tokuyama and Mori’s time-convolutionless formalism to obtain an infinite continued-fraction expansion through which the memory-function and the time-convolutionless formalism are connected to each other. A new approximation scheme for calculating the usual memory functions is suggested on the basis of the new continued fraction representation.