Arbitrarily slow decay of correlations in quasiperiodic systems

Abstract

For diffusive motion in random media it is widely believed that the velocity autocorrelation function c(t) exhibits power law decay as time t ..-->.. infinity. 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/sup (1+epsilon/)/ for any epsilon > 0. The irrationals producing such a slow decay of c(k, t) are very well approximated by rationals.