On the approximation of diffusion memory functions by time correlation functions in inhomogeneous systems

摘要

Approximations commonly used to relate memory functions to time correlation functions governed by Newtonian dynamics are shown to be incorrect for strongly inhomogeneous systems. An exact expression for the space dependent diffusion coefficient is given in terms of time correlation functions whose dynamics are governed by Newtonrsquo;s equations. The resulting expression is evaluated using both the Bhatnagarndash;Grossndash;Krook kinetic equation and the Fokkerndash;Planck equation to calculate the required time correlation functions for a system containing a specularly reflecting wall and for a system having a harmonic potential. For inhomogeneous systems, the memory function may not be approximated by the corresponding time correlation function. In addition, certain velocity correlations near a specularly reflecting wall are shown to contain atminus;1/2long time tail and a kinetic boundary layer whose thickness grows ast1/2; these features are absent from the memory function.