Pre-Gaussian process of particle diffusion in classical liquids in a mesoscopic time regime

A modified distribution law of classical particle self-diffusion toward that of the Gaussian process is extensively studied for Lennard–Jones liquid with 10 972 particles by molecular dynamics simulation. In a mesoscopic time scale of the order of 1–100 ps, a generalized isotropic distribution law P(r,t) of the particle displacement r at time t, P(r,t)/P(0,t)=exp{−ar2−γ(t)/t1−γ(t)} (a>0,1>γ(t) 0) ,is confirmed to exist at a range of temperature around and below the melting point. The γ(t) tends to vanish as time elapses. In this paper we show the refined version of that in the previous study of systems with 108 particles [Itagaki et al., Physica A 265 (1999) 97–110]. As a result we confirm that the pre-Gaussian process exists widely in classical liquids in some temperature range in a mesoscopic time regime. To find the relation between our distribution law and the slow dynamics observed in super-cooled liquids and glassy states, the imaginary part of the generalized susceptibility (self-part) χS″(k,ω) is also examined.