Transport properties Self-diffusion coefficient Einstein formula <r(t)-r(0)2>6Dt t→)∞ Expression in terms of velocity auto-correlation function(VACF) D-dt(v(ov(O) Diffusion equation opr d_DVdr) Solution with the initial condition, P(r, t=0=dr-ro (4mD)≈W 4DTransport properties Self-diffusion coefficient Einstein formula: <|r(t) - r(0)|2> 6Dt t →  Expression in terms of velocity auto-correlation function (VACF):   =  0 D dt v(t)v(0)   Diffusion equation: ( , ) ( , ) 2 D r t t r t      =   Solution with the initial condition, (r, t=0) = d(r - r0 ): ) 4 exp( 1 ( , ) 2 0 3/2 (4 ) Dt r t r r Dt    − = − p 