Geometric scaling of correlation decay in chaotic billiards.

Abstract

We investigate decay properties of correlation functions in a class of chaotic billiards. We provide numerical evidence that velocity autocorrelation functions decay exponentially, with a rate scaling in a simple way with the (uniform) curvature of the dispersing arcs. Return probabilities, i.e., correlation functions of characteristic functions of subsets of the phase space, appear to follow a slower than exponential decay law.