Asymptotic Time Behavior of Correlation Functions. I. Kinetic Terms

Study of Diffusion in Lattice-Gas Fluids and Colloids

“…The Alder-Wainwright results showed that in the long-time limit the functional form of the VACF was compatible with an algebraic decay t-D/2, where D is the dimension of the system. This behavior was explained by Alder and Wainwright using a dimensional argument, and subsequently also from linear hydrodynamics in the modecoupling theory by Ernst et al [15], and from kinetic theory by Dorfman and Cohen [16]. The mode-coupling theory has been extended to lattice gases by Ernst [17,18], so we can do a quantitative comparison between the lattice gas simulation results and the mode-coupling theory.…”

“…According to equation (10) the 'trajectory-averaged' VACF is = ci.u. (r, 1) (15) as the probability P(r; 1) of the tagged particle to arrive at site r at time t = 1 is equal to one, and zero for all other sites. This is for one configuration.…”

“…The explicit prediction for the long-time tail in the VACF (see also section 3) in a two-dimensionsal fluid is [14,15,16]:…”

Numerical Techniques to Study Complex Liquids

“…This observation had far-reaching implications because it demonstrated the breakdown of the 'Molecular Chaos' assumption, originally introduced by Boltzmann as the `Stolizahlansatz': Molecular Chaos immediately implies exponential decay of the VACF. The algebraic long-time tails are hydrodynamic in origin, as they are caused by the coupling between particle diffusion and shear modes in the fluid [137,138,139,140,141]. where p is the number density, Do the 'bare' self-diffusion constant, vo the kinematic viscosity and d the dimensionality.…”

Simulation of sub-molecular and supra-molecular fluids

“…The subsequent theoretical analyses of algebraic long-time tails were either based on an extension of kinetic theory [3] or on mode-coupling theory [4]. For a review, see ref.…”