The hard-disk fluid revisited

The hard-disk model plays a role of touchstone for testing and developing the transport theory. By large scale molecular dynamics simulations of this model, three important autocorrelation functions, and as a result the corresponding transport coefficients, i.e., the diffusion constant, the thermal conductivity and the shear viscosity, are found to deviate significantly from the predictions of the conventional transport theory beyond the dilute limit. To improve the theory, we consider both the kinetic process and the hydrodynamic process in the whole time range, rather than each process in a seperated time scale as the conventional transport theory does. With this consideration, a unified and coherent expression free of any fitting parameters is derived succesfully in the case of the velocity autocorrelation function, and its superiority to the conventional `piecewise' formula is shown. This expression applies to the whole time range and up to moderate densities, and thus bridges the kinetics and hydrodynamics approaches in a self-consistent manner.