Origin of Long-Time Tails in Strongly Chaotic Systems

The behavior of autocorrelation functions in a $K$ system (the stadium billiard) is studied, and the existence of long-time tails is demonstrated both analytically and numerically. The tails are shown to depend on the presence of arbitrary long segments of regular motion in the time evolution of the stochastic orbits. It is surmised that an analogous mechanism might be responsible for long-time tails in a large class of systems.