Asymptotic Time Behavior of Correlation Functions. I. Kinetic Terms

The asymptotic time behavior ($\sim c{t}^{-\frac{d}{2}}$, where $d$ is the dimensionality of the system) of the velocity autocorrelation function and of the kinetic parts of the correlation functions for the shear viscosity and the heat conductivity is derived on the basis of a local equilibrium assumption and the linearized Navier-Stokes equations. The coefficients $c$ are expressed in terms of the transport coefficients and thermodynamic quantities. The physical mechanism responsible for the long-time tail is indicated, and the connections between the present work and investigations based on molecular dynamics and on kinetic theory are discussed.