Journal of Statistical Physics, Vol, 52, Nos. 3/4, 1988, p. 1113-1118.
For diffusive motion in random media it is widely believed that the velocity autocorrelation function c(t) exhibits power law decay as time t->oo. We demonstrate that the decay of c(t) in quasiperiodic media can be arbitrarily slow within the class of integrable functions. For example, in d= 1 with a potential V(x)= cos x+cos kx, there is a dense set of irrational k's such that the decay of c(k, t) is slower than 1/t^(1+E) for any E > 0. The irrationals producing such a slow decay of c(k, t) are very well approximated by rationals.