Bilinear Contributions to Equilibrium Correlation Functions

The long-time behavior of autocorrelation functions of conserved variables and of their corresponding dissipative fluxes is studied using the Mori formalism. A set of variables including linear and bilinear forms of the conserved variables is treated and consistent expansions to quadratic order in the wave-vector dependence of the appropriate correlation functions are carried out. The treatment is self-consistent and does not involve factorization of time-dependent correlation functions. Explicit calculations for the wave vector →k and the frequency-dependent shear-viscosity coefficient are carried out in two dimensions. The asymptotic time dependence of the shear-viscosity correlation function is proportional to t^-1 when k→0. The effect of higher-order nonlinear forms of the conserved variables has not been studied; such a study is essential to ensure the validity of the asymptotic time dependence found here.