Decay of chaotic open stadium billiards is examined numerically. Certain open stadium systems are shown to exhibit other than simple exponential decay (i.e. nonstatistical) behavior. In addition, algebraic long time decay occurs in some cases. Observed decays are modeled with a minimally dynamic hybrid statistical theory based on mixing assumptions. These results are discussed in terms of other related results and those associated with integrable systems.
There is a longstanding effort to relate dynamical system behavior to the classification of systems, e.g. ergodic, mixing, K system, etc., advocated by ergodic theory. Such an effort is found in studies of classical Hamiltonian decay processes. These processes provide models for the unimolecular decay of excited chemical species, or classical analogues of nuclear fission. There is a widely held belief that the simple exponential decay often observed for such processes is connected to chaotic character of associated classical Hamiltonian systems. In recent years, this belief has been substantiated by ergodic theoretic studies ~ which relate asymptotic exponential decay rates of hyperbolic systems to ergodic properties of chaotic "repeller" sets in phase space. Furthermore, a recent numerical study of Bauer and Bertsch [2 ] revealed simple exponential decay for a certain model chaotic system. The system adopted in the latter study is a "K system" ~2. However, it is not strictly hyperbolic due to the existence of families of marginally stable periodic orbits.