Arbitrarily slow decay of correlations in quasiperiodic systems

Abstract

For diffusive motion in random media it is widely believed that the velocity autocorrelation functionc(t) exhibits power law decay as time;t→∞. We demonstrate that the decay ofc(t) in quasiperiodic media can be arbitrarily slow within the class of integrable functions. For example, ind=1 with a potentialV(x)=cosx+coskx, there is a dense set of irrationalk's such that the decay ofc(k, t) is slower than 1/t ^(1+ɛ) for anyɛ>0. The irrationals producing such a slow decay ofc(k, t) arevery well approximated by rationals.