Long-time tails and diffusion

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Abstract
The evidence for long-time tails as a part of the velocity autocorrelation function for a classical particle is examined. Computer simulations, theoretical treatments, and light-scattering experiments are discussed. It is argued that numerical error propagation in the computer simulations may give rise to long-time tails as an artifact which is of hydrodynamic character. The theoretical treatments of physicists, whether avowedly phenomenological or putatively rigorous, all rely on a hydrodynamic mechanism. The usual theoretical treatments by mathematicians, based on the differential topology of "dynamical systems," appear not to be in agreement with long-time tails. Recent experiments with polystyrene spheres, observed by light scattering, claim to see the effect of long-time tails. These experiments may be interpreted as observations of the Stokes-Boussinesq effect expected for "macroscopic" spheres, but not justified for truly microscopic, molecular-sized, particles. While long-time tails may yet be rigorously established by computer simulation, theory, and experiment, it is argued in this paper that this has not happened yet. Moreover, a firm basis for serious doubt is raised.